Showing 1–50 of 74 results for author: Blais, A

Toolbox for nonreciprocal dispersive models in circuit QED

Authors: Lautaro Labarca, Othmane Benhayoune-Khadraoui, Alexandre Blais, Adrian Parra-Rodriguez

Abstract: We provide a systematic method for constructing effective dispersive Lindblad master equations to describe weakly anharmonic superconducting circuits coupled by a generic dissipationless nonreciprocal linear system, with effective coupling parameters and decay rates written in terms of the immittance parameters characterizing the coupler. This article extends the foundational work of Solgun et al.… ▽ More We provide a systematic method for constructing effective dispersive Lindblad master equations to describe weakly anharmonic superconducting circuits coupled by a generic dissipationless nonreciprocal linear system, with effective coupling parameters and decay rates written in terms of the immittance parameters characterizing the coupler. This article extends the foundational work of Solgun et al. (2019) for linear reciprocal couplers described by an impedance response. Notably, we expand the existing toolbox to incorporate nonreciprocal elements, account for direct stray coupling between immittance ports, circumvent potential singularities, and include collective dissipative effects that arise from interactions with external common environments. We illustrate the use of our results with a circuit of weakly anharmonic Josephson junctions coupled to a multiport nonreciprocal environment and a dissipative port. The results obtained here can be used for the design of complex superconducting quantum processors with nontrivial routing of quantum information, as well as analog quantum simulators of condensed matter systems. △ Less

Submitted 18 September, 2024; v1 submitted 13 December, 2023; originally announced December 2023.

Comments: 41 pages, 13 figures. Comments are welcome. Published version

Journal ref: Phys. Rev. Applied 22, 034038, 2024

Multipartite Entanglement in Rabi Driven Superconducting Qubits

Authors: M. Lu, J. L. Ville, J. Cohen, A. Petrescu, S. Schreppler, L. Chen, C. Jünger, C. Pelletti, A. Marchenkov, A. Banerjee, W. Livingston, J. M. Kreikebaum, D. Santiago, A. Blais, I. Siddiqi

Abstract: Exploring highly connected networks of qubits is invaluable for implementing various quantum algorithms and simulations as it allows for entangling qubits with reduced circuit depth. Here, we demonstrate a multi-qubit STAR (Sideband Tone Assisted Rabi driven) gate. Our scheme is inspired by the ion qubit Mølmer-Sørensen gate and is mediated by a shared photonic mode and Rabi-driven superconducting… ▽ More Exploring highly connected networks of qubits is invaluable for implementing various quantum algorithms and simulations as it allows for entangling qubits with reduced circuit depth. Here, we demonstrate a multi-qubit STAR (Sideband Tone Assisted Rabi driven) gate. Our scheme is inspired by the ion qubit Mølmer-Sørensen gate and is mediated by a shared photonic mode and Rabi-driven superconducting qubits, which relaxes restrictions on qubit frequencies during fabrication and supports scalability. We achieve a two-qubit gate with maximum state fidelity of 0.95 in 310 ns, a three-qubit gate with state fidelity 0.905 in 217 ns, and a four-qubit gate with state fidelity 0.66 in 200 ns. Furthermore, we develop a model of the gate that show the four-qubit gate is limited by shared resonator losses and the spread of qubit-resonator couplings, which must be addressed to reach high-fidelity operations. △ Less

Submitted 19 July, 2022; v1 submitted 30 June, 2022; originally announced July 2022.

Comments: 16 pages, 14 figures

Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code

Authors: Sebastian Krinner, Nathan Lacroix, Ants Remm, Agustin Di Paolo, Elie Genois, Catherine Leroux, Christoph Hellings, Stefania Lazar, Francois Swiadek, Johannes Herrmann, Graham J. Norris, Christian Kraglund Andersen, Markus Müller, Alexandre Blais, Christopher Eichler, Andreas Wallraff

Abstract: Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 p… ▽ More Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments. In an error correction cycle taking only $1.1\,μ$s, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit- and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in postprocessing. We find a low error probability of $3\,\%$ per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error correction cycles, together with recent advances in ion traps, support our understanding that fault-tolerant quantum computation will be practically realizable. △ Less

Submitted 7 December, 2021; originally announced December 2021.

Comments: 28 pages, 17 figures

Journal ref: Nature 605, 669 (2022)

Accurate methods for the analysis of strong-drive effects in parametric gates

Authors: Alexandru Petrescu, Camille Le Calonnec, Catherine Leroux, Agustin Di Paolo, Pranav Mundada, Sara Sussman, Andrei Vrajitoarea, Andrew A. Houck, Alexandre Blais

Abstract: The ability to perform fast, high-fidelity entangling gates is an important requirement for a viable quantum processor. In practice, achieving fast gates often comes with the penalty of strong-drive effects that are not captured by the rotating-wave approximation. These effects can be analyzed in simulations of the gate protocol, but those are computationally costly and often hide the physics at p… ▽ More The ability to perform fast, high-fidelity entangling gates is an important requirement for a viable quantum processor. In practice, achieving fast gates often comes with the penalty of strong-drive effects that are not captured by the rotating-wave approximation. These effects can be analyzed in simulations of the gate protocol, but those are computationally costly and often hide the physics at play. Here, we show how to efficiently extract gate parameters by directly solving a Floquet eigenproblem using exact numerics and a perturbative analytical approach. As an example application of this toolkit, we study the space of parametric gates generated between two fixed-frequency transmon qubits connected by a parametrically driven coupler. Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT. These analytical results are supplemented by numerical Floquet computations from which we directly extract drive-dependent gate parameters. This approach has a considerable computational advantage over full simulations of time evolutions. More generally, our combined analytical and numerical strategy allows us to characterize two-qubit gates involving parametrically driven interactions, and can be applied to gate optimization and cross-talk mitigation such as the cancellation of unwanted ZZ interactions in multi-qubit architectures. △ Less

Submitted 5 July, 2021; originally announced July 2021.

Comments: 20 pages, 9 figures, 62 references

Journal ref: Phys. Rev. Applied 19, 044003 (2023)

Demonstration of an All-Microwave Controlled-Phase Gate between Far Detuned Qubits

Authors: S. Krinner, P. Kurpiers, B. Royer, P. Magnard, I. Tsitsilin, J. -C. Besse, A. Remm, A. Blais, A. Wallraff

Abstract: A challenge in building large-scale superconducting quantum processors is to find the right balance between coherence, qubit addressability, qubit-qubit coupling strength, circuit complexity and the number of required control lines. Leading all-microwave approaches for coupling two qubits require comparatively few control lines and benefit from high coherence but suffer from frequency crowding and… ▽ More A challenge in building large-scale superconducting quantum processors is to find the right balance between coherence, qubit addressability, qubit-qubit coupling strength, circuit complexity and the number of required control lines. Leading all-microwave approaches for coupling two qubits require comparatively few control lines and benefit from high coherence but suffer from frequency crowding and limited addressability in multi-qubit settings. Here, we overcome these limitations by realizing an all-microwave controlled-phase gate between two transversely coupled transmon qubits which are far detuned compared to the qubit anharmonicity. The gate is activated by applying a single, strong microwave tone to one of the qubits, inducing a coupling between the two-qubit $|f,g\rangle$ and $|g,e\rangle$ states, with $|g\rangle$, $|e\rangle$, and $|f\rangle$ denoting the lowest energy states of a transmon qubit. Interleaved randomized benchmarking yields a gate fidelity of $97.5\pm 0.3 \%$ at a gate duration of $126\,\rm{ns}$, with the dominant error source being decoherence. We model the gate in presence of the strong drive field using Floquet theory and find good agreement with our data. Our gate constitutes a promising alternative to present two-qubit gates and could have hardware scaling advantages in large-scale quantum processors as it neither requires additional drive lines nor tunable couplers. △ Less

Submitted 18 June, 2020; originally announced June 2020.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. Applied 14, 044039 (2020)

Experimental realization of an intrinsically error-protected superconducting qubit

Authors: Andras Gyenis, Pranav S. Mundada, Agustin Di Paolo, Thomas M. Hazard, Xinyuan You, David I. Schuster, Jens Koch, Alexandre Blais, Andrew A. Houck

Abstract: Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting $0-π$ qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy me… ▽ More Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting $0-π$ qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy measurements reveal the energy level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. We find that the parity symmetry of the qubit results in charge-insensitive levels connecting the protected states, allowing for logical operations. The measured relaxation (1.6 ms) and dephasing times (25 $μ$s) demonstrate that our implementation of the $0-π$ circuit not only broadens the family of superconducting qubits, but also represents a promising candidate for the building block of a fault-tolerant quantum processor. △ Less

Submitted 16 October, 2019; originally announced October 2019.

Journal ref: PRX Quantum 2, 010339 (2021)

Bifluxon: Fluxon-Parity-Protected Superconducting Qubit

Authors: Konstantin Kalashnikov, Wen Ting Hsieh, Wenyuan Zhang, Wen-Sen Lu, Plamen Kamenov, Agustin Di Paolo, Alexandre Blais, Michael E. Gershenson, Matthew Bell

Abstract: We have developed and characterized a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noise, and dephasing from flux noise. The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, thus forming a superconducting loop. Provided the offset charge on the CPB island is an odd number of electrons, the qubit… ▽ More We have developed and characterized a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noise, and dephasing from flux noise. The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, thus forming a superconducting loop. Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a $\cos φ/ 2$ Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference. In this regime, the logical-state wavefunctions reside in disjoint regions of phase space, thereby ensuring the protection against energy decay. By switching the protection on, we observed a ten-fold increase of the decay time, reaching up to $100 μ\mathrm{s}$. Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds $1 μ\mathrm{s}$. Implementation of the full dephasing protection can be achieved in the next-generation devices by combining several $\cos φ/ 2$ Josephson elements in a small array. △ Less

Submitted 8 October, 2019; originally announced October 2019.

Comments: 13 pages, 13 figures

Journal ref: PRX Quantum 1, 010307 (2020)

Quantum communication with time-bin encoded microwave photons

Authors: Philipp Kurpiers, Marek Pechal, Baptiste Royer, Paul Magnard, Theo Walter, Johannes Heinsoo, Yves Salathé, Abdulkadir Akin, Simon Storz, Jean-Claude Besse, Simone Gasparinetti, Alexandre Blais, Andreas Wallraff

Abstract: Heralding techniques are useful in quantum communication to circumvent losses without resorting to error correction schemes or quantum repeaters. Such techniques are realized, for example, by monitoring for photon loss at the receiving end of the quantum link while not disturbing the transmitted quantum state. We describe and experimentally benchmark a scheme that incorporates error detection in a… ▽ More Heralding techniques are useful in quantum communication to circumvent losses without resorting to error correction schemes or quantum repeaters. Such techniques are realized, for example, by monitoring for photon loss at the receiving end of the quantum link while not disturbing the transmitted quantum state. We describe and experimentally benchmark a scheme that incorporates error detection in a quantum channel connecting two transmon qubits using traveling microwave photons. This is achieved by encoding the quantum information as a time-bin superposition of a single photon, which simultaneously realizes high communication rates and high fidelities. The presented scheme is straightforward to implement in circuit QED and is fully microwave-controlled, making it an interesting candidate for future modular quantum computing architectures. △ Less

Submitted 19 November, 2018; originally announced November 2018.

Journal ref: Phys. Rev. Applied 12, 044067 (2019)

Coherent microwave photon mediated coupling between a semiconductor and a superconductor qubit

Authors: P. Scarlino, D. J. van Woerkom, U. C. Mendes, J. V. Koski, A. J. Landig, C. K. Andersen, S. Gasparinetti, C. Reichl, W. Wegscheider, K. Ensslin, T. Ihn, A. Blais, A. Wallraff

Abstract: Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wav… ▽ More Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle, which represents a significant constraint towards scaling to reach dense 1D or 2D arrays of QD qubits. Following the success of circuit quantum eletrodynamics [6], the strong coupling regime between the charge [7, 8] and spin [9, 10, 11] degrees of freedom of electrons confined in semiconducting QDs interacting with individual photons stored in a microwave resonator has recently been achieved. In this letter, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus [12, 13, 14]. The transmon-charge qubit coherent coupling rate ($ \sim$ 21 MHz) exceeds the linewidth of both the transmon ($ \sim$ 0.8 MHz) and the DQD charge ($ \sim$ 3 MHz) qubit. By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of the two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits. The methods and techniques presented here are transferable to QD devices based on other material systems and can be beneficial for spin-based hybrid systems. △ Less

Submitted 26 June, 2018; originally announced June 2018.

Comments: 9 pages, 6 figures

Journal ref: Nature Communications 10, 3011 (2019)

Nanowire Superinductance Fluxonium Qubit

Authors: T. M. Hazard, András Gyenis, A. Di Paolo, A. T. Asfaw, S. A. Lyon, A. Blais, A. A. Houck

Abstract: We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multip… ▽ More We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of $T_\mathrm{1}=20$ $μ$s. By measuring $T_1$ at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses. △ Less

Submitted 29 January, 2019; v1 submitted 2 May, 2018; originally announced May 2018.

Journal ref: Phys. Rev. Lett. 122, 010504 (2019)

Parametric amplification and squeezing with an ac- and dc-voltage biased superconducting junction

Authors: Udson C. Mendes, Sébastien Jezouin, Philippe Joyez, Bertrand Reulet, Alexandre Blais, Fabien Portier, Christophe Mora, Carles Altimiras

Abstract: We theoretically investigate a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction. Photon-assisted tunneling, resulting from the combination of dc- and ac-voltage bias, gives rise to a strong parametric interaction for the electromagnetic modes reflected by the junction coupled to a transm… ▽ More We theoretically investigate a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction. Photon-assisted tunneling, resulting from the combination of dc- and ac-voltage bias, gives rise to a strong parametric interaction for the electromagnetic modes reflected by the junction coupled to a transmission line. We show phase-sensitive and phase-preserving amplification, together with single- and two-mode squeezing. For an aluminum junction pumped at twice the center frequency, $ω_0/2π=6$~GHz, we predict narrow-band phase-sensitive amplification of microwaves signals to more than 20 dB, and broadband phase-preserving amplification of 20 dB over a 1.2 GHz 3-dB bandwidth. We also predict single- and two-mode squeezing reaching more than -12 dB over 5.3 GHz 3-dB bandwidth. Moreover, with a simple impedance matching circuit, we demonstrate 3 dB bandwidth reaching 4.3 GHz for 20 dB of gain. A key feature of the device is that its performance can be controlled in-situ with the applied dc- and ac-voltage biases. △ Less

Submitted 6 March, 2019; v1 submitted 20 February, 2018; originally announced February 2018.

Comments: Accepted for publication at the Physical Review Applied. 12 pages and 9 figures

Journal ref: Phys. Rev. Applied 11, 034035 (2019)

Fast and Unconditional All-Microwave Reset of a Superconducting Qubit

Authors: Paul Magnard, Philipp Kurpiers, Baptiste Royer, Theo Walter, Jean-Claude Besse, Simone Gasparinetti, Marek Pechal, Johannes Heinsoo, Simon Storz, Alexandre Blais, Andreas Wallraff

Abstract: Active qubit reset is a key operation in many quantum algorithms, and particularly in error correction codes. Here, we experimentally demonstrate a reset scheme of a three level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the $|f,0\rangle$ and $|g,1\rangle$ states of the coupled transmon-resonator system, with… ▽ More Active qubit reset is a key operation in many quantum algorithms, and particularly in error correction codes. Here, we experimentally demonstrate a reset scheme of a three level transmon artificial atom coupled to a large bandwidth resonator. The reset protocol uses a microwave-induced interaction between the $|f,0\rangle$ and $|g,1\rangle$ states of the coupled transmon-resonator system, with $|g\rangle$ and $|f\rangle$ denoting the ground and second excited states of the transmon, and $|0\rangle$ and $|1\rangle$ the photon Fock states of the resonator. We characterize the reset process and demonstrate reinitialization of the transmon-resonator system to its ground state with $0.2\%$ residual excitation in less than $500 \, \rm{ns}$. Our protocol is of practical interest as it has no requirements on the architecture, beyond those for fast and efficient single-shot readout of the transmon, and does not require feedback. △ Less

Submitted 23 January, 2018; originally announced January 2018.

Journal ref: Phys. Rev. Lett. 121, 060502 (2018)

Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons

Authors: Philipp Kurpiers, Paul Magnard, Theo Walter, Baptiste Royer, Marek Pechal, Johannes Heinsoo, Yves Salathé, Abdulkadir Akin, Simon Storz, Jean-Claude Besse, Simone Gasparinetti, Alexandre Blais, Andreas Wallraff

Abstract: Sharing information coherently between nodes of a quantum network is at the foundation of distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers connected by classical and quantum channels. A direct quantum channel, which connects nodes deterministically, rather than probabilistically, is advantageo… ▽ More Sharing information coherently between nodes of a quantum network is at the foundation of distributed quantum information processing. In this scheme, the computation is divided into subroutines and performed on several smaller quantum registers connected by classical and quantum channels. A direct quantum channel, which connects nodes deterministically, rather than probabilistically, is advantageous for fault-tolerant quantum computation because it reduces the threshold requirements and can achieve larger entanglement rates. Here, we implement deterministic state transfer and entanglement protocols between two superconducting qubits fabricated on separate chips. Superconducting circuits constitute a universal quantum node capable of sending, receiving, storing, and processing quantum information. Our implementation is based on an all-microwave cavity-assisted Raman process which entangles or transfers the qubit state of a transmon-type artificial atom to a time-symmetric itinerant single photon. We transfer qubit states at a rate of $50 \, \rm{kHz}$ using the emitted photons which are absorbed at the receiving node with a probability of $98.1 \pm 0.1 \%$ achieving a transfer process fidelity of $80.02 \pm 0.07 \%$. We also prepare on demand remote entanglement with a fidelity as high as $78.9 \pm 0.1 \%$. Our results are in excellent agreement with numerical simulations based on a master equation description of the system. This deterministic quantum protocol has the potential to be used as a backbone of surface code quantum error correction across different nodes of a cryogenic network to realize large-scale fault-tolerant quantum computation in the circuit quantum electrodynamic architecture. △ Less

Submitted 22 December, 2017; originally announced December 2017.

Comments: 11 pages 8 Figures

Journal ref: Nature 558, 264-267 (2018)

Strong spin-photon coupling in silicon

Authors: N. Samkharadze, G. Zheng, N. Kalhor, D. Brousse, A. Sammak, U. C. Mendes, A. Blais, G. Scappucci, L. M. K. Vandersypen

Abstract: We report the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, t… ▽ More We report the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. This result opens the way to the realization of large networks of quantum dot based spin qubit registers, removing a major roadblock to scalable quantum computing with spin qubits. △ Less

Submitted 6 November, 2017; originally announced November 2017.

Coherent spin-qubit photon coupling

Authors: A. J. Landig, J. V. Koski, P. Scarlino, U. C. Mendes, A. Blais, C. Reichl, W. Wegscheider, A. Wallraff, K. Ensslin, T. Ihn

Abstract: Electron spins hold great promise for quantum computation due to their long coherence times. An approach to realize interactions between distant spin-qubits is to use photons as carriers of quantum information. We demonstrate strong coupling between single microwave photons in a NbTiN high impedance cavity and a three-electron spin-qubit in a GaAs triple quantum dot. We resolve the vacuum Rabi mod… ▽ More Electron spins hold great promise for quantum computation due to their long coherence times. An approach to realize interactions between distant spin-qubits is to use photons as carriers of quantum information. We demonstrate strong coupling between single microwave photons in a NbTiN high impedance cavity and a three-electron spin-qubit in a GaAs triple quantum dot. We resolve the vacuum Rabi mode splitting with a coupling strength of $g/2π\simeq31$ MHz and a qubit decoherence of $γ_2/2π\simeq 20$ MHz. We can tune the decoherence electrostatically and obtain a minimal $γ_2/2π\simeq 10$ MHz for $g/2π\simeq 23$ MHz. The dependence of the qubit-photon coupling strength on the tunable electric dipole moment of the qubit is measured directly using the ac Stark effect. Our demonstration of strong spin-photon interaction is an important step towards coherent long-distance coupling of spin-qubits. △ Less

Submitted 6 November, 2017; originally announced November 2017.

Journal ref: Nature 560, 179-184 (2018)

Effect of higher-order nonlinearities on amplification and squeezing in Josephson parametric amplifiers

Authors: Samuel Boutin, David M. Toyli, Aditya V. Venkatramani, Andrew W. Eddins, Irfan Siddiqi, Alexandre Blais

Abstract: Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric… ▽ More Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance. △ Less

Submitted 17 November, 2017; v1 submitted 31 July, 2017; originally announced August 2017.

Comments: 21 pages, 13 figures

Journal ref: Phys. Rev. Applied 8, 054030 (2017)

Widely tunable on-chip microwave circulator for superconducting quantum circuits

Authors: Benjamin J. Chapman, Eric I. Rosenthal, Joseph Kerckhoff, Bradley A. Moores, Leila R. Vale, Gene C. Hilton, Kevin Lalumière, Alexandre Blais, K. W. Lehnert

Abstract: We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in t… ▽ More We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Non-reciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW ($\approx 10^3$ circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz. △ Less

Submitted 6 November, 2017; v1 submitted 14 July, 2017; originally announced July 2017.

Comments: 8 pages with 8 page appendix

Journal ref: Phys. Rev. X 7, 041043 (2017)

Hamiltonian engineering for robust quantum state transfer and qubit readout in cavity QED

Authors: Félix Beaudoin, Alexandre Blais, W. A. Coish

Abstract: Quantum state transfer into a memory, state shuttling over long distances via a quantum bus, and high-fidelity readout are important tasks for quantum technology. Realizing these tasks is challenging in the presence of realistic couplings to an environment. Here, we introduce and assess protocols that can be used in cavity QED to perform high-fidelity quantum state transfer and fast quantum nondem… ▽ More Quantum state transfer into a memory, state shuttling over long distances via a quantum bus, and high-fidelity readout are important tasks for quantum technology. Realizing these tasks is challenging in the presence of realistic couplings to an environment. Here, we introduce and assess protocols that can be used in cavity QED to perform high-fidelity quantum state transfer and fast quantum nondemolition qubit readout through Hamiltonian engineering. We show that high-fidelity state transfer between a cavity and a single qubit can be performed, even in the limit of strong dephasing due to inhomogeneous broadening. We generalize this result to state transfer between a cavity and a logical qubit encoded in a collective mode of a large ensemble of $N$ physical qubits. Under a decoupling sequence, we show that inhomogeneity in the ensemble couples two collective bright states to only two other collective modes, leaving the remaining $N-3$ single-excitation states dark. Moreover, we show that large signal-to-noise and high single-shot fidelity can be achieved in a cavity-based qubit readout, even in the weak-coupling limit. These ideas may be important for novel systems coupling single spins to a microwave cavity. △ Less

Submitted 21 February, 2017; v1 submitted 16 February, 2016; originally announced February 2016.

Comments: 26 pages, 5 figures

Journal ref: New J. Phys. 19, 023041 (2017)

Quantum Zeno effect in the strong measurement regime of circuit quantum electrodynamics

Authors: D. H. Slichter, C. Müller, R. Vijay, S. J. Weber, A. Blais, I. Siddiqi

Abstract: We observe the quantum Zeno effect -- where the act of measurement slows the rate of quantum state transitions -- in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following amplifier. Under simultaneous strong measurement and qubit drive, the qubit undergoes a series of quantum jumps between states. These jumps are visible in the experiment… ▽ More We observe the quantum Zeno effect -- where the act of measurement slows the rate of quantum state transitions -- in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following amplifier. Under simultaneous strong measurement and qubit drive, the qubit undergoes a series of quantum jumps between states. These jumps are visible in the experimental measurement record and are analyzed using maximum likelihood estimation to determine qubit transition rates. The observed rates agree with both analytical predictions and numerical simulations. The analysis methods are suitable for processing general noisy random telegraph signals. △ Less

Submitted 13 December, 2015; originally announced December 2015.

Comments: 15 pages, 8 figures

Journal ref: New J. Phys. 18, 053031 (2016)

Quantum optics theory of electronic noise in coherent conductors

Authors: Farzad Qassemi, Arne L. Grimsmo, Bertrand Reulet, Alexandre Blais

Abstract: We consider the electromagnetic field generated by a coherent conductor in which electron transport is described quantum mechanically. We obtain an input-output relation linking the quantum current in the conductor to the measured electromagnetic field. This allows us to compute the outcome of measurements on the field in terms of the statistical properties of the current. We moreover show how und… ▽ More We consider the electromagnetic field generated by a coherent conductor in which electron transport is described quantum mechanically. We obtain an input-output relation linking the quantum current in the conductor to the measured electromagnetic field. This allows us to compute the outcome of measurements on the field in terms of the statistical properties of the current. We moreover show how under ac-bias the conductor acts as a tunable medium for the field, allowing for the generation of single- and two-mode squeezing through fermionic reservoir engineering. These results explain the recently observed squeezing using normal tunnel junctions [G. Gasse et al., Phys. Rev. Lett. 111 136601 (2013); J.-C. Forgues et al., Phys. Rev. Lett. 114 130403 (2015)]. △ Less

Submitted 1 July, 2015; originally announced July 2015.

Journal ref: Phys. Rev. Lett. 116, 043602 (2016)

Fast quantum non-demolition readout from longitudinal qubit-oscillator interaction

Authors: Nicolas Didier, Jérôme Bourassa, Alexandre Blais

Abstract: We show how to realize high-fidelity quantum non-demolition qubit readout using longitudinal qubit-oscillator interaction. This is realized by modulating the longitudinal coupling at the cavity frequency. The qubit-oscillator interaction then acts as a qubit-state dependent drive on the cavity, a situation that is fundamentally different from the standard dispersive case. Single-mode squeezing can… ▽ More We show how to realize high-fidelity quantum non-demolition qubit readout using longitudinal qubit-oscillator interaction. This is realized by modulating the longitudinal coupling at the cavity frequency. The qubit-oscillator interaction then acts as a qubit-state dependent drive on the cavity, a situation that is fundamentally different from the standard dispersive case. Single-mode squeezing can be exploited to exponentially increase the signal-to-noise ratio of this readout protocol. We present an implementation of this idea in circuit quantum electrodynamics and a possible multi-qubit architecture. △ Less

Submitted 15 April, 2015; originally announced April 2015.

Comments: 5 pages, 3 figures, Supplemental Material

Journal ref: Phys. Rev. Lett. 115, 203601 (2015)

On-chip superconducting microwave circulator from synthetic rotation

Authors: Joseph Kerckhoff, Kevin Lalumière, Benjamin J. Chapman, Alexandre Blais, K. W. Lehnert

Abstract: We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is ba… ▽ More We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dynamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that function as nearly linear, tunable inductors. The connection to familiar ferrite-based circulators is a simple frame boost in the internal dynamics' equation of motion. In addition to the general, schematic analysis, we also give an overview of many considerations necessary to achieve a practical design with a tunable center frequency in the 4-8 GHz frequency band, a bandwidth of 240 MHz, reflections at the -20 dB level, and a maximum signal power of approximately order 100 microwave photons per inverse bandwidth. △ Less

Submitted 20 February, 2015; originally announced February 2015.

Comments: 14 pages, 7 figures

Journal ref: Phys. Rev. Applied 4, 034002 (2015)

Heisenberg-limited qubit readout with two-mode squeezed light

Authors: Nicolas Didier, Archana Kamal, William D. Oliver, Alexandre Blais, Aashish A. Clerk

Abstract: We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint… ▽ More We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics. △ Less

Submitted 28 August, 2015; v1 submitted 2 February, 2015; originally announced February 2015.

Comments: 5 pages, 4 figures, Supplemental Material

Journal ref: Phys. Rev. Lett. 115, 093604 (2015)

Multiplexed Readout of Transmon Qubits with Josephson Bifurcation Amplifiers

Authors: V. Schmitt, X. Zhou, K. Juliusson, A. Blais, P. Bertet, D. Vion, D. Esteve

Abstract: Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bif… ▽ More Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators. △ Less

Submitted 24 October, 2014; v1 submitted 19 September, 2014; originally announced September 2014.

Comments: 7 pages, 6 figures, and 31 references

Photon-mediated interactions between distant artificial atoms

Authors: Arjan F. van Loo, Arkady Fedorov, Kevin Lalumière, Barry C. Sanders, Alexandre Blais, Andreas Wallraff

Abstract: Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations and quantum information processing. The exchange of real and virtual photons between atoms gives rise to non-trivial interactions the strength of which decreases rapidly with distance in three dimensions. Here we study much stronger photon mediated interactions using two superconducting… ▽ More Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations and quantum information processing. The exchange of real and virtual photons between atoms gives rise to non-trivial interactions the strength of which decreases rapidly with distance in three dimensions. Here we study much stronger photon mediated interactions using two superconducting qubits in an open onedimensional transmission line. Making use of the unique possibility to tune these qubits by more than a quarter of their transition frequency we observe both coherent exchange interactions at an effective separation of $3λ/4$ and the creation of super- and sub-radiant states at a separation of one photon wavelength $λ$. This system is highly suitable for exploring collective atom/photon interactions and applications in quantum communication technology. △ Less

Submitted 24 July, 2014; originally announced July 2014.

Comments: 4 pages, 4 figures and supplementary material (1 page)

Journal ref: Science 342, 1494 (2013)

Perfect squeezing by damping modulation in circuit quantum electrodynamics

Authors: Nicolas Didier, Farzad Qassemi, Alexandre Blais

Abstract: Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a vacuum squeezed state of arbitrary squeezing strength, thereby constituting a mechanism allowing perfect squeezing. Given the recent experimental realizations in circ… ▽ More Dissipation-driven quantum state engineering uses the environment to steer the state of quantum systems and preserve quantum coherence in the steady state. We show that modulating the damping rate of a microwave resonator generates a vacuum squeezed state of arbitrary squeezing strength, thereby constituting a mechanism allowing perfect squeezing. Given the recent experimental realizations in circuit QED of a microwave resonator with a tunable damping rate [Yin et al., Phys. Rev. Lett. 110, 107001 (2013)], superconducting circuits are an ideal playground to implement this technique. By dispersively coupling a qubit to the microwave resonator, it is possible to obtain qubit-state dependent squeezing. △ Less

Submitted 27 January, 2014; v1 submitted 19 July, 2013; originally announced July 2013.

Comments: 10 pages, 5 figures

Journal ref: Phys. Rev. A 89, 013820 (2014)

Detection and Manipulation of Majorana Fermions in Circuit QED

Authors: Clemens Müller, Jérôme Bourassa, Alexandre Blais

Abstract: Motivated by recent experimental progress towards the measurement and manipulation of Majorana fermions with superconducting circuits, we propose a device interfacing Majorana fermions with circuit quantum electrodynamics. The proposed circuit acts as a charge parity detector changing the resonance frequency of a superconducting $λ/4$ - resonator conditioned on the parity of charges on nearby gate… ▽ More Motivated by recent experimental progress towards the measurement and manipulation of Majorana fermions with superconducting circuits, we propose a device interfacing Majorana fermions with circuit quantum electrodynamics. The proposed circuit acts as a charge parity detector changing the resonance frequency of a superconducting $λ/4$ - resonator conditioned on the parity of charges on nearby gates. Operating at both charge and flux sweet spots, this device is highly insensitive to environmental noise. It enables high-fidelity single-shot quantum non demolition readout of the state of a pair of Majorana fermions encoding a topologically protected qubit. Additionally, the interaction permits the realization of an arbitrary phase gate on the topological qubit, closing the loop for computational completeness. Away from the charge sweet spot, this device can be used as a highly sensitive charge detector with a sensitivity better than $10^{-4} \text{e} / \sqrt{\text{Hz}}$ and bandwidth larger than $1$ MHz. △ Less

Submitted 30 November, 2013; v1 submitted 6 June, 2013; originally announced June 2013.

Comments: 13 pages, 11 figures

Journal ref: Phys. Rev. B 88, 235401 (2013)

Signatures of Hong-Ou-Mandel Interference at Microwave Frequencies

Authors: M. J. Woolley, C. Lang, C. Eichler, A. Wallraff, A. Blais

Abstract: Two-photon quantum interference at a beam splitter, commonly known as Hong-Ou-Mandel interference, was recently demonstrated with \emph{microwave-frequency} photons by Lang \emph{et al.}\,\cite{lang:microwaveHOM}. This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the mic… ▽ More Two-photon quantum interference at a beam splitter, commonly known as Hong-Ou-Mandel interference, was recently demonstrated with \emph{microwave-frequency} photons by Lang \emph{et al.}\,\cite{lang:microwaveHOM}. This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of \emph{pulsed} Gaussian or Lorentzian single microwave photons, and (ii) resonant fluorescent microwave fields from \emph{continuously-driven} circuit QED systems. The calculations include the effects of the finite bandwidth of the detection scheme. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Ref. \onlinecite{lang:microwaveHOM} was performed with trains of \emph{Lorentzian} single photons, and very good agreement between the calculations and the experimental data was obtained. △ Less

Submitted 22 April, 2013; originally announced April 2013.

Comments: 11 pages, 3 figures

Journal ref: New J. Phys. 15, 105025 (2013)

Comment on `Vacuum Rabi Splitting in a Semiconductor Circuit QED System' by Toida et al., Phys. Rev. Lett. 110, 066802 - Published 6 February 2013

Authors: A. Wallraff, A. Stockklauser, T. Ihn, J. R. Petta, A. Blais

Abstract: Toida et al. claim in their recent article [Phys. Rev. Lett. 110, 066802 (2013)] that they `report a direct observation of vacuum Rabi splitting in a GaAs/AlGaAs double quantum dot (DQD) based charge qubit coupled with a superconducting coplanar waveguide (CPW) resonator'. In this comment, we challenge the main claims made in their paper and show that their results: a) do not provide any evidence… ▽ More Toida et al. claim in their recent article [Phys. Rev. Lett. 110, 066802 (2013)] that they `report a direct observation of vacuum Rabi splitting in a GaAs/AlGaAs double quantum dot (DQD) based charge qubit coupled with a superconducting coplanar waveguide (CPW) resonator'. In this comment, we challenge the main claims made in their paper and show that their results: a) do not provide any evidence of vacuum Rabi oscillations and b) do not provide any direct evidence of vacuum Rabi splitting. △ Less

Submitted 12 April, 2013; originally announced April 2013.

Comments: 2 pages, 2 figures

Journal ref: Phys. Rev. Lett. 111, 249701 (2013)

Probing Correlations, Indistinguishability and Entanglement in Microwave Two-Photon Interference

Authors: C. Lang, C. Eichler, L. Steffen, J. M. Fink, M. J. Woolley, A. Blais, A. Wallraff

Abstract: Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1].… ▽ More Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order cross- and auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5]. △ Less

Submitted 18 January, 2013; originally announced January 2013.

Journal ref: Nature Physics 9, 345-348 (2013)

First-order sideband transitions with flux-driven asymmetric transmon qubits

Authors: J. D. Strand, Matthew Ware, Félix Beaudoin, T. A. Ohki, B. R. Johnson, Alexandre Blais, B. L. T. Plourde

Abstract: We demonstrate rapid, first-order sideband transitions between a superconducting resonator and a frequency-modulated transmon qubit. The qubit contains a substantial asymmetry between its Josephson junctions leading to a linear portion of the energy band near the resonator frequency. The sideband transitions are driven with a magnetic flux signal of a few hundred MHz coupled to the qubit. This mod… ▽ More We demonstrate rapid, first-order sideband transitions between a superconducting resonator and a frequency-modulated transmon qubit. The qubit contains a substantial asymmetry between its Josephson junctions leading to a linear portion of the energy band near the resonator frequency. The sideband transitions are driven with a magnetic flux signal of a few hundred MHz coupled to the qubit. This modulates the qubit splitting at a frequency near the detuning between the dressed qubit and resonator frequencies, leading to rates up to 85 MHz for exchanging quanta between the qubit and resonator. △ Less

Submitted 21 June, 2013; v1 submitted 3 January, 2013; originally announced January 2013.

Comments: 4.5 pages, 4 figures; published version

Journal ref: Physical Review B 87, 220505(R) (2013)

Quantum Heating of a nonlinear resonator probed by a superconducting qubit

Authors: F. R. Ong, M. Boissonneault, F. Mallet, A. C. Doherty, A. Blais, D. Vion, D. Esteve, P. Bertet

Abstract: We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These are found to be in agreement with theoretical predictions; in particular we experimentally observe the phenomenon of quantum heating. We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These are found to be in agreement with theoretical predictions; in particular we experimentally observe the phenomenon of quantum heating. △ Less

Submitted 23 October, 2012; v1 submitted 12 October, 2012; originally announced October 2012.

Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise

Authors: D. H. Slichter, R. Vijay, S. J. Weber, S. Boutin, M. Boissonneault, J. M. Gambetta, A. Blais, I. Siddiqi

Abstract: We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extr… ▽ More We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^α$ fit to the measured flux noise spectral density below 1 Hz. △ Less

Submitted 12 October, 2012; v1 submitted 29 June, 2012; originally announced June 2012.

Comments: 5 pages, 4 figures. Final journal version

Journal ref: Phys. Rev. Lett. 109, 153601 (2012)

Improved qubit bifurcation readout in the straddling regime of circuit QED

Authors: Maxime Boissonneault, J. M. Gambetta, A. Blais

Abstract: We study bifurcation measurement of a multi-level superconducting qubit using a nonlinear resonator biased in the straddling regime, where the resonator frequency sits between two qubit transition frequencies. We find that high-fidelity bifurcation measurements are possible because of the enhanced qubit-state-dependent pull of the resonator frequency, the behavior of qubit-induced nonlinearities a… ▽ More We study bifurcation measurement of a multi-level superconducting qubit using a nonlinear resonator biased in the straddling regime, where the resonator frequency sits between two qubit transition frequencies. We find that high-fidelity bifurcation measurements are possible because of the enhanced qubit-state-dependent pull of the resonator frequency, the behavior of qubit-induced nonlinearities and the reduced Purcell decay rate of the qubit that can be realized in this regime. Numerical simulations find up to a threefold improvement in qubit readout fidelity when operating in, rather than outside of, the straddling regime. High-fidelity measurements can be obtained at much smaller qubit-resonator couplings than current typical experimental realizations, reducing spectral crowding and potentially simplifying the implementation of multi-qubit devices. △ Less

Submitted 6 June, 2012; originally announced June 2012.

Comments: 9 pages, 6 figures

Journal ref: Phys. Rev. A 86, 022326 (2012)

Quantum error correction benchmarks for continuous weak parity measurements

Authors: Gabrielle Denhez, Alexandre Blais, David Poulin

Abstract: We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and to perform certain recovery operations conditioned on measurement outcomes. As a consequence, the experimental benchmark of a QEC scheme is a tall order becaus… ▽ More We present an experimental procedure to determine the usefulness of a measurement scheme for quantum error correction (QEC). A QEC scheme typically requires the ability to prepare entangled states, to carry out multi-qubit measurements, and to perform certain recovery operations conditioned on measurement outcomes. As a consequence, the experimental benchmark of a QEC scheme is a tall order because it requires the conjuncture of many elementary components. Our scheme opens the path to experimental benchmarks of individual components of QEC. Our numerical simulations show that certain parity measurements realized in circuit quantum electrodynamics are on the verge of being useful for QEC. △ Less

Submitted 17 April, 2012; originally announced April 2012.

Journal ref: Phys. Rev. A 86, 032318 (2012)

Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon

Authors: J. Bourassa, F. Beaudoin, Jay M. Gambetta, A. Blais

Abstract: We provide a general method to find the Hamiltonian of a linear circuit in the presence of a nonlinearity. Focussing on the case of a Josephson junction embedded in a transmission-line resonator, we solve for the normal modes of the system by taking into account exactly the effect of the quadratic (i.e. inductive) part of the Josephson potential. The nonlinearity is then found to lead to self and… ▽ More We provide a general method to find the Hamiltonian of a linear circuit in the presence of a nonlinearity. Focussing on the case of a Josephson junction embedded in a transmission-line resonator, we solve for the normal modes of the system by taking into account exactly the effect of the quadratic (i.e. inductive) part of the Josephson potential. The nonlinearity is then found to lead to self and cross-Kerr effect, as well as beam-splitter type interactions between modes. By adjusting the parameters of the circuit, the Kerr coefficient K can be made to reach values that are weak (K < κ), strong (K > κ) or even very strong (K >> κ) with respect to the photon-loss rate κ. In the latter case, the resonator+junction circuit corresponds to an in-line version of the transmon. By replacing the single junction by a SQUID, the Kerr coefficient can be tuned in-situ, allowing for example the fast generation of Schrödinger cat states of microwave light. Finally, we explore the maximal strength of qubit-resonator coupling that can be reached in this setting. △ Less

Submitted 17 July, 2012; v1 submitted 10 April, 2012; originally announced April 2012.

Comments: 15 pages, 12 figures; Published version with minor changes and corrections

Journal ref: Phys. Rev. A 86, 013814 (2012)

Backaction of a driven nonlinear resonator on a superconducting qubit

Authors: Maxime Boissonneault, A. C. Doherty, F. R. Ong, P. Bertet, D. Vion, D. Esteve, A. Blais

Abstract: We study the backaction of a driven nonlinear resonator on a multi-level superconducting qubit. Using unitary transformations on the multi-level Jaynes-Cummings Hamiltonian and quantum optics master equation, we derive an analytical model that goes beyond linear response theory. Within the limits of validity of the model, we obtain quantitative agreement with experimental and numerical data, both… ▽ More We study the backaction of a driven nonlinear resonator on a multi-level superconducting qubit. Using unitary transformations on the multi-level Jaynes-Cummings Hamiltonian and quantum optics master equation, we derive an analytical model that goes beyond linear response theory. Within the limits of validity of the model, we obtain quantitative agreement with experimental and numerical data, both in the bifurcation and in the parametric amplification regimes of the nonlinear resonator. We show in particular that the measurement-induced dephasing rate of the qubit can be rather small at high drive power. This is in contrast to measurement with a linear resonator where this rate increases with the drive power. Finally, we show that, for typical parameters of circuit quantum electrodynamics, correctly describing measurement-induced dephasing requires a model going beyond linear response theory, such as the one presented here. △ Less

Submitted 1 November, 2011; originally announced November 2011.

Comments: 17 pages, 7 figures

Journal ref: Phys. Rev. A 85, 022305 (2012)

Dipole coupling of a double quantum dot to a microwave resonator

Authors: T. Frey, P. J. Leek, M. Beck, A. Blais, T. Ihn, K. Ensslin, A. Wallraff

Abstract: Quantum coherence in solid-state systems has been demonstrated in superconducting circuits and in semiconductor quantum dots. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons. Coherent coupling of superconducting circuits to microwave photons, circuit qua… ▽ More Quantum coherence in solid-state systems has been demonstrated in superconducting circuits and in semiconductor quantum dots. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons. Coherent coupling of superconducting circuits to microwave photons, circuit quantum electrodynamics (QED), has opened up new research directions and enabled long distance coupling of qubits. Here we demonstrate how the electromagnetic field of a superconducting microwave resonator can be coupled to a semiconductor double quantum dot. The charge stability diagram of the double dot, typically measured by direct current (DC) transport techniques, is investigated via dispersive frequency shifts of the coupled resonator. This hybrid all-solid-state approach offers the potential to coherently couple multiple quantum dot and superconducting qubits together on one chip, and offers a method for high resolution spectroscopy of semiconductor quantum structures. △ Less

Submitted 26 August, 2011; originally announced August 2011.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 108, 046807 (2012)

Observation of Resonant Photon Blockade at Microwave Frequencies using Correlation Function Measurements

Authors: C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov Jr., M. Baur, S. Filipp, M. P. da Silva, A. Blais, A. Wallraff

Abstract: Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of phot… ▽ More Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra. △ Less

Submitted 2 February, 2011; originally announced February 2011.

Journal ref: Phys. Rev. Lett. 106, 243601 (2011)

Circuit QED with a Nonlinear Resonator : ac-Stark Shift and Dephasing

Authors: F. R. Ong, M. Boissonneault, F. Mallet, A. Palacios-Laloy, A. Dewes, A. C. Doherty, A. Blais, P. Bertet, D. Vion, D. Esteve

Abstract: We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which… ▽ More We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier. △ Less

Submitted 27 April, 2011; v1 submitted 29 October, 2010; originally announced October 2010.

Comments: Paper : 4 pages, 3 figures; Supplementary material : 1 page, 1 figure

Journal ref: Phys. Rev. Lett. 106, 167002 (2011)

A superconducting qubit with Purcell protection and tunable coupling

Authors: J. M. Gambetta, A. A. Houck, Alexandre Blais

Abstract: We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable coupling strength g. We show that this coupling strength can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0 the qubit is in a decoherence free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore we show that in… ▽ More We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable coupling strength g. We show that this coupling strength can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0 the qubit is in a decoherence free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore we show that in the decoherence free subspace the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement. △ Less

Submitted 22 September, 2010; originally announced September 2010.

Comments: 4 pages, 3 figures

Journal ref: Phys. Rev. Lett. 106, 030502 (2011)

Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities

Authors: Maxime Boissonneault, J. M. Gambetta, Alexandre Blais

Abstract: In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level st… ▽ More In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed {\it et al.} [arXiv:1004.4323v1]. △ Less

Submitted 7 September, 2010; v1 submitted 30 April, 2010; originally announced May 2010.

Comments: 4 pages, 5 figures

Journal ref: Phys. Rev. Lett. 105, 100504 (2010)

Schemes for the observation of photon correlation functions in circuit QED with linear detectors

Authors: Marcus P. da Silva, Deniz Bozyigit, Andreas Wallraff, Alexandre Blais

Abstract: Correlations are important tools in the characterization of quantum fields. They can be used to describe statistical properties of the fields, such as bunching and anti-bunching, as well as to perform field state tomography. Here we analyse experiments by Bozyigit et al. [arXiv:1002.3738] where correlation functions can be observed using the measurement records of linear detectors (i.e. quadrature… ▽ More Correlations are important tools in the characterization of quantum fields. They can be used to describe statistical properties of the fields, such as bunching and anti-bunching, as well as to perform field state tomography. Here we analyse experiments by Bozyigit et al. [arXiv:1002.3738] where correlation functions can be observed using the measurement records of linear detectors (i.e. quadrature measurements), instead of relying on intensity or number detectors. We also describe how large amplitude noise introduced by these detectors can be quantified and subtracted from the data. This enables, in particular, the observation of first- and second-order coherence functions of microwave photon fields generated using circuit quantum-electrodynamics and propagating in superconducting transmission lines under the condition that noise is sufficiently low. △ Less

Submitted 4 June, 2010; v1 submitted 22 April, 2010; originally announced April 2010.

Comments: v1: 11 pages, 7 figures , v2: Minor revisions throughout for clarity. Added a few references and an appendix

Journal ref: Phys. Rev. A 82, 043804 (2010)

Electromagnetically-induced transparency with amplification in superconducting circuits

Authors: Jaewoo Joo, Jerome Bourassa, Alexandre Blais, Barry C. Sanders

Abstract: We show that electromagnetically-induced transparency and lasing without inversion are simultaneously achieved for microwave fields by using a fluxonium superconducting circuit. As a result of the $Δ$ energy-level structure of this artificial three-level atom, we find the surprising phenomenon that the electromagnetically-induced transparency window in the frequency domain is sandwiched between ab… ▽ More We show that electromagnetically-induced transparency and lasing without inversion are simultaneously achieved for microwave fields by using a fluxonium superconducting circuit. As a result of the $Δ$ energy-level structure of this artificial three-level atom, we find the surprising phenomenon that the electromagnetically-induced transparency window in the frequency domain is sandwiched between absorption on one side and amplification on the other side. △ Less

Submitted 11 April, 2010; originally announced April 2010.

Comments: 4 pages, 5 figures

Journal ref: Physical Review Letters 105: 073601 (4 pp.), 9 August 2010

Measurements of the Correlation Function of a Microwave Frequency Single Photon Source

Authors: D. Bozyigit, C. Lang, L. Steffen, J. M. Fink, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, M. P. da Silva, A. Blais, A. Wallraff

Abstract: At optical frequencies the radiation produced by a source, such as a laser, a black body or a single photon source, is frequently characterized by analyzing the temporal correlations of emitted photons using single photon counters. At microwave frequencies, however, there are no efficient single photon counters yet. Instead, well developed linear amplifiers allow for efficient measurement of the… ▽ More At optical frequencies the radiation produced by a source, such as a laser, a black body or a single photon source, is frequently characterized by analyzing the temporal correlations of emitted photons using single photon counters. At microwave frequencies, however, there are no efficient single photon counters yet. Instead, well developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate how the properties of a microwave single photon source can be characterized using correlation measurements of the emitted radiation with such detectors. We also demonstrate the cooling of a thermal field stored in a cavity, an effect which we detect using a cross-correlation measurement of the radiation emitted at the two ends of the cavity. △ Less

Submitted 19 February, 2010; originally announced February 2010.

Comments: 5 pages, 4 figures

Journal ref: Nature Physics 7, 154-158 (2011)

Thermal Excitation of Multi-Photon Dressed States in Circuit Quantum Electrodynamics

Authors: J. M. Fink, M. Baur, R. Bianchetti, S. Filipp, M. Göppl, P. J. Leek, L. Steffen, A. Blais, A. Wallraff

Abstract: The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up… ▽ More The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Our data indicates that the role of thermal fields in resonant cavity QED can be studied in detail using superconducting circuits. △ Less

Submitted 19 November, 2009; originally announced November 2009.

Comments: ArXiv version of manuscript to be published in the Physica Scripta topical issue on the Nobel Symposium 141: Qubits for Future Quantum Computers(2009), 13 pages, 6 figures, hi-res version at http://qudev.ethz.ch/content/science/PubsPapers.html

Journal ref: Phys. Scr. T137, 014013 (2009)

Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics

Authors: R. Bianchetti, S. Filipp, M. Baur, J. M. Fink, M. Göppl, P. J. Leek, L. Steffen, A. Blais, A. Wallraff

Abstract: The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurem… ▽ More The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements. △ Less

Submitted 9 November, 2009; v1 submitted 15 July, 2009; originally announced July 2009.

Comments: Revised version: corrected typos, 8 pages, 6 figures, version with high resolution figures available at http://qudev.ethz.ch/content/science/PubsPapers.html

Journal ref: Phys. Rev. A 80, 043840 (2009)

Ultrastrong coupling regime of cavity QED with phase-biased flux qubits

Authors: J. Bourassa, J. M. Gambetta, A. A. Abdumalikov Jr, O. Astafiev, Y. Nakamura, A. Blais

Abstract: We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [Abdumalikov et al. Phys. Rev. B 78, 180502 (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinit… ▽ More We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [Abdumalikov et al. Phys. Rev. B 78, 180502 (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinity of the qubit. In addition to yielding stronger coupling with respect to other proposals for flux qubit based circuit QED, this approach leads to a qubit-resonator coupling strength g which does not scale as the area of the qubit but is proportional to the total inductance shared between the resonator and the qubit. Strong coupling can thus be attained while still minimizing sensitivity to flux noise. Finally, we show that by taking advantage of the the large kinetic inductance of a Josephson junction in the center conductor of the resonator can lead to coupling energies of several tens of percent of the resonator frequency, reaching the ultrastrong coupling regime of cavity QED where the rotating-wave approximation breaks down. This should allow an on-chip implementation of the E x B Jahn-Teller model. △ Less

Submitted 16 September, 2009; v1 submitted 8 June, 2009; originally announced June 2009.

Comments: 9 pages, 7 figures. Published version with minor changes and corrections

Journal ref: Phys. Rev. A 80, 032109 (2009)

Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor

Authors: L. DiCarlo, J. M. Chow, J. M. Gambetta, Lev S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, R. J. Schoelkopf

Abstract: By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final st… ▽ More By harnessing the superposition and entanglement of physical states, quantum computers could outperform their classical counterparts in solving problems of technological impact, such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Simultaneously meeting the conflicting requirements of long coherence, state preparation, universal gate operations, and qubit readout makes building quantum processors challenging. Few-qubit processors have already been shown in nuclear magnetic resonance, cold ion trap and optical systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch-Jozsa quantum algorithms. We employ a novel two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond time scales, which is mediated by a cavity bus in a circuit quantum electrodynamics (cQED) architecture. This interaction allows generation of highly-entangled states with concurrence up to 94%. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfill the promise of a scalable technology. △ Less

Submitted 4 May, 2009; v1 submitted 11 March, 2009; originally announced March 2009.

Comments: 6 pages, 1 table, 4 figures, and Supplementary Information (3 pages, 3 figures); Expanded author list, updated references, and minor improvements to text and figures

Journal ref: Nature 460, 240-244 (2009)

Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System

Authors: J. M. Fink, M. Goeppl, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, A. Wallraff

Abstract: The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavi… ▽ More The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a hallmark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity. △ Less

Submitted 11 February, 2009; originally announced February 2009.

Comments: ArXiv version of manuscript published in Nature in July 2008, 5 pages, 5 figures, hi-res version at http://www.finkjohannes.com/SqrtNArxivPreprint.pdf

Journal ref: Nature 454, 315-318 (Jul 2008)