Showing 1–50 of 99 results for author: Pfau, T

High-NA vectorial hologram optimization

Authors: Michael Wischert, Fiona Hellstern, Paul Uerlings, Tilman Pfau, Stephan Welte, Ralf Klemt

Abstract: We present a vectorial phase-only framework for the gradient-based optimization of computer-generated holograms. Our approach addresses a critical limitation in high numerical aperture (NA) optical systems, where standard scalar approximations often experience significant fidelity degradation. We highlight the limitations of scalar diffraction models (Fraunhofer and Debye) at high NA for represent… ▽ More We present a vectorial phase-only framework for the gradient-based optimization of computer-generated holograms. Our approach addresses a critical limitation in high numerical aperture (NA) optical systems, where standard scalar approximations often experience significant fidelity degradation. We highlight the limitations of scalar diffraction models (Fraunhofer and Debye) at high NA for representative classes of target intensities, namely tweezer arrays and extended flat-top profiles. Using a differentiable Richards-Wolf forward model, we numerically demonstrate stable algorithmic convergence and the generation of highly uniform intensity profiles in the deep non-paraxial regime. At NA=0.9, Richards-Wolf (RW) optimization reaches flat-top and tweezer uniformities of 99.97 % and 99.98 %, respectively, with a mean tweezer ellipticity of $\varepsilon=$1.007, while scalar forward models show target-dependent degradation in plateau fidelity or focal geometry. Furthermore, because the RW model returns the full vectorial field, the same framework can optimize objectives that depend on local polarization. We demonstrate this for a polarization-sensitive optical-dipole-potential target, where direct RW-potential optimization reduces the mean normalized residual by more than an order of magnitude when including vector and tensor light-shift terms. △ Less

Submitted 31 July, 2026; originally announced July 2026.

Comments: 23 pages, 7 figures

Magnetic field free nonreciprocity in tapered atomic cladded nano waveguide

Authors: Ilan Sher, Benyamin Shnirman, Arieh Grosman, Roy Zektzer, Markus Greul, Mathias Kaschel, Tilman Pfau, Robert Löw, Uriel Levy

Abstract: Optical nonreciprocity is a fundamental requirement for modern optical communications and quantum information processing, where it is essential to protect sensitive sources from destabilizing feedback and preserving quantum coherence. Conventional nonreciprocal devices are based on the Faraday effect; however, their dependence on bulky permanent magnets poses a significant barrier to chip-scale in… ▽ More Optical nonreciprocity is a fundamental requirement for modern optical communications and quantum information processing, where it is essential to protect sensitive sources from destabilizing feedback and preserving quantum coherence. Conventional nonreciprocal devices are based on the Faraday effect; however, their dependence on bulky permanent magnets poses a significant barrier to chip-scale integration and scalability. Moreover, the application of a magnetic field is undesired in many quantum atomic systems. In this work, we demonstrate magnet-free optical nonreciprocity on a fully integrated platform utilizing a Nanophotonic Alkali Silicon Waveguide (NASWAG) interfaced with hot rubidium vapor. By employing velocity-selective optical pumping (VSOP), we break time reversal symmetry by taking advantage of the Doppler effect-generated by the thermally moving atoms, a phenomenon traditionally viewed as a limitation in atomic spectroscopy. We show that the use of suspended tapered waveguides significantly mitigates transit-time broadening, thereby enabling the observation of a robust nonreciprocal response. We further characterize the dependence of the isolation contrast on pump power, finding that the experimental measurements and numerical simulations correspond and provide mutual support for the underlying physical model. With proper optimization, the demonstrated effect may be used in the future for applications such as magnetic free optical isolators. △ Less

Submitted 3 June, 2026; originally announced June 2026.

Comments: 10 pages, 3 figures

MSC Class: 78-05

Collective Strong Coupling of Thermal Atoms to Integrated Microring Resonators

Authors: Xiaoyu Cheng, Benyamin Shnirman, Alexandra Köpf, Guangcanlan Yang, Hong X. Tang, Hadiseh Alaeian, Tilman Pfau, Robert Löw

Abstract: Strong coupling between atomic ensembles and high-quality optical cavities enables collective and nonlinear phenomena that are central to cavity quantum electrodynamics (cQED). Although many experiments have been performed on this topic, most of them have focused on cold atoms. Here, we experimentally demonstrate collective strong coupling between thermal rubidium (Rb) vapor and high-quality silic… ▽ More Strong coupling between atomic ensembles and high-quality optical cavities enables collective and nonlinear phenomena that are central to cavity quantum electrodynamics (cQED). Although many experiments have been performed on this topic, most of them have focused on cold atoms. Here, we experimentally demonstrate collective strong coupling between thermal rubidium (Rb) vapor and high-quality silicon nitride microring resonators (MRRs) on an integrated photonic chip. We observe cavity mode splitting, with a measured collective coupling strength of $g_N/2π\approx 1\,\mathrm{GHz}$ and a collective cooperativity of $C_N\approx2$ at $110\,^\circ\mathrm{C}$, indicating coherent energy exchange between the atomic ensemble and the cavity mode despite rapid decoherence in the thermal vapor system. We infer an average of $20$ atoms participating in the collective interaction, yielding a single-atom cooperativity of $C_0=0.1$ and approaching the single-atom strong-coupling regime. Our results establish the integrated thermal vapor MRR platform as a robust, compact, and scalable system for studying collective and nonlinear phenomena in cQED. △ Less

Submitted 27 April, 2026; originally announced April 2026.

Comments: 9 pages(4 pages of main content + 3 pages of appendix + 2 pages of references), 8 figures

Two-dimensional shelving spectroscopy of ultraviolet ground state transitions in dysprosium

Authors: Kevin S. H. Ng, Paul Uerlings, Fiona Hellstern, Jens Hertkorn, Luis Weiß, Stephan Welte, Tilman Pfau, Ralf Klemt

Abstract: The open inner-shell electronic structure of lanthanides with large magnetic moments gives rise to a rich spectrum of transitions available for laser cooling, trapping, and coherent control. Despite this, the large number of ultraviolet (UV) transitions below 400nm have so far been rarely utilized in dipolar atom experiments. Here, we investigate multiple UV ground state transitions in dysprosium.… ▽ More The open inner-shell electronic structure of lanthanides with large magnetic moments gives rise to a rich spectrum of transitions available for laser cooling, trapping, and coherent control. Despite this, the large number of ultraviolet (UV) transitions below 400nm have so far been rarely utilized in dipolar atom experiments. Here, we investigate multiple UV ground state transitions in dysprosium. Several of these UV excited states have the largest decay strengths to the ultralong-lived, low-lying first excited state which are comparable to the most commonly used strongest transitions found in dipolar atoms. Using two-dimensional shelving spectroscopy which improves detection sensitivity and provides a straightforward way to determine the hyperfine-isotope structure and excited state total angular momentum $J$, we measure isotope shifts, hyperfine coefficients, and create King plots to determine their electronic nature. Such knowledge of these UV transitions which analogously exist in other magnetic atoms is important for optically populating the first excited state and can be used towards creating an optical clock, high resolution imaging in quantum gas microscopy, and probing lanthanide nuclei with enhanced Schiff moments in search of physics beyond the standard model. △ Less

Submitted 28 April, 2026; v1 submitted 8 April, 2026; originally announced April 2026.

Comments: 9 pages, 4 figures, 7 pages supplementary material

Microscopic Rydberg electron orbit manipulation with optical tweezers

Authors: Homar Rivera-Rodríguez, Matthew T. Eiles, Tilman Pfau, Florian Meinert

Abstract: Laser cooling and trapping of atomic matter waves in optical potentials has enabled rapid progress in quantum science, particularly when combined with Rydberg excitation of the atoms to induce long-range interactions. Here, we propose the local manipulation and spatio-temporal sculpting of the electronic matter wave of a Rydberg atom by a laser field focused so that its beam width is smaller than… ▽ More Laser cooling and trapping of atomic matter waves in optical potentials has enabled rapid progress in quantum science, particularly when combined with Rydberg excitation of the atoms to induce long-range interactions. Here, we propose the local manipulation and spatio-temporal sculpting of the electronic matter wave of a Rydberg atom by a laser field focused so that its beam width is smaller than the Rydberg electron orbit. We compute the electronic eigenstates in the presence of a sharply focused Gaussian laser beam, and find strong Rydberg state mixing leading to large kilo-Debye dipole moments. These can be modulated with high bandwidth controlled by the local tweezer intensity. Oscillations in the position-dependent level shifts, analogous to the potential wells allowing ultralong-range Rydberg molecules to form, provide opportunities for eccentric radial trapping of the Rydberg electron via ponderomotive forces acting on sub-orbital length scales. △ Less

Submitted 26 May, 2026; v1 submitted 17 February, 2026; originally announced February 2026.

Journal ref: Phys. Rev. Lett. 137, 013401 (2026)

Josephson vortices and persistent current in a double-ring supersolid system

Authors: Malte Schubert, Koushik Mukherjee, Tilman Pfau, Stephanie Reimann

Abstract: We theoretically investigate the properties of ultra-cold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The non-rotating ground-state phases are investigated across the superfluid-supersolid phase transition, revealing a particle imbalance between the two rings and a preferential density modulation in the outer ring in the absence of rotation. Near the… ▽ More We theoretically investigate the properties of ultra-cold dipolar atoms in radially coupled, concentric annular traps created by a potential barrier. The non-rotating ground-state phases are investigated across the superfluid-supersolid phase transition, revealing a particle imbalance between the two rings and a preferential density modulation in the outer ring in the absence of rotation. Near the phase transition on the superfluid side, applying rotation can induce density modulations in either ring, depending on the angular momentum and barrier strength. For low angular momentum, such rotation-induced density modulation forms in the outer ring, while for high angular momentum and weak barriers, it emerges in the inner ring. Rotation can lead to persistent currents and the nucleation of a vortex residing either at the center (central vortex) or at the ring junction (Josephson vortex). Josephson vortices can also form at the junctions of the localized density sites induced by rotation in the inner ring, a behavior that is unique to our system. By switching off the trap and allowing the system to expand, distinct interference patterns emerge, which can be analyzed to identify and distinguish between various vortex configurations, and thus can be observed in current state-of-the-art experiments. △ Less

Submitted 27 June, 2025; v1 submitted 14 March, 2025; originally announced March 2025.

Comments: 7 figures, 12 pages

Journal ref: Phys. Rev. Research 7, 033110 (2025)

Topological transport of a classical droplet in a lattice of time

Authors: Tapio Simula, Niels Kjærgaard, Tilman Pfau

Abstract: Thouless charge pumps are quantum mechanical devices whose operation relies on topology. They provide the means for transporting quantum matter in space lattices with a single quantum precision. Contrasting space crystals that spontaneously break a continuous spatial translation symmetry and form crystals in space,time crystals have emerged as novel states of matter that organize into time lattice… ▽ More Thouless charge pumps are quantum mechanical devices whose operation relies on topology. They provide the means for transporting quantum matter in space lattices with a single quantum precision. Contrasting space crystals that spontaneously break a continuous spatial translation symmetry and form crystals in space,time crystals have emerged as novel states of matter that organize into time lattices and spontaneously break a discrete time translation symmetry. The utility of Thouless pumps that enable topologically protected quantised transport of electrons and neutral atoms in spatial superlattices leads to the question if corresponding devices exist for time crystals? Here we show that topological pumps can be realized for time solids by transporting droplets of a liquid forward and backward in time lattices and we measure the topological index that characterises such pumping processes. By exploiting a synthetic time dimension classical time crystals can circumvent the quantum tunneling that underpins Thouless charge pumps. Our results establish topological pumping through time instead of space and pave the way for applications of time crystals. △ Less

Submitted 11 March, 2024; originally announced March 2024.

Comments: 18 pages, 7 figures

$In$ $situ$ observation of non-polar to strongly polar atom-ion collision dynamics

Authors: Moritz Berngruber, Daniel J. Bosworth, Oscar A. Herrera-Sancho, Viraatt S. V. Anasuri, Nico Zuber, Frederic Hummel, Jennifer Krauter, Florian Meinert, Robert Löw, Peter Schmelcher, Tilman Pfau

Abstract: The onset of collision dynamics between an ion and a Rydberg atom is studied in a regime characterized by a multitude of collision channels. These channels arise from coupling between a non-polar Rydberg state and numerous highly polar Stark states. The interaction potentials formed by the polar Stark states show a substantial difference in spatial gradient compared to the non-polar state leading… ▽ More The onset of collision dynamics between an ion and a Rydberg atom is studied in a regime characterized by a multitude of collision channels. These channels arise from coupling between a non-polar Rydberg state and numerous highly polar Stark states. The interaction potentials formed by the polar Stark states show a substantial difference in spatial gradient compared to the non-polar state leading to a separation of collisional timescales, which is observed in situ. For collision energies in the range of $k_\textrm{B}\cdotμ$K to $k_\textrm{B}\cdot$K, the dynamics exhibit a counter-intuitive dependence on temperature, resulting in faster collision dynamics for cold - initially "slow" - systems. Dipole selection rules enable us to prepare the collision pair on the non-polar potential in a highly controlled manner, which determines occupation of the collision channels. The experimental observations are supported by semi-classical simulations, which model the pair state evolution and provide evidence for tunable non-adiabatic dynamics. △ Less

Submitted 22 January, 2024; originally announced January 2024.

Journal ref: Phys. Rev. Lett. 133, 083001 (2024)

A Single Photon Source based on a Long-Range Interacting Room Temperature Vapor

Authors: Felix Moumtsilis, Max Mäusezahl, Haim Nakav, Annika Belz, Robert Löw, Tilman Pfau

Abstract: We report on the current development of a single photon source based on a long-range interacting room temperature rubidium vapor. We discuss the history of the project, the production of vapor cells, and the observation of Rabi-oscillations in the four-wave-mixing excitation scheme. We report on the current development of a single photon source based on a long-range interacting room temperature rubidium vapor. We discuss the history of the project, the production of vapor cells, and the observation of Rabi-oscillations in the four-wave-mixing excitation scheme. △ Less

Submitted 22 January, 2024; originally announced January 2024.

Comments: 8 pages, 6 figures

Coherent Control of the Fine-Structure Qubit in a Single Alkaline-Earth Atom

Authors: Govind Unnikrishnan, Philipp Ilzhöfer, Achim Scholz, Christian Hölzl, Aaron Götzelmann, Ratnesh Kumar Gupta, Jiachen Zhao, Jennifer Krauter, Sebastian Weber, Nastasia Makki, Hans Peter Büchler, Tilman Pfau, Florian Meinert

Abstract: We report on the first realization of a novel neutral atom qubit encoded in the metastable fine-structure states ${^3\rm{P}_0}$ and ${^3\rm{P}_2}$ of single $^{88}$Sr atoms trapped in an optical tweezer. Raman coupling of the qubit states promises rapid single-qubit rotations on par with the fast Rydberg-mediated two-body gates. We demonstrate preparation, read-out, and coherent control of the qub… ▽ More We report on the first realization of a novel neutral atom qubit encoded in the metastable fine-structure states ${^3\rm{P}_0}$ and ${^3\rm{P}_2}$ of single $^{88}$Sr atoms trapped in an optical tweezer. Raman coupling of the qubit states promises rapid single-qubit rotations on par with the fast Rydberg-mediated two-body gates. We demonstrate preparation, read-out, and coherent control of the qubit. In addition to driving Rabi oscillations bridging an energy gap of more than 17 THz using a pair of phase-locked clock lasers, we also carry out Ramsey spectroscopy to extract the transverse qubit coherence time $T_2$. When the tweezer is tuned into magic trapping conditions, which is achieved in our setup by tuning the tensor polarizability of the ${^3\rm{P}_2}$ state via an external control magnetic field, we measure $T_2 = 1.2$ ms. A microscopic quantum mechanical model is used to simulate our experiments including dominant noise sources. We identify the main constraints limiting the observed coherence time and project improvements to our system in the immediate future. Our work opens the door for a so far unexplored qubit encoding concept for neutral atom based quantum computing. △ Less

Submitted 13 March, 2024; v1 submitted 19 January, 2024; originally announced January 2024.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. Lett. 132, 150606 (2024)

Manipulating the Dipolar Interactions and Cooperative Effects in Confined Geometries

Authors: Hadiseh Alaeian, Artur Skljarow, Stefan Scheel, Tilman Pfau, Robert Löw

Abstract: To facilitate the transition of quantum effects from the controlled laboratory environment to practical real-world applications, there is a pressing need for scalable platforms. One promising strategy involves integrating thermal vapors with nanostructures designed to manipulate atomic interactions. In this tutorial, we aim to gain deeper insights into this by examining the behavior of thermal vap… ▽ More To facilitate the transition of quantum effects from the controlled laboratory environment to practical real-world applications, there is a pressing need for scalable platforms. One promising strategy involves integrating thermal vapors with nanostructures designed to manipulate atomic interactions. In this tutorial, we aim to gain deeper insights into this by examining the behavior of thermal vapors that are confined within nanocavities or waveguides and exposed to near-resonant light. We explore the interactions between atoms in confined dense thermal vapors. Our investigation reveals deviations from the predictions of continuous electrodynamics models, including density-dependent line shifts and broadening effects. In particular, our results demonstrate that by carefully controlling the saturation of single atoms and the interactions among multiple atoms using nanostructures, along with controlling the geometry of the atomic cloud, it becomes possible to manipulate the effective optical nonlinearity of the entire atomic ensemble. This capability renders the hybrid thermal atom-nanophotonic platform a distinctive and valuable one for manipulating the collective effect and achieving substantial optical nonlinearities. △ Less

Submitted 16 January, 2024; originally announced January 2024.

Comments: 28 pages and 4 figures

Collisional shift and broadening of Rydberg states in nitric oxide at room temperature

Authors: Fabian Munkes, Alexander Trachtmann, Patrick Kaspar, Florian Anschütz, Philipp Hengel, Yannick Schellander, Patrick Schalberger, Norbert Fruehauf, Jens Anders, Robert Löw, Tilman Pfau, Harald Kübler

Abstract: We report on the collisional shift and line broadening of Rydberg states in nitric oxide (NO) with increasing density of a background gas at room temperature. As a background gas we either use NO itself or nitrogen (N$_{2}$). The precision spectroscopy is performed by a sub-Doppler three-photon excitation scheme with a subsequent readout of the Rydberg states realized by the amplification of a cur… ▽ More We report on the collisional shift and line broadening of Rydberg states in nitric oxide (NO) with increasing density of a background gas at room temperature. As a background gas we either use NO itself or nitrogen (N$_{2}$). The precision spectroscopy is performed by a sub-Doppler three-photon excitation scheme with a subsequent readout of the Rydberg states realized by the amplification of a current generated by free charges due to collisions. The shift shows a dependence on the rotational quantum state of the ionic core and no dependence on the principle quantum number of the orbiting Rydberg electron. The experiment was performed in the context of developing a trace-gas sensor for breath-gas analysis in a medical application. △ Less

Submitted 22 March, 2024; v1 submitted 27 October, 2023; originally announced October 2023.

In situ observation of chemistry in Rydberg molecules within a coherent solvent

Authors: Felix Engel, Shiva Kant Tiwari, Tilman Pfau, Sebastian Wüster, Florian Meinert

Abstract: We often infer the state of systems in nature indirectly, for example, in high-energy physics by the interaction of particles with an ambient medium. We adapt this principle to energies $9$ orders of magnitude smaller, to classify the final state of exotic molecules after internal conversion of their electronic state, through their interaction with an ambient quantum fluid, a Bose-Einstein condens… ▽ More We often infer the state of systems in nature indirectly, for example, in high-energy physics by the interaction of particles with an ambient medium. We adapt this principle to energies $9$ orders of magnitude smaller, to classify the final state of exotic molecules after internal conversion of their electronic state, through their interaction with an ambient quantum fluid, a Bose-Einstein condensate (BEC). The BEC is the ground-state of a million bosonic atoms near zero temperature, and a single embedded ultra-long range Rydberg molecule can coherently excite waves in this fluid, which carry telltale signatures of its dynamics. Bond lengths exceeding a micrometer allow us to observe the molecular fingerprint on the BEC in-situ, via optical microscopy. Interpreting images in comparison with simulations strongly suggests that the molecular electronic state rapidly converts from the initially excited S and D orbitals to a much more complex molecular state (called "trilobite''), marked by a maximally localized electron. This internal conversion liberates energy, such that one expects final-state particles to move rapidly through the medium, which is however ruled out by comparing experiment and simulations. The molecule thus must strongly decelerate in the medium, for which we propose a plausible mechanism. Our experiment demonstrates a medium that facilitates and records an electronic state change of embedded exotic molecules in ultra-cold chemistry, with sufficient sensitivity to constrain velocities of final-state particles. △ Less

Submitted 12 August, 2024; v1 submitted 26 August, 2023; originally announced August 2023.

Comments: 12 pages and 11 figures

Journal ref: Phys. Rev. Research 6, 033150 (2024)

Analyzing the collective emission of a Rydberg-blockaded single-photon source based on an ensemble of thermal atoms

Authors: Jan A. P. Reuter, Max Mäusezahl, Felix Moumtsilis, Tilman Pfau, Tommaso Calarco, Robert Löw, Matthias M. Müller

Abstract: An ensemble of Rubidum atoms can be excited with lasers such that it evolves into an entangled state with just one collective excitation within the Rydberg blockade radius. The decay of this state leads to the emission of a single, antibunched photon. For a hot vapor of Rubidium atoms in a micro cell we numerically study the feasibility of such a single-photon source under different experimental c… ▽ More An ensemble of Rubidum atoms can be excited with lasers such that it evolves into an entangled state with just one collective excitation within the Rydberg blockade radius. The decay of this state leads to the emission of a single, antibunched photon. For a hot vapor of Rubidium atoms in a micro cell we numerically study the feasibility of such a single-photon source under different experimental conditions like the atomic density distribution and the choice of electronic states addressed by the lasers. For the excitation process with three rectangular lasers pulses, we simulate the coherent dynamics of the system in a truncated Hilbert space. We investigate the radiative behavior of the moving Rubidum atoms and optimize the laser pulse sequence accordingly. We find that the collective decay of the single-excitation leads to a fast and directed photon emission and further, that a pulse sequence similar to a spin echo increases the directionality of the photon. Finally, we analyze the residual double-excitations and find that they do not exhibit these collective decay properties and play only a minor deleterious role. △ Less

Submitted 28 November, 2023; v1 submitted 7 March, 2023; originally announced March 2023.

Comments: 12 pages, 6 figures, 1 table. Removed 6P state calculations for brevity. Added new results for 5P state calculations. Added new Appendix. Updated color in figures

Observation of vibrational dynamics of orientated Rydberg-atom-ion molecules

Authors: Yi-Quan Zou, Moritz Berngruber, Viraatt S. V. Anasuri, Nicolas Zuber, Florian Meinert, Robert Löw, Tilman Pfau

Abstract: Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecul… ▽ More Vibrational dynamics in conventional molecules usually takes place on a timescale of picoseconds or shorter. A striking exception are ultralong-range Rydberg molecules, for which dynamics is dramatically slowed down as a consequence of the huge bond length of up to several micrometers. Here, we report on the direct observation of vibrational dynamics of a recently observed Rydberg-atom-ion molecule. By applying a weak external electric field of a few mV/cm, we are able to control the orientation of the photoassociated ultralong-range Rydberg molecules and induce vibrational dynamics by quenching the electric field. A high resolution ion microscope allows us to detect the molecule's orientation and its temporal vibrational dynamics in real space. Our study opens the door to the control of molecular dynamics in Rydberg molecules. △ Less

Submitted 16 January, 2023; v1 submitted 16 August, 2022; originally announced August 2022.

Comments: 7 pages, 4 figures

Journal ref: Phys. Rev. Lett. 130, 023002 (2023)

Doppler-free high resolution continuous wave optical UV-spectroscopy on the $\mathrm{A}\,^2Σ^+ \leftarrow \mathrm{X}\,^2Π_{3/2}$ transition in nitric oxide

Authors: Patrick Kaspar, Fabian Munkes, Philipp Neufeld, Lea Ebel, Yannick Schellander, Robert Löw, Tilman Pfau, Harald Kübler

Abstract: We report on Doppler-free continuous-wave optical UV-spectroscopy resolving the hyperfine structure of the $\mathrm{A}\,^2Σ^+ \leftarrow \mathrm{X}\,^2Π_{3/2}$ transition in nitric oxide for total angular momenta $J_X=1.5-19.5$ on the $\mathrm{oP_{12ee}}$ branch. The resulting line splittings are compared to calculated splittings and fitted determining new values for the molecular constants… ▽ More We report on Doppler-free continuous-wave optical UV-spectroscopy resolving the hyperfine structure of the $\mathrm{A}\,^2Σ^+ \leftarrow \mathrm{X}\,^2Π_{3/2}$ transition in nitric oxide for total angular momenta $J_X=1.5-19.5$ on the $\mathrm{oP_{12ee}}$ branch. The resulting line splittings are compared to calculated splittings and fitted determining new values for the molecular constants $b, c, eQq_0$ and $b_F$ for the $\mathrm{A}\,^2Σ^+$ state. The constants are in good agreement with values previously determined by quantum beat spectroscopy. △ Less

Submitted 30 June, 2022; originally announced June 2022.

Comments: 8 Pages, 4 figures

Error-budgeting for a controlled-phase gate with strontium-88 Rydberg atoms

Authors: Alice Pagano, Sebastian Weber, Daniel Jaschke, Tilman Pfau, Florian Meinert, Simone Montangero, Hans Peter Büchler

Abstract: We study the implementation of a high fidelity controlled-phase gate in a Rydberg quantum computer. The protocol is based on a symmetric gate with respect to the two qubits as experimentally realized by Levine et al [Phys. Rev. Lett. 123, 170503 (2019)], but allows for arbitrary pulse shapes with time-dependent detuning. Optimizing the pulse shapes, we introduce laser pulses which shorten the time… ▽ More We study the implementation of a high fidelity controlled-phase gate in a Rydberg quantum computer. The protocol is based on a symmetric gate with respect to the two qubits as experimentally realized by Levine et al [Phys. Rev. Lett. 123, 170503 (2019)], but allows for arbitrary pulse shapes with time-dependent detuning. Optimizing the pulse shapes, we introduce laser pulses which shorten the time spent in the Rydberg state by 10% and reduce the leading contribution to the gate infidelity, i.e., the decay from the Rydberg state. Remarkably, this reduction can be achieved for smooth pulses in detuning and smooth turning on of the Rabi frequency as required in any experimental realization. We carefully analyze the influence of fundamental error sources such as the photon recoil, the microscopic interaction potential, as well as the harmonic trapping of the atoms for an experimentally realistic setup based on strontium-88 atoms. We find that an average gate fidelity above 99.9% is possible for a very conservative estimation of experimental parameters. △ Less

Submitted 12 May, 2022; v1 submitted 28 February, 2022; originally announced February 2022.

Comments: 11 pages, 5 figures, 2 tables

Journal ref: Phys. Rev. Research 4, 033019 (2022)

Dipolar physics: A review of experiments with magnetic quantum gases

Authors: Lauriane Chomaz, Igor Ferrier-Barbut, Francesca Ferlaino, Bruno Laburthe-Tolra, Benjamin L. Lev, Tilman Pfau

Abstract: Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions play a crucial role. In this review, we aim to present the aspects of t… ▽ More Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. △ Less

Submitted 31 October, 2022; v1 submitted 7 January, 2022; originally announced January 2022.

Purcell-enhanced dipolar interactions in nanostructures

Authors: Artur Skljarow, Harald Kübler, Charles S. Adams, Tilman Pfau, Robert Löw, Hadiseh Alaeian

Abstract: Strong light-induced interactions between atoms are known to cause nonlinearities at a few-photon level which are crucial for applications in quantum information processing. Compared to free space, the scattering and the light-induced dipolar interaction of atoms can be enhanced by a dielectric environment. For this \emph{Purcell effect}, either a cavity or a waveguide can be used. Here, we combin… ▽ More Strong light-induced interactions between atoms are known to cause nonlinearities at a few-photon level which are crucial for applications in quantum information processing. Compared to free space, the scattering and the light-induced dipolar interaction of atoms can be enhanced by a dielectric environment. For this \emph{Purcell effect}, either a cavity or a waveguide can be used. Here, we combine the high densities achievable in thermal atomic vapors with an efficient coupling to a slot waveguide. In contrast to free-space interactions, atoms aligned within the slot exhibit repulsive interactions that are further enhanced by a factor of 8 due to the Purcell effect. The corresponding blueshift of the transition frequency of atoms arranged in the essentially one-dimensional geometry vanishes above the saturation, providing a controllable nonlinearity at the few-photon level. The experimental results are in good agreement with Monte-Carlo simulations that include the dielectric environment, dipolar interactions, and motional effects. The results pave the way towards a robust scalable platform for quantum nonlinear optics and all-optical quantum information processing at room temperature. △ Less

Submitted 21 December, 2021; originally announced December 2021.

Comments: 12 pages, 7 figures

Spatial imaging of a novel type of molecular ions

Authors: N. Zuber, V. S. V. Anasuri, M. Berngruber, Y. -Q. Zou, F. Meinert, R. Löw, T. Pfau

Abstract: Atoms with a highly excited electron, called Rydberg atoms, can form unusual types of molecular bonds. The bond differs from the well known ionic and covalent bonds not only by its binding mechanism, but also by its bond length ranging up to several micrometres. Here, we observe a new type of molecular ion based on the interaction between the ionic charge and a flipping induced dipole of a Rydberg… ▽ More Atoms with a highly excited electron, called Rydberg atoms, can form unusual types of molecular bonds. The bond differs from the well known ionic and covalent bonds not only by its binding mechanism, but also by its bond length ranging up to several micrometres. Here, we observe a new type of molecular ion based on the interaction between the ionic charge and a flipping induced dipole of a Rydberg atom with a bond length of several micrometres. We measure the vibrational spectrum and spatially resolve the bond length and the angular alignment of the molecule using a high-resolution ion microscope. As a consequence of the large bond length, the molecular dynamics is extremely slow. These results pave the way for future studies of spatio-temporal effects in molecular dynamics, e.g., beyond Born-Oppenheimer physics. △ Less

Submitted 4 November, 2021; originally announced November 2021.

Journal ref: Nature 605 (2022) 453-456

Transient Density-Induced Dipolar Interactions in a Thin Vapor Cell

Authors: Florian Christaller, Max Mäusezahl, Felix Moumtsilis, Annika Belz, Harald Kübler, Hadiseh Alaeian, Charles S. Adams, Robert Löw, Tilman Pfau

Abstract: We exploit the effect of light-induced atomic desorption to produce high atomic densities ($n\gg k^3$) in a rubidium vapor cell. An intense off-resonant laser is pulsed for roughly one nanosecond on a micrometer-sized sapphire-coated cell, which results in the desorption of atomic clouds from both internal surfaces. We probe the transient atomic density evolution by time-resolved absorption spectr… ▽ More We exploit the effect of light-induced atomic desorption to produce high atomic densities ($n\gg k^3$) in a rubidium vapor cell. An intense off-resonant laser is pulsed for roughly one nanosecond on a micrometer-sized sapphire-coated cell, which results in the desorption of atomic clouds from both internal surfaces. We probe the transient atomic density evolution by time-resolved absorption spectroscopy.With a temporal resolution of $\approx1\,\mathrm{ns}$, we measure the broadening and line shift of the atomic resonances. Both broadening and line shift are attributed to dipole-dipole interactions. This fast switching of the atomic density and dipolar interactions could be the basis for future quantum devices based on the excitation blockade. △ Less

Submitted 28 April, 2022; v1 submitted 1 October, 2021; originally announced October 2021.

Comments: 13 pages, 4+6 figures

Journal ref: Phys. Rev. Lett. 128, 173401 (2022)

Pattern Formation in Quantum Ferrofluids: from Supersolids to Superglasses

Authors: J. Hertkorn, J. -N. Schmidt, M. Guo, F. Böttcher, K. S. H. Ng, S. D. Graham, P. Uerlings, T. Langen, M. Zwierlein, T. Pfau

Abstract: Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, quantum ferrofluids formed from ultracold atoms were recently shown to spontaneously develop coherent density patterns, manifesting a supersolid. We theoretically investigate the phase diagram of such quantum ferrofluids in oblate trap geometries and find an even wider range of exotic… ▽ More Pattern formation is a ubiquitous phenomenon observed in nonlinear and out-of-equilibrium systems. In equilibrium, quantum ferrofluids formed from ultracold atoms were recently shown to spontaneously develop coherent density patterns, manifesting a supersolid. We theoretically investigate the phase diagram of such quantum ferrofluids in oblate trap geometries and find an even wider range of exotic states of matter. Two-dimensional supersolid crystals formed from individual ferrofluid quantum droplets dominate the phase diagram at low densities. For higher densities we find honeycomb and labyrinthine states, as well as a pumpkin phase. We discuss scaling relations which allow us to find these phases for a wide variety of trap geometries, interaction strengths, and atom numbers. Our study illuminates the origin of the various possible patterns of quantum ferrofluids and shows that their occurrence is generic of strongly dipolar interacting systems stabilized by beyond mean-field effects. △ Less

Submitted 25 March, 2021; originally announced March 2021.

Comments: 16 pages, 5+2 figures

Journal ref: Phys. Rev. Research 3, 033125 (2021)

Supersolidity in Two-Dimensional Trapped Dipolar Droplet Arrays

Authors: J. Hertkorn, J. -N. Schmidt, M. Guo, F. Böttcher, K. S. H. Ng, S. D. Graham, P. Uerlings, H. P. Büchler, T. Langen, M. Zwierlein, T. Pfau

Abstract: We theoretically investigate the ground states and the spectrum of elementary excitations across the superfluid to droplet crystallization transition of an oblate dipolar Bose-Einstein condensate. We systematically identify regimes where spontaneous rotational symmetry breaking leads to the emergence of a supersolid phase with characteristic collective excitations, such as the Higgs amplitude mode… ▽ More We theoretically investigate the ground states and the spectrum of elementary excitations across the superfluid to droplet crystallization transition of an oblate dipolar Bose-Einstein condensate. We systematically identify regimes where spontaneous rotational symmetry breaking leads to the emergence of a supersolid phase with characteristic collective excitations, such as the Higgs amplitude mode. Furthermore, we study the dynamics across the transition and show how these supersolids can be realized with standard protocols in state-of-the-art experiments. △ Less

Submitted 17 March, 2021; originally announced March 2021.

Comments: 10 pages, 2+1 figures

Journal ref: Phys. Rev. Lett. 127, 155301 (2021)

Roton Excitations in an Oblate Dipolar Quantum Gas

Authors: Jan-Niklas Schmidt, Jens Hertkorn, Mingyang Guo, Fabian Böttcher, Matthias Schmidt, Kevin S. H. Ng, Sean D. Graham, Tim Langen, Martin Zwierlein, Tilman Pfau

Abstract: We observe signatures of radial and angular roton excitations around a droplet crystallization transition in dipolar Bose-Einstein condensates. In situ measurements are used to characterize the density fluctuations near this transition. The static structure factor is extracted and used to identify the radial and angular roton excitations by their characteristic symmetries. These fluctuations peak… ▽ More We observe signatures of radial and angular roton excitations around a droplet crystallization transition in dipolar Bose-Einstein condensates. In situ measurements are used to characterize the density fluctuations near this transition. The static structure factor is extracted and used to identify the radial and angular roton excitations by their characteristic symmetries. These fluctuations peak as a function of interaction strength indicating the crystallization transition of the system. We compare our observations to a theoretically calculated excitation spectrum allowing us to connect the crystallization mechanism with the softening of the angular roton modes. △ Less

Submitted 2 February, 2021; originally announced February 2021.

Comments: 10 pages, 4 + 4 figures

Journal ref: Phys. Rev. Lett. 126, 193002 (2021)

An atomic Faraday beam splitter for light generated from pump degenerate four-wave mixing in a hollow-core photonic crystal fiber

Authors: Ioannis Caltzidis, Harald Kübler, Tilman Pfau, Robert Löw, Mark A. Zentile

Abstract: We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of… ▽ More We demonstrate an atomic Faraday dichroic beam splitter suitable to spatially separate signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode $90^{\circ}$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm0.1)$ and $(-21.2\pm0.1)$ dB in the two outputs, with a corresponding transmission of 97 and 99 %. This technique avoids the need to use spatial separation of four-wave mixing modes and thus opens the door for the process efficiency to be enhanced in waveguide experiments. As a proof-of-principle we generate light via four-wave mixing in $^{87}$Rb loaded into a hollow-core photonic crystal fiber and interface it with the atomic Faraday dichroic beam splitter. △ Less

Submitted 7 December, 2020; originally announced December 2020.

Comments: 8 pages, 7 figures

Journal ref: Phys. Rev. A 103, 043501 (2021)

Inelastic collision dynamics of a single cold ion immersed in a Bose-Einstein condensate

Authors: Thomas Dieterle, Moritz Berngruber, Christian Hölzl, Robert Löw, Krzysztof Jachymski, Tilman Pfau, Florian Meinert

Abstract: We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in… ▽ More We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resolved field-dissociation technique to trace the relaxation dynamics of the recombination products. Our observations are in good agreement with numerical simulations based on Langevin capture dynamics and provide complementary means to study stability and reaction dynamics of ionic impurities in ultracold quantum gases. △ Less

Submitted 19 November, 2020; originally announced November 2020.

Comments: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2007.00309

Journal ref: Phys. Rev. A 102, 041301(R) (2020)

Density Fluctuations across the Superfluid-Supersolid Phase Transition in a Dipolar Quantum Gas

Authors: J. Hertkorn, J. -N. Schmidt, F. Böttcher, M. Guo, M. Schmidt, K. S. H. Ng, S. D. Graham, H. P. Büchler, T. Langen, M. Zwierlein, T. Pfau

Abstract: Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter -- a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of dens… ▽ More Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter -- a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations and image the dominant fluctuation patterns. We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation. Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which have been theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons. △ Less

Submitted 18 September, 2020; originally announced September 2020.

Comments: 11 pages, 5 + 3 figures

Journal ref: Phys. Rev. X 11, 011037 (2021)

A pulsed ion microscope to probe quantum gases

Authors: C. Veit, N. Zuber, O. A. Herrera-Sancho, V. S. V. Anasuri, T. Schmid, F. Meinert, R. Löw, T. Pfau

Abstract: The advent of the quantum gas microscope allowed for the in situ probing of ultracold gaseous matter on an unprecedented level of spatial resolution. The study of phenomena on ever smaller length scales as well as the probing of three-dimensional systems is, however, fundamentally limited by the wavelength of the imaging light, for all techniques based on linear optics. Here we report on a high-re… ▽ More The advent of the quantum gas microscope allowed for the in situ probing of ultracold gaseous matter on an unprecedented level of spatial resolution. The study of phenomena on ever smaller length scales as well as the probing of three-dimensional systems is, however, fundamentally limited by the wavelength of the imaging light, for all techniques based on linear optics. Here we report on a high-resolution ion microscope as a versatile and powerful experimental tool to investigate quantum gases. The instrument clearly resolves atoms in an optical lattice with a spacing of $532\,\text{nm}$ over a field of view of 50 sites and offers an extremely large depth of field on the order of at least $70\,μ\text{m}$. With a simple model, we extract an upper limit for the achievable resolution of approximately $200\,\text{nm}$ from our data. We demonstrate a pulsed operation mode which in the future will enable 3D imaging and allow for the study of ionic impurities and Rydberg physics. △ Less

Submitted 19 August, 2020; originally announced August 2020.

Journal ref: Phys. Rev. X 11, 011036 (2021)

New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids

Authors: Fabian Böttcher, Jan-Niklas Schmidt, Jens Hertkorn, Kevin S. H. Ng, Sean D. Graham, Mingyang Guo, Tim Langen, Tilman Pfau

Abstract: Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like selfbound quantum droplets and supersolid crystals formed from these droplet… ▽ More Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like selfbound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future. △ Less

Submitted 22 September, 2020; v1 submitted 13 July, 2020; originally announced July 2020.

Transport of a single cold ion immersed in a Bose-Einstein condensate

Authors: Thomas Dieterle, Moritz Berngruber, Christian Hölzl, Robert Löw, Krzysztof Jachymski, Tilman Pfau, Florian Meinert

Abstract: We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurit… ▽ More We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allows us to study a regime of frequent collisions of the impurity within only tens of microseconds. Comparison of our measurements with stochastic trajectory simulations based on sequential Langevin collisions indicate diffusive transport properties of the impurity and allows us to measure its mobility. Furthermore, working with a free and untrapped ion provides unique means to distinguish single realizations, where the impurity is subject to inelastic molecular-ion formation via three-body recombination. We study the cold chemistry of these events and find evidence for subsequent rovibrational quenching collisions of the produced molecule. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter. △ Less

Submitted 19 November, 2020; v1 submitted 1 July, 2020; originally announced July 2020.

Comments: 10 pages, 9 figures

Journal ref: Phys. Rev. Lett. 126, 033401 (2021)

Integrating two-photon nonlinear spectroscopy of rubidium atoms with silicon photonics

Authors: Artur Skljarow, Nico Gruhler, Wolfram Pernice, Harald Kübler, Tilman Pfau, Robert Löw, Hadiseh Alaeian

Abstract: We study an integrated silicon photonic chip, composed of several sub-wavelength ridge waveguides, and immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observe that the waveguide transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. Due to the enhanced electric field in t… ▽ More We study an integrated silicon photonic chip, composed of several sub-wavelength ridge waveguides, and immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observe that the waveguide transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. Due to the enhanced electric field in the waveguide cladding, the atomic transition can be saturated at a photon number $\approx$ 80 times less than a free-propagating beam case. The non-linearity of the atom-clad Si-waveguide is about 4 orders of magnitude larger than maximum achievable value in doped Si photonics. The measured spectra corroborate well with a generalized effective susceptibility model that includes the Casimir-Polder potentials, due to the dielectric surface, and the transient interaction between flying atoms and the evanescent waveguide mode. This work paves the way towards a miniaturized, low-power, and integrated hybrid atomic-photonic system compatible with CMOS technologies. △ Less

Submitted 13 March, 2020; v1 submitted 10 March, 2020; originally announced March 2020.

Comments: 9 pages, 8 figures, added references for section 1

The Fate of the Higgs Mode in a Trapped Dipolar Supersolid

Authors: Jens Hertkorn, Fabian Böttcher, Mingyang Guo, Jan-Niklas Schmidt, Tim Langen, Hans Peter Büchler, Tilman Pfau

Abstract: We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs and Nambu-Goldstone modes that emerge from the softening roton modes of the dipolar BEC at the phase transition point. On the supersolid side of the transition, the energy of the Higgs mode increases… ▽ More We theoretically investigate the spectrum of elementary excitations of a trapped dipolar quantum gas across the BEC-supersolid phase transition. Our calculations reveal the existence of distinct Higgs and Nambu-Goldstone modes that emerge from the softening roton modes of the dipolar BEC at the phase transition point. On the supersolid side of the transition, the energy of the Higgs mode increases rapidly, leading to a strong coupling to higher-lying modes. Our study highlights how the symmetry-breaking nature of the supersolid state translates to finite-size systems. △ Less

Submitted 22 July, 2019; originally announced July 2019.

Journal ref: Phys. Rev. Lett. 123, 193002 (2019)

Cavity QED Based on Thermal Atoms Interacting with a Photonic Crystal Cavity: A Feasibility Study

Authors: Hadiseh Alaeian, Ralf Ritter, Muamera Basic, Robert Loew, Tilman Pfau

Abstract: The paradigm of cavity QED is a two-level emitter interacting with a high quality factor single mode optical resonator. The hybridization of the emitter and photon wave functions mandates large vacuum Rabi frequencies and long coherence times; features that so far have been successfully realized with trapped cold atoms and ions and localized solid state quantum emitters such as superconducting cir… ▽ More The paradigm of cavity QED is a two-level emitter interacting with a high quality factor single mode optical resonator. The hybridization of the emitter and photon wave functions mandates large vacuum Rabi frequencies and long coherence times; features that so far have been successfully realized with trapped cold atoms and ions and localized solid state quantum emitters such as superconducting circuits, quantum dots, and color centers. Thermal atoms on the other hand, provide us with a dense emitter ensemble and in comparison to the cold systems are more compatible with integration, hence enabling large-scale quantum systems. However, their thermal motion and large transit time broadening is a major challenge that has to be circumvented. A promising remedy could benefit from the highly controllable and tunable electromagnetic fields of a nano-photonic cavity with strong local electric-field enhancements. Utilizing this feature, here we calculate the interaction between fast moving, thermal atoms and a nano-beam photonic crystal cavity (PCC) with large quality factor and small mode volume. Through fully quantum mechanical calculations, including Casimir-Polder potential (i.e. the effect of the surface on radiation properties of an atom) we show, when designed properly, the achievable coupling between the flying atom and the cavity photon would be strong enough to lead to Rabi flopping in spite of short interaction times. In addition, the time-resolved detection of different trajectories can be used to identify single and multiple atom counts. This probabilistic approach will find applications in cavity QED studies in dense atomic media and paves the way towards realizing coherent quantum control schemes in large-scale macroscopic systems aimed at out of the lab quantum devices. △ Less

Submitted 10 July, 2019; originally announced July 2019.

The low-energy Goldstone mode in a trapped dipolar supersolid

Authors: Mingyang Guo, Fabian Böttcher, Jens Hertkorn, Jan-Niklas Schmidt, Matthias Wenzel, Hans Peter Büchler, Tim Langen, Tilman Pfau

Abstract: A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. Since the first prediction in the 1950s, experimental efforts to realize this state have focussed mainly on Helium, where supersolidity remains elusive. Recently, supersolidity has also been studied intensively in ultracold quantum ga… ▽ More A supersolid is a counter-intuitive state of matter that combines the frictionless flow of a superfluid with the crystal-like periodic density modulation of a solid. Since the first prediction in the 1950s, experimental efforts to realize this state have focussed mainly on Helium, where supersolidity remains elusive. Recently, supersolidity has also been studied intensively in ultracold quantum gases, and some of its defining properties have been induced in spin-orbit coupled Bose-Einstein condensates (BECs) and BECs coupled to two crossed optical cavities. However, the periodicity of the crystals in both systems is fixed to the wavelength of the applied periodic optical potentials. Recently, hallmark properties of a supersolid -- the periodic density modulation and simultaneous global phase coherence -- have been observed in arrays of dipolar quantum droplets, where the crystallization happens in a self-organized manner due to intrinsic interactions. In this letter, we prove the genuine supersolid nature of these droplet arrays by directly observing the low-energy Goldstone mode. The dynamics of this mode is reminiscent of the effect of second sound in other superfluid systems and features an out-ofphase oscillation of the crystal array and the superfluid density. This mode exists only due to the phase rigidity of the experimentally realized state, and therefore confirms the genuine superfluidity of the supersolid. △ Less

Submitted 11 June, 2019; originally announced June 2019.

Journal ref: Nature 574, 386-389 (2019)

Precision spectroscopy of negative-ion resonances in ultralong-range Rydberg molecules

Authors: Felix Engel, Thomas Dieterle, Frederic Hummel, Christian Fey, Peter Schmelcher, Robert Löw, Tilman Pfau, Florian Meinert

Abstract: The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into… ▽ More The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so far unobserved fine structure of the $^3P_J$ triplet of Rb$^-$ and allow us to extract parameters of the associated $p$-wave scattering resonances which deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion. △ Less

Submitted 10 August, 2019; v1 submitted 17 April, 2019; originally announced April 2019.

Comments: 11 pages, 6 figures

Journal ref: Phys. Rev. Lett. 123, 073003 (2019)

Transient supersolid properties in an array of dipolar quantum droplets

Authors: Fabian Böttcher, Jan-Niklas Schmidt, Matthias Wenzel, Jens Hertkorn, Mingyang Guo, Tim Langen, Tilman Pfau

Abstract: We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent arrays of quantum droplets. In the latter the droplets are connected by a finite superfluid density, which leads - in addition to the periodic… ▽ More We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate, incoherent and coherent arrays of quantum droplets. In the latter the droplets are connected by a finite superfluid density, which leads - in addition to the periodic density modulation - to a robust phase coherence throughout the whole system. We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is only limited by three-body losses. Experimentally we probe and confirm the signatures of the phase diagram by observing the in-situ density modulation as well as the phase coherence using matter wave interference. △ Less

Submitted 8 March, 2019; v1 submitted 23 January, 2019; originally announced January 2019.

Journal ref: Phys. Rev. X 9, 011051 (2019)

The interplay between thermal Rydberg gases and plasmas

Authors: Daniel Weller, James P. Shaffer, Tilman Pfau, Robert Löw, Harald Kübler

Abstract: We investigate the phenomenon of bistability in a thermal gas of cesium atoms excited to Rydberg states. We present both measurements and a numerical model of the phenomena based on collisions. By directly measuring the plasma frequency, we show that the origin of the bistable behavior lies in the creation of a plasma formed by ionized Rydberg atoms. Recombination of ions and electrons manifests a… ▽ More We investigate the phenomenon of bistability in a thermal gas of cesium atoms excited to Rydberg states. We present both measurements and a numerical model of the phenomena based on collisions. By directly measuring the plasma frequency, we show that the origin of the bistable behavior lies in the creation of a plasma formed by ionized Rydberg atoms. Recombination of ions and electrons manifests as fluorescence which allows us to characterize the plasma properties and study the transient dynamics of the hysteresis that occurs. We determine scaling parameters for the point of plasma formation, and verify our numerical model by comparing measured and simulated spectra. These measurements yield a detailed microscopic picture of ionization and avalanche processes occurring in thermal Rydberg gases. From this set of measurements, we conclude that plasma formation is a fundamental ingredient in the optical bistability taking place in thermal Rydberg gases and imposes a limit on usable Rydberg densities for many applications. △ Less

Submitted 23 January, 2019; originally announced January 2019.

Comments: 13 pages, 10 figures

Journal ref: Phys. Rev. A 99, 043418 (2019)

Observation of Rydberg Blockade Induced by a Single Ion

Authors: Felix Engel, Thomas Dieterle, Thomas Schmid, Christian Tomschitz, Christian Veit, Nicolas Zuber, Robert Löw, Tilman Pfau, Florian Meinert

Abstract: We study the long-range interaction of a single ion with a highly excited ultracold Rydberg atom and report on the direct observation of ion-induced Rydberg excitation blockade mediated over tens of micrometer distances. Our hybrid ion-atom system is directly produced from an ultracold atomic ensemble via near-threshold photo-ionization of a single Rydberg excitation, employing a two-photon scheme… ▽ More We study the long-range interaction of a single ion with a highly excited ultracold Rydberg atom and report on the direct observation of ion-induced Rydberg excitation blockade mediated over tens of micrometer distances. Our hybrid ion-atom system is directly produced from an ultracold atomic ensemble via near-threshold photo-ionization of a single Rydberg excitation, employing a two-photon scheme which is specifically suited for generating a very low-energy ion. The ion's motion is precisely controlled by small electric fields, which allows us to analyze the blockade mechanism for a range of principal quantum numbers. Finally, we explore the capability of the ion as a high-sensitivity single-atom-based electric field sensor. The observed ion - Rydberg-atom interaction is of current interest for entanglement generation or studies of ultracold chemistry in hybrid ion-atom systems. △ Less

Submitted 4 September, 2018; originally announced September 2018.

Comments: 7 pages, 7 figures

Journal ref: Phys. Rev. Lett. 121, 193401 (2018)

A fermionic impurity in a dipolar quantum droplet

Authors: Matthias Wenzel, Tilman Pfau, Igor Ferrier-Barbut

Abstract: In this article we develop the framework to describe Bose-Fermi mixtures of magnetic atoms, focusing on the interaction of bosonic self-bound dipolar quantum droplets with a small number of fermions. We find an attractive interaction potential due to the dipolar interaction with several bound states, which can be occupied by one fermion each, resulting in a very weak back-action on the bosons. We… ▽ More In this article we develop the framework to describe Bose-Fermi mixtures of magnetic atoms, focusing on the interaction of bosonic self-bound dipolar quantum droplets with a small number of fermions. We find an attractive interaction potential due to the dipolar interaction with several bound states, which can be occupied by one fermion each, resulting in a very weak back-action on the bosons. We conclude, that these impurities might act as unique probes giving access to inherent properties of dipolar quantum droplets. △ Less

Submitted 2 July, 2018; originally announced July 2018.

Comments: To appear in the "Focus issue: Quantum Optics and Beyond - in honour of Wolfgang Schleich" of Physica Scripta

A room temperature single-photon source based on strongly interacting Rydberg atoms

Authors: F. Ripka, H. Kübler, R. Löw, T. Pfau

Abstract: Tailored quantum states of light can be created via a transfer of collective quantum states of matter to light modes. Such collective quantum states emerge in interacting many-body systems if thermal fluctuations are overcome by sufficient interaction strengths. Therefore, typically ultracold temperatures or strong confinement are required. We show that the exaggerated interactions between giant R… ▽ More Tailored quantum states of light can be created via a transfer of collective quantum states of matter to light modes. Such collective quantum states emerge in interacting many-body systems if thermal fluctuations are overcome by sufficient interaction strengths. Therefore, typically ultracold temperatures or strong confinement are required. We show that the exaggerated interactions between giant Rydberg atoms allow for collective quantum states even above room temperature. The emerging Rydberg blockade allows then only for a single Rydberg excitation. We experimentally implement a four-wave mixing scheme to demonstrate an on-demand single-photon source. The combination of glass cell technology, identical atoms, and operation around room temperature promises scalability and integrability. This approach has the potential for various applications in quantum information processing and communication. △ Less

Submitted 6 June, 2018; originally announced June 2018.

Comments: 12 pages, 5 figures total, supplementary information

Anisotropic Superfluid Behavior of a Dipolar Bose-Einstein Condensate

Authors: Matthias Wenzel, Fabian Böttcher, Jan-Niklas Schmidt, Michael Eisenmann, Tim Langen, Tilman Pfau, Igor Ferrier-Barbut

Abstract: We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of Dy-162 with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. This observation is compatible with an anisotropic critical velocity for the breakdown of dissipationless flow, which, in the spirit of the Landau… ▽ More We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of Dy-162 with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. This observation is compatible with an anisotropic critical velocity for the breakdown of dissipationless flow, which, in the spirit of the Landau criterion, can directly be connected to the anisotropy of the underlying dipolar excitation spectrum. In addition, the heating rate above this critical velocity reflects the same anisotropy. Our observations are in excellent agreement with simulations based on the Gross-Pitaevskii equation and highlight the effect of dipolar interactions on macroscopic transport properties, rendering dissipation anisotropic. △ Less

Submitted 18 July, 2018; v1 submitted 12 April, 2018; originally announced April 2018.

Journal ref: Phys. Rev. Lett. 121, 030401 (2018)

An ionic impurity in a Bose-Einstein condensate at sub-microkelvin temperatures

Authors: Kathrin S. Kleinbach, Felix Engel, Thomas Dieterle, Robert Löw, Tilman Pfau, Florian Meinert

Abstract: Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with principal quantum number up to $n = 190$ are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size o… ▽ More Rydberg atoms immersed in a Bose-Einstein condensate interact with the quantum gas via electron-atom and ion-atom interaction. To suppress the typically dominant electron-neutral interaction, Rydberg states with principal quantum number up to $n = 190$ are excited from a dense and tightly trapped micron-sized condensate. This allows us to explore a regime where the Rydberg orbit exceeds the size of the atomic sample by far. In this case, a detailed lineshape analysis of the Rydberg excitation spectrum provides clear evidence for ion-atom interaction at temperatures well below a microkelvin. Our results may open up ways to enter the quantum regime of ion-atom scattering for the exploration of charged quantum impurities and associated polaron physics. △ Less

Submitted 11 April, 2018; v1 submitted 23 February, 2018; originally announced February 2018.

Comments: 9 pages, 6 figures

Journal ref: Phys. Rev. Lett. 120, 193401 (2018)

Proof of concept for an optogalvanic gas sensor for NO based on Rydberg excitations

Authors: Johannes Schmidt, Markus Fiedler, Ralf Albrecht, Denis Djekic, Patrick Schalberger, Holger Baur, Robert Löw, Norbert Fruehauf, Tilman Pfau, Jens Anders, Edward R. Grant, Harald Kübler

Abstract: We demonstrate the applicability of 2-photon Rydberg excitations of nitric oxide (NO) at room temperature in a gas mixture with helium (He) as an optogalvanic gas sensor. The charges created initially from succeeding collisions of excited NO Rydberg molecules with free electrons are measured as a current on metallic electrodes inside a glass cell and amplified using a custom-designed highbandwidth… ▽ More We demonstrate the applicability of 2-photon Rydberg excitations of nitric oxide (NO) at room temperature in a gas mixture with helium (He) as an optogalvanic gas sensor. The charges created initially from succeeding collisions of excited NO Rydberg molecules with free electrons are measured as a current on metallic electrodes inside a glass cell and amplified using a custom-designed highbandwidth transimpedance amplifier attached to the cell. We fnd that this gas sensing method is capable of detecting NO concentrations lower than 10 ppm even at atmospheric pressures, currently only limited by the way we prepare the gas dilutions. △ Less

Submitted 11 June, 2018; v1 submitted 29 January, 2018; originally announced January 2018.

Journal ref: Appl. Phys. Lett. 113, 011113 (2018)

Scissors mode of dipolar quantum droplets of dysprosium atoms

Authors: Igor Ferrier-Barbut, Matthias Wenzel, Fabian Böttcher, Tim Langen, Mathieu Isoard, Sandro Stringari, Tilman Pfau

Abstract: We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic field. By modulating the orientation of this magnetic field, we introduce a new spectroscopic technique for studying dipolar quantum droplets. This… ▽ More We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic field. By modulating the orientation of this magnetic field, we introduce a new spectroscopic technique for studying dipolar quantum droplets. This provides a precise probe for interactions in the system allowing to extract a background scattering length for \textsuperscript{164}Dy of $69(4)\,a_0$. Our results establish an analogy between quantum droplets and atomic nuclei, where the existence of the scissors mode is also only due to internal interactions. They further open the possibility to explore physics beyond the available theoretical models for strongly-dipolar quantum gases. △ Less

Submitted 25 March, 2018; v1 submitted 19 December, 2017; originally announced December 2017.

Journal ref: Phys. Rev. Lett. 120, 160402 (2018)

Onset of a modulational instability in trapped dipolar Bose-Einstein condensates

Authors: Igor Ferrier-Barbut, Matthias Wenzel, Matthias Schmitt, Fabian Böttcher, Tilman Pfau

Abstract: We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either an adiabatic transformation between a BEC and a quantum droplet is obtained or, above a critical trap aspect ratio $λ_{\rm c}=1.87(14)$, a modu… ▽ More We explore the phase diagram of a finite-sized dysprosium dipolar Bose-Einstein condensate in a cylindrical harmonic trap. We monitor the final state after the scattering length is lowered from the repulsive BEC regime to the quantum droplet regime. Either an adiabatic transformation between a BEC and a quantum droplet is obtained or, above a critical trap aspect ratio $λ_{\rm c}=1.87(14)$, a modulational instability results in the formation of multiple droplets. This is in full agreement with the predicted structure of the phase diagram with a crossover region below $λ_{\rm c}$ and a multistable region above. Our results provide the missing piece connecting the previously explored regimes resulting in a single or multiple dipolar quantum droplets. △ Less

Submitted 23 January, 2018; v1 submitted 20 November, 2017; originally announced November 2017.

Journal ref: Phys. Rev. A 97, 011604 (2018)

Rydberg molecules for ion-atom scattering in the ultracold regime

Authors: T. Schmid, C. Veit, N. Zuber, R. Löw, T. Pfau, M. Tarana, M. Tomza

Abstract: We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. Key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of h… ▽ More We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. Key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wavefunction, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initio calculations of the interaction potential. We demonstrate that, in the predicted bounds, the scattering length can be experimentally determined from the velocity of the scattered wavepacket in the case of $^\textsf{6}\textsf{Li}^\textsf{+}$ - $^\textsf{6}\textsf{Li}$, and from the molecular ion fraction in the case of $^\textsf{7}\textsf{Li}^\textsf{+}$ - $^\textsf{7}\textsf{Li}$. The proposed method to utilize Rydberg molecules for ultracold ion-atom scattering, here particularized for the lithium ion-atom system, is readily applicable to other ion-atom systems as well. △ Less

Submitted 16 April, 2018; v1 submitted 29 September, 2017; originally announced September 2017.

Comments: 12 pages, 7 figures

Journal ref: Phys. Rev. Lett. 120, 153401 (2018)

Striped states in a many-body system of tilted dipoles

Authors: Matthias Wenzel, Fabian Böttcher, Tim Langen, Igor Ferrier-Barbut, Tilman Pfau

Abstract: We study theoretically and experimentally the behaviour of a strongly confined dipolar Bose-Einstein condensate, in the regime of quantum-mechanical stabilization by beyond-mean-field effects. Theoretically, we demonstrate that self-organized striped ground states are predicted in the framework of the extended Gross-Pitaevskii theory. Experimentally, by tilting the magnetic dipoles we show that se… ▽ More We study theoretically and experimentally the behaviour of a strongly confined dipolar Bose-Einstein condensate, in the regime of quantum-mechanical stabilization by beyond-mean-field effects. Theoretically, we demonstrate that self-organized striped ground states are predicted in the framework of the extended Gross-Pitaevskii theory. Experimentally, by tilting the magnetic dipoles we show that self-organized striped states can be generated, likely in their metastable state. Matter-wave interference experiments with multiple stripes show that there is no long-range off-diagonal order (global phase coherence). We outline a parameter range where global phase coherence could be established, thus paving the way towards the observation of supersolid states in this system. △ Less

Submitted 28 November, 2017; v1 submitted 28 June, 2017; originally announced June 2017.

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. A 96, 053630 (2017)

Photo-association of trilobite Rydberg molecules via resonant spin-orbit coupling

Authors: Kathrin S. Kleinbach, Florian Meinert, Felix Engel, Woo Jin Kwon, Robert Löw, Tilman Pfau, Georg Raithel

Abstract: We report on a novel method for photo-association of strongly polar trilobite Rydberg molecules. This exotic ultralong-range dimer, consisting of a ground-state atom bound to the Rydberg electron via electron-neutral scattering, inherits its polar character from the admixture of high angular momentum electronic orbitals. The absence of low-$L$ character hinders standard photo-association technique… ▽ More We report on a novel method for photo-association of strongly polar trilobite Rydberg molecules. This exotic ultralong-range dimer, consisting of a ground-state atom bound to the Rydberg electron via electron-neutral scattering, inherits its polar character from the admixture of high angular momentum electronic orbitals. The absence of low-$L$ character hinders standard photo-association techniques. Here, we show that for suitable principal quantum numbers resonant coupling of the orbital motion with the nuclear spin of the perturber, mediated by electron-neutral scattering, hybridizes the trilobite molecular potential with the more conventional ${\rm{S}}$-type molecular state. This provides a general path to associate trilobite molecules with large electric dipole moments, as demonstrated via high-resolution spectroscopy. We find a dipole moment of 135(45) D for the trilobite state. Our results are compared to theoretical predictions based on a Fermi-model. △ Less

Submitted 4 May, 2017; v1 submitted 3 March, 2017; originally announced March 2017.

Comments: 8 pages, 4 figures

Journal ref: Phys. Rev. Lett. 118, 223001 (2017)

Condensate losses and oscillations induced by Rydberg atoms

Authors: Tomasz Karpiuk, Mirosław Brewczyk, Kazimierz Rzążewski, Anita Gaj, Alexander T. Krupp, Robert Löw, Sebastian Hofferberth, Tilman Pfau

Abstract: We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investiga… ▽ More We numerically analyze the impact of a single Rydberg electron onto a Bose-Einstein condensate. Both $S-$ and $D-$ Rydberg states are studied. The radial size of $S-$ and $D-$states are comparable, hence the only difference is due to the angular dependence of the wavefunctions. We find the atom losses in the condensate after the excitation of a sequence of Rydberg atoms. Additionally, we investigate the mechanical effect in which the Rydberg atoms force the condensate to oscillate. Our numerical analysis is based on the classical fields approximation. Finally, we compare numerical results to experimental data. △ Less

Submitted 12 October, 2016; originally announced October 2016.

Comments: 6 pages, 4 figures, 4 tables

Journal ref: J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 055003

Liquid quantum droplets of ultracold magnetic atoms

Authors: Igor Ferrier-Barbut, Matthias Schmitt, Matthias Wenzel, Holger Kadau, Tilman Pfau

Abstract: The simultaneous presence of two competing inter-particle interactions can lead to the emergence of new phenomena in a many-body system. Among others, such effects are expected in dipolar Bose-Einstein condensates, subject to dipole-dipole interaction and short-range repulsion. Magnetic quantum gases and in particular Dysprosium gases, offering a comparable short-range contact and a long-range dip… ▽ More The simultaneous presence of two competing inter-particle interactions can lead to the emergence of new phenomena in a many-body system. Among others, such effects are expected in dipolar Bose-Einstein condensates, subject to dipole-dipole interaction and short-range repulsion. Magnetic quantum gases and in particular Dysprosium gases, offering a comparable short-range contact and a long-range dipolar interaction energy, remarkably exhibit such emergent phenomena. In addition an effective cancellation of mean-field effects of the two interactions results in a pronounced importance of quantum-mechanical beyond mean-field effects. For a weakly-dominant dipolar interaction the striking consequence is the existence of a new state of matter equilibrated by the balance between weak mean-field attraction and beyond mean-field repulsion. Though exemplified here in the case of dipolar Bose gases, this state of matter should appear also with other microscopic interactions types, provided a competition results in an effective cancellation of the total mean-field. The macroscopic state takes the form of so-called quantum droplets. We present the effects of a long-range dipolar interaction between these droplets. △ Less

Submitted 13 September, 2016; originally announced September 2016.

Comments: Revised manuscript for publication in a special issue of JPhysB

Journal ref: Journal of Physics B: Atomic, Molecular and Optical Physics 49, 214004 (2016)