Showing 1–50 of 53 results for author: Grimm, R

Large anomalous shifts of potassium-39 Feshbach resonances

Authors: Ali Zaheer, Mohammed Bouras, Krzysztof Giergiel, Rudolf Grimm, Andrei Sidorov, Peter Hannaford

Abstract: We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally w… ▽ More We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally with trap depth and approach zero at zero depth. We show that the large observed shifts originate from a large differential ac Stark shift between the incoming pair of potassium-39 atoms and the weakly bound Feshbach molecule, which in turn originates from an unexpectedly large dynamic polarizability of the Feshbach molecule. The polarizabilities of the Feshbach molecules extracted from the measured shifts of the 33.6 G and 39.9 G resonances are about four to seven times the sum of the polarizabilities of the two incoming potassium-39 atoms, that is, about four to seven times larger than the usual polarizability of weakly bound Feshbach molecules. The large polarizabilities of the Feshbach molecules are attributed to a near-coincidence between the frequency of the 1063.9 nm ODT laser and the frequency of a molecular transition from the last vibrational level of the lowest triplet a3Σ+u potential to a vibrational level of the excited b3Σ+g potential. Other potassium-39 Feshbach resonances we have studied exhibit a zero or very small shift, corresponding to molecular polarizabilities close to the sum of the polarizabilities of the two incoming potassium-39 atoms. △ Less

Submitted 5 August, 2026; originally announced August 2026.

Comments: 14 pages, 10 figures

Site-selective preparation of two-dimensional dipolar quantum gases in an optical beat-note lattice

Authors: Niclas Höllrigl, Marian Kreyer, Rudolf Grimm, Emil Kirilov

Abstract: High-resolution microscopy of two-dimensional dipolar quantum gases requires selecting individual atomic layers, a task complicated for strongly magnetic lanthanide atoms by the limited applicability of standard magnetic-gradient techniques. We present an all-optical method for the deterministic spatial selection of single- and bilayer samples of cold dipolar atoms using spatially selective parame… ▽ More High-resolution microscopy of two-dimensional dipolar quantum gases requires selecting individual atomic layers, a task complicated for strongly magnetic lanthanide atoms by the limited applicability of standard magnetic-gradient techniques. We present an all-optical method for the deterministic spatial selection of single- and bilayer samples of cold dipolar atoms using spatially selective parametric heating within a beat-note superlattice. By utilizing a high-resolution microscope objective as a common retroreflector for both optical frequency components, the lattice planes are passively stabilized. This renders their positions exceptionally robust against experimental drifts and structure-borne vibrations, even eliminating the need for active laser stabilization over millimeter-scale separations from the reflecting surface. We validate this approach by demonstrating the robust isolation of one or two atomic layers in precise coincidence with the focal plane of our objective. This enables future single-atom-resolved studies of long-range interacting systems. △ Less

Submitted 30 June, 2026; v1 submitted 13 May, 2026; originally announced May 2026.

Stochastic Path Compression for Spectral Tensor Networks on Cyclic Graphs

Authors: Ryan T. Grimm, Joel D. Eaves

Abstract: We develop a new approach to compress cyclic tensor networks called stochastic path compression (SPC) that uses an iterative importance sampling procedure to target edges with large bond-dimensions. Closed random walks in SPC form compression pathways that spatially localize large bond-dimensions in the tensor network. Analogous to the phase separation of two immiscible liquids, SPC separates the… ▽ More We develop a new approach to compress cyclic tensor networks called stochastic path compression (SPC) that uses an iterative importance sampling procedure to target edges with large bond-dimensions. Closed random walks in SPC form compression pathways that spatially localize large bond-dimensions in the tensor network. Analogous to the phase separation of two immiscible liquids, SPC separates the graph of bond-dimensions into spatially distinct high and low density regions. When combined with our integral decimation algorithm, SPC facilitates the accurate compression of cyclic tensor networks with continuous degrees of freedom. To benchmark and illustrate the methods, we compute the absolute thermodynamics of $q$-state clock models on two-dimensional square lattices and an XY model on a Watts-Strogatz graph, which is a small-world network with random connectivity between spins. △ Less

Submitted 7 January, 2026; originally announced January 2026.

Comments: 7 pages, 3 figures

Optically trapped Feshbach molecules of fermionic $^{161}$Dy and $^{40}$K: Role of light-induced and collisional losses

Authors: Alberto Canali, Chun-Kit Wong, Luc Absil, Zhu-Xiong Ye, Marian Kreyer, Emil Kirilov, Rudolf Grimm

Abstract: We study the decay of a dense, ultracold sample of weakly bound DyK dimers stored in an optical dipole trap. Our bosonic dimers are composed of the fermionic isotopes $^{161}$Dy and $^{40}$K, which is of particular interest for experiments related to pairing and superfluidity in fermionic systems with mass imbalance. We have realized dipole traps with near-infrared laser light in four different wa… ▽ More We study the decay of a dense, ultracold sample of weakly bound DyK dimers stored in an optical dipole trap. Our bosonic dimers are composed of the fermionic isotopes $^{161}$Dy and $^{40}$K, which is of particular interest for experiments related to pairing and superfluidity in fermionic systems with mass imbalance. We have realized dipole traps with near-infrared laser light in four different wavelength regions between 1050 and 2002 nm. We have identified trap-light-induced processes as the overall dominant source of losses, except for wavelengths around 2000 nm, where light-induced losses appeared to be much weaker. In a trap near 1550 nm, we found a plateau of minimal light-induced losses, and by carefully tuning the wavelength, we reached conditions where losses from inelastic collisions between the trapped dimers became observable. For very weakly bound dimers close to the center of a magnetically tuned Feshbach resonance, we demonstrate the Pauli suppression of collisional losses by about an order of magnitude. △ Less

Submitted 13 May, 2026; v1 submitted 15 December, 2025; originally announced December 2025.

Comments: 12 pages, 5 figures

Journal ref: Phys. Rev. A 113, 053306 (2026)

The Integral Decimation Method for Quantum Dynamics and Statistical Mechanics

Authors: Ryan T. Grimm, Alexander J. Staat, Joel D. Eaves

Abstract: The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number of dimensions, a phenomenon called the curse of dimensionality. The problem is so substantial that one usually employs sampling methods, like Monte Carlo, to avo… ▽ More The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number of dimensions, a phenomenon called the curse of dimensionality. The problem is so substantial that one usually employs sampling methods, like Monte Carlo, to avoid integration altogether. Here, we derive and implement a quantum-inspired algorithm to decompose a multidimensional integrand into a product of matrix-valued functions -- a spectral tensor train -- changing the computational complexity of integration from exponential to polynomial. The algorithm constructs a spectral tensor train representation of the integrand by applying a sequence of quantum gates, where each gate corresponds to an interaction that involves increasingly more degrees of freedom in the action. Because it allows for the systematic elimination of small contributions to the integral through decimation, we call the method integral decimation. The functions in the spectral basis are analytically differentiable and integrable, and in applications to the partition function, integral decimation numerically factorizes an interacting system into a product of non-interacting ones. We illustrate integral decimation by evaluating the absolute free energy and entropy of a chiral XY model as a continuous function of temperature. We also compute the nonequilibrium time-dependent reduced density matrix of a quantum chain with between two and forty levels, each coupled to colored noise. When other methods provide numerical solutions to these models, they quantitatively agree with integral decimation. When conventional methods become intractable, integral decimation can be a powerful alternative. △ Less

Submitted 7 April, 2026; v1 submitted 12 June, 2025; originally announced June 2025.

Comments: 14 pages, 7 figures, Accepted Quantum Version

Journal ref: Quantum 10, 2064 (2026)

The QTF-Backbone: Proposal for a Nationwide Optical Fibre Backbone in Germany for Quantum Technology and Time and Frequency Metrology

Authors: Tara Cubel Liebisch, Peter Kaufmann, Harald Schnatz, Susanne Naegele-Jackson, Jochen Kronjäger, Klaus Blaum, Stefan Kück, Dieter Meschede, Stephan Schiller, Laura Agazzi, Soroosh Alighanbari, Joachim Ankerhold, Georgy V. Astakhov, Stefanie Barz, Ingo Baumann, Rainer Baumgart, Christoph Becher, Hendrik Bekker, Oliver Benson, Paolo Bianco, Ronald Bieber, Immanuel Bloch, Ulrike Blumröder, Rainer Bockholt, Johannes Bouman , et al. (144 additional authors not shown)

Abstract: The recent breakthroughs in the distribution of quantum information and high-precision time and frequency (T&F) signals over long-haul optical fibre networks have transformative potential for physically secure communications, resilience of timing infrastructure (such as that supporting Global Navigation Satellite Systems (GNSS)) and fundamental physics. To date, these capabilities remain confined… ▽ More The recent breakthroughs in the distribution of quantum information and high-precision time and frequency (T&F) signals over long-haul optical fibre networks have transformative potential for physically secure communications, resilience of timing infrastructure (such as that supporting Global Navigation Satellite Systems (GNSS)) and fundamental physics. To date, these capabilities remain confined to isolated testbeds, with quantum and T&F signals accessible, for example in Germany, to only a few institutions. In this white paper we propose the QTF Backbone: a dedicated national fibre-optic infrastructure in Germany for the networked distribution of Quantum and T&F signals using dark fibres and specialised hardware. The QTF Backbone is planned as a four-phase deployment over ten years to ensure scalable, sustainable access for research institutions and industry. The concept builds on successful demonstrations of time and frequency distribution at high Technology Readiness Levels (TRLs) across Europe, including PTB-MPQ links in Germany, REFIMEVE in France, and the Italian LIFT network. The QTF Backbone will enable transformative Research and Development (R&D), support a nationwide QTF ecosystem, and ensure the transition from innovation to deployment. As a national and European hub, it will position Germany and Europe at the forefront of quantum networking, as well as T&F transfer. △ Less

Submitted 16 August, 2026; v1 submitted 4 June, 2025; originally announced June 2025.

Comments: 60 pages, 7 figures This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1140/epjs/s11734-026-02451-3

Journal ref: Liebisch, T.C., Kaufmann, P., Schnatz, H. et al. The QTF Backbone: proposal for a nationwide optical fibre backbone in Germany for quantum technology and time and frequency metrology. Eur. Phys. J. Spec. Top. 235, 3353-3387 (2026)

Accurate Numerical Simulations of Open Quantum Systems Using Spectral Tensor Trains

Authors: Ryan T. Grimm, Joel D. Eaves

Abstract: Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-AS… ▽ More Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. The spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales linearly with the system size once the number of states is larger than the number of basis functions. △ Less

Submitted 15 July, 2024; originally announced July 2024.

Comments: 6 figures. 13 Pages

Mediated interactions between Fermi polarons and the role of impurity quantum statistics

Authors: Cosetta Baroni, Bo Huang, Isabella Fritsche, Erich Dobler, Gregor Anich, Emil Kirilov, Rudolf Grimm, Miguel A. Bastarrachea-Magnani, Pietro Massignan, Georg Bruun

Abstract: The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle, a polaron, is an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. As an inherent and important property such quasi-particles interact with each other v… ▽ More The notion of quasi-particles is essential for understanding the behaviour of complex many-body systems. A prototypical example of a quasi-particle, a polaron, is an impurity strongly interacting with a surrounding medium. Fermi polarons, created in a Fermi sea, provide a paradigmatic realization of this concept. As an inherent and important property such quasi-particles interact with each other via modulation of the medium. While quantum simulation experiments with ultracold atoms have significantly improved our understanding of individual polarons, the detection of their interactions has remained elusive in these systems. Here, we report the unambiguous observation of mediated interactions between Fermi polarons consisting of K impurities embedded in a Fermi sea of Li atoms. Our results confirm two landmark predictions of Landau's Fermi-liquid theory: the shift of the polaron energy due to mediated interactions, linear in the concentration of impurities, and its sign inversion with impurity quantum statistics. For weak to moderate interactions between the impurities and the medium, we find excellent agreement with the static (zero-momentum and energy) predictions of Fermi-liquid theory. For stronger impurity-medium interactions, we show that the observed behaviour at negative energies can be explained by a more refined many-body treatment including retardation and molecule formation △ Less

Submitted 8 May, 2023; originally announced May 2023.

Journal ref: Nat.Phys. 20 (2024) 68-73

Optically trapped Feshbach molecules of fermionic 161Dy and 40K

Authors: E. Soave, A. Canali, Zhu-Xiong Ye, M. Kreyer, E. Kirilov, R. Grimm

Abstract: We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, which are composed of the fermionic isotopes 161Dy and 40K. Employing a magnetic sweep across a resonance located near 7.3 G, we produce up to 5000 molecules at a temperature of about 50 nK. For purification from the remaining atoms, we apply a Stern-Gerlach technique based on magnetic levitation of the mole… ▽ More We report on the preparation of a pure ultracold sample of bosonic DyK Feshbach molecules, which are composed of the fermionic isotopes 161Dy and 40K. Employing a magnetic sweep across a resonance located near 7.3 G, we produce up to 5000 molecules at a temperature of about 50 nK. For purification from the remaining atoms, we apply a Stern-Gerlach technique based on magnetic levitation of the molecules in a very weak optical dipole trap. With the trapped molecules we finally reach a high phase-space density of about 0.1. We measure the magnetic field dependence of the molecular binding energy and the magnetic moment, refining our knowledge of the resonance parameters. We also demonstrate a peculiar anisotropic expansion effect observed when the molecules are released from the trap and expand freely in the magnetic levitation field. Moreover, we identify an important lifetime limitation that is imposed by the 1064-nm infrared trap light itself and not by inelastic collisions. The light-induced decay rate is found to be proportional to the trap light intensity and the closed-channel fraction of the Feshbach molecule. These observations suggest a one-photon coupling to electronically excited states to limit the lifetime and point to the prospect of loss suppression by optimizing the wavelength of the trapping light. Our results represent important insights and experimental steps on the way to achieve quantum-degenerate samples of DyK molecules and novel superfluids based on mass-imbalanced fermion mixtures. △ Less

Submitted 11 November, 2023; v1 submitted 16 April, 2023; originally announced April 2023.

Observation of low-field Feshbach resonances between $^{161}$Dy and $^{40}$K

Authors: Zhu-Xiong Ye, Alberto Canali, Elisa Soave, Marian Kreyer, Yaakov Yudkin, Cornelis Ravensbergen, Emil Kirilov, Rudolf Grimm

Abstract: We report on the observation of Feshbach resonances at low magnetic field strength (below 10 G) in the Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for applications, we consider a resonance near 7.29 G, which combines accurate magnetic tunability… ▽ More We report on the observation of Feshbach resonances at low magnetic field strength (below 10 G) in the Fermi-Fermi mixture of $^{161}$Dy and $^{40}$K. We characterize five resonances by measurements of interspecies thermalization rates and molecular binding energies. As a case of particular interest for applications, we consider a resonance near 7.29 G, which combines accurate magnetic tunability and access to the universal regime of interactions with experimental simplicity. We show that lifetimes of a few 100 ms can be achieved for the optically trapped, resonantly interacting mixture. We also demonstrate the hydrodynamic expansion of the mixture in the strongly interacting regime and the formation of DyK Feshbach molecules. Our work opens up new experimental possibilities in view of mass-imbalanced superfluids and related phenomena. △ Less

Submitted 17 October, 2022; v1 submitted 7 July, 2022; originally announced July 2022.

Journal ref: Phys. Rev. A 106, 043314 (2022)

The Lunar Geophysical Network Landing Sites Science Rationale

Authors: Heidi Fuqua Haviland, Renee C. Weber, Clive R. Neal, Philippe Lognonné, Raphaël F. Garcia, Nicholas Schmerr, Seiichi Nagihara, Robert Grimm, Douglas G. Currie, Simone Dell'Agnello, Thomas R. Watters, Mark P. Panning, Catherine L. Johnson, Ryuhei Yamada, Martin Knapmeyer, Lillian R. Ostrach, Taichi Kawamura, Noah Petro, Paul M. Bremner

Abstract: The Lunar Geophysical Network (LGN) mission is proposed to land on the Moon in 2030 and deploy packages at four locations to enable geophysical measurements for 6-10 years. Returning to the lunar surface with a long-lived geophysical network is a key next step to advance lunar and planetary science. LGN will greatly expand our primarily Apollo-based knowledge of the deep lunar interior by identify… ▽ More The Lunar Geophysical Network (LGN) mission is proposed to land on the Moon in 2030 and deploy packages at four locations to enable geophysical measurements for 6-10 years. Returning to the lunar surface with a long-lived geophysical network is a key next step to advance lunar and planetary science. LGN will greatly expand our primarily Apollo-based knowledge of the deep lunar interior by identifying and characterizing mantle melt layers, as well as core size and state. To meet the mission objectives, the instrument suite provides complementary seismic, geodetic, heat flow, and electromagnetic observations. We discuss the network landing site requirements and provide example sites that meet these requirements. Landing site selection will continue to be optimized throughout the formulation of this mission. Possible sites include the P-5 region within the Procellarum KREEP Terrane (PKT; (lat:$15^{\circ}$; long:$-35^{\circ}$), Schickard Basin (lat:$-44.3^{\circ}$; long:$-55.1^{\circ}$), Crisium Basin (lat:$18.5^{\circ}$; long:$61.8^{\circ}$), and the farside Korolev Basin (lat:$-2.4^{\circ}$; long:$-159.3^{\circ}$). Network optimization considers the best locations to observe seismic core phases, e.g., ScS and PKP. Ray path density and proximity to young fault scarps are also analyzed to provide increased opportunities for seismic observations. Geodetic constraints require the network to have at least three nearside stations at maximum limb distances. Heat flow and electromagnetic measurements should be obtained away from terrane boundaries and from magnetic anomalies at locations representative of global trends. An in-depth case study is provided for Crisium. In addition, we discuss the consequences for scientific return of less than optimal locations or number of stations. △ Less

Submitted 13 July, 2021; originally announced July 2021.

Comments: 34 pages, 12 figures, 3 tables, 1 appendix. Accepted manuscript, The Planetary Science Journal

Measurement of the dynamic polarizability of Dy atoms near the 626-nm intercombination line

Authors: Marian Kreyer, Jeong Ho Han, Cornelis Ravensbergen, Vincent Corre, Elisa Soave, Emil Kirilov, Rudolf Grimm

Abstract: We report on measurements of the anisotropic dynamical polarizability of Dy near the 626-nm intercombination line, employing modulation spectroscopy in a one-dimensional optical lattice. To eliminate large systematic uncertainties resulting from the limited knowledge of the spatial intensity distribution, we use K as a reference species with accurately known polarizability. This method can be appl… ▽ More We report on measurements of the anisotropic dynamical polarizability of Dy near the 626-nm intercombination line, employing modulation spectroscopy in a one-dimensional optical lattice. To eliminate large systematic uncertainties resulting from the limited knowledge of the spatial intensity distribution, we use K as a reference species with accurately known polarizability. This method can be applied independently of the sign of the polarizability, i.e., for both attractive and repulsive optical fields on both sides of a resonance. By variation of the laser polarization we extract the scalar and the tensorial part. To characterize the strength of the transition, we also derive the natural linewidth. We find our result to be in excellent agreement with literature values, which provide a sensitive benchmark for the accuracy of our method. In addition we demonstrate optical dipole trapping on the intercombination line, confirming the expected long lifetimes and low heating rates. This provides an additional tool to tailor optical potentials for Dy atoms and for the species-specific manipulation of atoms in the Dy-K mixture. △ Less

Submitted 14 September, 2021; v1 submitted 22 March, 2021; originally announced March 2021.

Journal ref: Phys. Rev. A 104, 033106 (2021)

Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance

Authors: M. Pini, P. Pieri, R. Grimm, G. Calvanese Strinati

Abstract: A detailed description is given of the phase diagram for a two-component unitary Fermi gas with mass and population imbalance, for both homogeneous and trapped systems. This aims at providing quantitative benchmarks for the normal-to-superfluid phase transition of a mass-imbalanced Fermi gas in the temperature-polarization parameter space. A self-consistent t-matrix approach is adopted, which has… ▽ More A detailed description is given of the phase diagram for a two-component unitary Fermi gas with mass and population imbalance, for both homogeneous and trapped systems. This aims at providing quantitative benchmarks for the normal-to-superfluid phase transition of a mass-imbalanced Fermi gas in the temperature-polarization parameter space. A self-consistent t-matrix approach is adopted, which has already proven to accurately describe the thermodynamic properties of the mass and population balanced unitary Fermi gas. Our results provide a guideline for the ongoing experiments on heteronuclear Fermi mixtures. △ Less

Submitted 16 February, 2021; v1 submitted 3 December, 2020; originally announced December 2020.

Comments: 10 pages, 10 figures, final version

Journal ref: Phys. Rev. A 103, 023314 (2021)

Resonantly Interacting Fermi-Fermi Mixture of $^{161}$Dy and $^{40}$K

Authors: C. Ravensbergen, E. Soave, V. Corre, M. Kreyer, B. Huang, E. Kirilov, R. Grimm

Abstract: We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of $^{161}$Dy and $^{40}$K, we identify a broad Feshbach resonance centered at a magnetic field of $217\,$G. Hydrodynamic expansion profiles in the resonant interaction regime reveal a bimodal behavior resulting from mass imbal… ▽ More We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of $^{161}$Dy and $^{40}$K, we identify a broad Feshbach resonance centered at a magnetic field of $217\,$G. Hydrodynamic expansion profiles in the resonant interaction regime reveal a bimodal behavior resulting from mass imbalance. Lifetime studies on resonance show a suppression of inelastic few-body processes by orders of magnitude, which we interpret as a consequence of the fermionic nature of our system. The resonant mixture opens up intriguing perspectives for studies on novel states of strongly correlated fermions with mass imbalance. △ Less

Submitted 2 April, 2020; v1 submitted 8 September, 2019; originally announced September 2019.

Comments: Revised version v3; Supplemental Material available as ancillary file

Journal ref: Phys. Rev. Lett. 124, 203402 (2020)

Accurate Determination of the Dynamical Polarizability of Dysprosium

Authors: C. Ravensbergen, V. Corre, E. Soave, M. Kreyer, S. Tzanova, E. Kirilov, R. Grimm

Abstract: We report a measurement of the dynamical polarizability of dysprosium atoms in their electronic ground state at the optical wavelength of 1064 nm, which is of particular interest for laser trapping experiments. Our method is based on collective oscillations in an optical dipole trap, and reaches unprecedented accuracy and precision by comparison with an alkali atom (potassium) as a reference speci… ▽ More We report a measurement of the dynamical polarizability of dysprosium atoms in their electronic ground state at the optical wavelength of 1064 nm, which is of particular interest for laser trapping experiments. Our method is based on collective oscillations in an optical dipole trap, and reaches unprecedented accuracy and precision by comparison with an alkali atom (potassium) as a reference species. We obtain values of 184.4(2.4) a.u. and 1.7(6) a.u. for the scalar and tensor polarizability, respectively. Our experiments have reached a level that permits meaningful tests of current theo- retical descriptions and provides valuable information for future experiments utilizing the intriguing properties of heavy lanthanide atoms. △ Less

Submitted 6 June, 2018; v1 submitted 17 January, 2018; originally announced January 2018.

Comments: 4 pages and 4 figures. The Supplemental Materials are located in the Ancillary files

Journal ref: Phys. Rev. Lett. 120, 223001 (2018)

Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice

Authors: Lukas Reichsöllner, Andreas Schindewolf, Tetsu Takekoshi, Rudolf Grimm, Hanns-Christoph Nägerl

Abstract: We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold 87Rb133Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently p… ▽ More We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold 87Rb133Cs Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions. △ Less

Submitted 10 February, 2017; v1 submitted 21 July, 2016; originally announced July 2016.

Comments: 10 pages, 6 figures (4 in the main text, 2 in Supplemental Material)

Journal ref: Phys. Rev. Lett. 118, 073201 (2017)

Finite-temperature effects on a triatomic Efimov resonance in ultracold cesium

Authors: Bo Huang, Leonid A. Sidorenkov, Rudolf Grimm

Abstract: We report a thorough investigation of finite-temperature effects on three-body recombination near a triatomic Efimov resonance in an ultracold gas of cesium atoms. Our measurements cover a wide range from a near-ideal realization of the zero-temperature limit to a strongly temperature-dominated regime. The experimental results are analyzed within a recently introduced theoretical model based on a… ▽ More We report a thorough investigation of finite-temperature effects on three-body recombination near a triatomic Efimov resonance in an ultracold gas of cesium atoms. Our measurements cover a wide range from a near-ideal realization of the zero-temperature limit to a strongly temperature-dominated regime. The experimental results are analyzed within a recently introduced theoretical model based on a universal zero-range theory. The temperature-induced shift of the resonance reveals a contribution that points to an energy-dependence of the three-body parameter. We interpret this contribution in terms of the finite range of the van der Waals interaction in real atomic systems and we quantify it in an empirical way based on length scale arguments. A universal character of the corresponding resonance shift is suggested by observations related to other Efimov resonances and the comparison with a theoretical finite-temperature approach that explicitly takes the van der Waals interaction into account. Our findings are of importance for the precise determination of Efimov resonance positions from experiments at finite temperatures. △ Less

Submitted 21 April, 2015; originally announced April 2015.

Comments: 8 pages, 5 figures

Journal ref: Phys. Rev. A 91, 063622 (2015)

Ultracold Dipolar Molecules Composed of Strongly Magnetic Atoms

Authors: A. Frisch, M. Mark, K. Aikawa, S. Baier, R. Grimm, A. Petrov, S. Kotochigova, G. Quéméner, M. Lepers, O. Dulieu, F. Ferlaino

Abstract: In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we de… ▽ More In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two dimensional geometry can be reduced by using the anisotropy of the dipole-dipole interaction and that this reduction follows a universal dipolar behavior. △ Less

Submitted 23 November, 2015; v1 submitted 17 April, 2015; originally announced April 2015.

Comments: 8 pages, 5 figures, including supplemental material

Journal ref: Phys. Rev. Lett. 115, 203201 (2015)

Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state

Authors: Tetsu Takekoshi, Lukas Reichsöllner, Andreas Schindewolf, Jeremy M. Hutson, C. Ruth Le Sueur, Olivier Dulieu, Francesca Ferlaino, Rudolf Grimm, Hanns-Christoph Nägerl

Abstract: We produce ultracold dense trapped samples of 87Rb133Cs molecules in their rovibrational ground state, with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with efficiencies of 90%. We observe the onset of hyperfine-changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift o… ▽ More We produce ultracold dense trapped samples of 87Rb133Cs molecules in their rovibrational ground state, with full nuclear hyperfine state control, by stimulated Raman adiabatic passage (STIRAP) with efficiencies of 90%. We observe the onset of hyperfine-changing collisions when the magnetic field is ramped so that the molecules are no longer in the hyperfine ground state. A strong quadratic shift of the transition frequencies as a function of applied electric field shows the strongly dipolar character of the RbCs ground-state molecule. Our results open up the prospect of realizing stable bosonic dipolar quantum gases with ultracold molecules. △ Less

Submitted 19 November, 2014; v1 submitted 23 May, 2014; originally announced May 2014.

Comments: 7 pages, 5 figures; improved ground-state decay measurement, two-body decay model added

Journal ref: Phys. Rev. Lett. 113, 205301 (2014)

Anisotropic relaxation dynamics in a dipolar Fermi gas driven out of equilibrium

Authors: K. Aikawa, A. Frisch, M. Mark, S. Baier, R. Grimm, J. L. Bohn, D. S. Jin, G. M. Bruun, F. Ferlaino

Abstract: We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic $^{167}$Er fermions, spin-polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalizati… ▽ More We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic $^{167}$Er fermions, spin-polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalization experiments, we observe a strong anisotropy of the scattering, which manifests itself in a large angular dependence of the thermal relaxation dynamics. Our result is in very good agreement with recent theoretical predictions. Furthermore, we measure the rethermalization rate as a function of temperature for different angles and find that the suppression of collisions by Pauli blocking is not influenced by the dipole orientation. △ Less

Submitted 21 November, 2014; v1 submitted 7 May, 2014; originally announced May 2014.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 113, 263201 (2014)

Observation of the Second Triatomic Resonance in Efimov's Scenario

Authors: Bo Huang, Leonid A. Sidorenkov, Rudolf Grimm, Jeremy M. Hutson

Abstract: We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the $s$-wave scattering length. The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms. This observation, together with a finite-tem… ▽ More We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the $s$-wave scattering length. The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms. This observation, together with a finite-temperature analysis and the known first resonance, allows the most accurate demonstration to date of the discrete scaling behavior at the heart of Efimov physics. For the system of three identical bosons, we obtain a scaling factor of $21.0(1.3)$, close to the ideal value of $22.7$. △ Less

Submitted 26 April, 2014; v1 submitted 25 February, 2014; originally announced February 2014.

Comments: 5 pages, 2 figures, 1 table, 1 supplemental material

Journal ref: Phys. Rev. Lett. 112, 190401 (2014)

Reaching Fermi degeneracy via universal dipolar scattering

Authors: K. Aikawa, A. Frisch, M. Mark, S. Baier, R. Grimm, F. Ferlaino

Abstract: We report on the creation of a degenerate dipolar Fermi gas of erbium atoms. We force evaporative cooling in a fully spin-polarized sample down to temperatures as low as 0.2 times the Fermi temperature. The strong magnetic dipole-dipole interaction enables elastic collisions between identical fermions even in the zero-energy limit. The measured elastic scattering cross section agrees well with the… ▽ More We report on the creation of a degenerate dipolar Fermi gas of erbium atoms. We force evaporative cooling in a fully spin-polarized sample down to temperatures as low as 0.2 times the Fermi temperature. The strong magnetic dipole-dipole interaction enables elastic collisions between identical fermions even in the zero-energy limit. The measured elastic scattering cross section agrees well with the predictions from dipolar scattering theory, which follow a universal scaling law depending only on the dipole moment and on the atomic mass. Our approach to quantum degeneracy proceeds with very high cooling efficiency and provides large atomic densities, and it may be extended to various dipolar systems. △ Less

Submitted 18 December, 2013; v1 submitted 21 October, 2013; originally announced October 2013.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. Lett. 112, 010404 (2014)

Quantum degenerate mixtures of strontium and rubidium atoms

Authors: Benjamin Pasquiou, Alex Bayerle, Slava Tzanova, Simon Stellmer, Jacek Szczepkowski, Mark Parigger, Rudolf Grimm, Florian Schreck

Abstract: We report on the realization of quantum degenerate gas mixtures of the alkaline-earth element strontium with the alkali element rubidium. A key ingredient of our scheme is sympathetic cooling of Rb by Sr atoms that are continuously laser cooled on a narrow linewidth transition. This versatile technique allows us to produce ultracold gas mixtures with a phase-space density of up to 0.06 for both el… ▽ More We report on the realization of quantum degenerate gas mixtures of the alkaline-earth element strontium with the alkali element rubidium. A key ingredient of our scheme is sympathetic cooling of Rb by Sr atoms that are continuously laser cooled on a narrow linewidth transition. This versatile technique allows us to produce ultracold gas mixtures with a phase-space density of up to 0.06 for both elements. By further evaporative cooling we create double Bose-Einstein condensates of 87Rb with either 88Sr or 84Sr, reaching more than 10^5 condensed atoms per element for the 84Sr-87Rb mixture. These quantum gas mixtures constitute an important step towards the production of a quantum gas of polar, open-shell RbSr molecules. △ Less

Submitted 25 May, 2013; originally announced May 2013.

Comments: 9 pages, 5 figures

Journal ref: Phys. Rev. A 88, 023601 (2013)

Higher-nodal collective modes in a resonantly interacting Fermi gas

Authors: Edmundo R. Sanchez Guajardo, Meng Khoon Tey, Leonid A. Sidorenkov, Rudolf Grimm

Abstract: We report on experimental investigations of longitudinal collective oscillations in a highly elongated, harmonically trapped two-component Fermi gas with resonantly tuned s-wave interactions ('unitary Fermi gas'). We focus on higher-nodal axial modes, which in contrast to the elementary modes have received little attention so far. We show how these modes can be efficiently excited using a resonant… ▽ More We report on experimental investigations of longitudinal collective oscillations in a highly elongated, harmonically trapped two-component Fermi gas with resonantly tuned s-wave interactions ('unitary Fermi gas'). We focus on higher-nodal axial modes, which in contrast to the elementary modes have received little attention so far. We show how these modes can be efficiently excited using a resonant local excitation scheme and sensitively analyzed by a Fourier transformation of the detected time evolution of the axial density profile. We study the temperature dependence of the mode frequencies across the superfluid phase transition. The behavior is qualitatively different from the elementary modes, where the mode frequencies are independent of the temperature as long as the gas stays in the hydrodynamic regime. Our results are compared to theoretical predictions based on Landau's two-fluid theory and available experimental knowledge of the equation of state. The comparison shows excellent agreement and thus both represents a sensitive test for the validity of the theoretical approach and provides an independent test of the equation of state. The present results obtained on modes of first-sound character represent benchmarks for the observation of second-sound propagation and corresponding oscillation modes. △ Less

Submitted 18 April, 2013; originally announced April 2013.

Comments: 11 pages, 10 figures

Second sound and the superfluid fraction in a resonantly interacting Fermi gas

Authors: Leonid A. Sidorenkov, Meng Khoon Tey, Rudolf Grimm, Yan-Hua Hou, Lev Pitaevskii, Sandro Stringari

Abstract: Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid m… ▽ More Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and neutron stars. More recently, ultracold atomic gases have emerged as new superfluid systems with unprecedented possibilities to control interactions and external confinement. Here we report the first observation of `second sound' in an ultracold Fermi gas with resonant interactions. Second sound is a striking manifestation of the two-component nature of a superfluid and corresponds to an entropy wave, where the superfluid and the non-superfluid components oscillate in opposite phase, different from ordinary sound (`first sound'), where they oscillate in phase. The speed of second sound depends explicitly on the value of the superfluid fraction, a quantity sensitive to the spectrum of elementary excitations. Our measurements allow us to extract the temperature dependence of the superfluid fraction, which in strongly interacting quantum gases has been an inaccessible quantity so far. △ Less

Submitted 12 February, 2013; originally announced February 2013.

Comments: 6 pages, 4 figures

Laser cooling to quantum degeneracy

Authors: Simon Stellmer, Benjamin Pasquiou, Rudolf Grimm, Florian Schreck

Abstract: We report on Bose-Einstein condensation (BEC) in a gas of strontium atoms, using laser cooling as the only cooling mechanism. The condensate is formed within a sample that is continuously Doppler cooled to below 1\muK on a narrow-linewidth transition. The critical phase-space density for BEC is reached in a central region of the sample, in which atoms are rendered transparent for laser cooling pho… ▽ More We report on Bose-Einstein condensation (BEC) in a gas of strontium atoms, using laser cooling as the only cooling mechanism. The condensate is formed within a sample that is continuously Doppler cooled to below 1\muK on a narrow-linewidth transition. The critical phase-space density for BEC is reached in a central region of the sample, in which atoms are rendered transparent for laser cooling photons. The density in this region is enhanced by an additional dipole trap potential. Thermal equilibrium between the gas in this central region and the surrounding laser cooled part of the cloud is established by elastic collisions. Condensates of up to 10^5 atoms can be repeatedly formed on a timescale of 100ms, with prospects for the generation of a continuous atom laser. △ Less

Submitted 21 January, 2013; originally announced January 2013.

Comments: 18 pages, 13 figures, 3 tables

Journal ref: Phys. Rev. Lett. 110, 263003 (2013)

Feshbach resonances, weakly bound molecular states and coupled-channel potentials for cesium at high magnetic fields

Authors: Martin Berninger, Alessandro Zenesini, Bo Huang, Walter Harm, Hanns-Christoph Nägerl, Francesca Ferlaino, Rudolf Grimm, Paul S. Julienne, Jeremy M. Hutson

Abstract: We explore the scattering properties of ultracold ground-state Cs atoms at magnetic fields between 450 G (45 mT) and 1000 G. We identify 17 new Feshbach resonances, including two very broad ones near 549 G and 787 G. We measure the binding energies of several different dimer states by magnetic field modulation spectroscopy. We use least-squares fitting to these experimental results, together with… ▽ More We explore the scattering properties of ultracold ground-state Cs atoms at magnetic fields between 450 G (45 mT) and 1000 G. We identify 17 new Feshbach resonances, including two very broad ones near 549 G and 787 G. We measure the binding energies of several different dimer states by magnetic field modulation spectroscopy. We use least-squares fitting to these experimental results, together with previous measurements at lower field, to determine a new 6-parameter model of the long-range interaction potential, designated M2012. Coupled-channels calculations using M2012 provide an accurate mapping between the s-wave scattering length and the magnetic field over the entire range of fields considered. This mapping is crucial for experiments that rely on precise tuning of the scattering length, such as those on Efimov physics. △ Less

Submitted 3 April, 2013; v1 submitted 21 December, 2012; originally announced December 2012.

Comments: 19 pages, 18 figures

Journal ref: Phys. Rev. A 87, 032517 (2013)

Production of quantum degenerate strontium gases: Larger, better, faster, colder

Authors: Simon Stellmer, Rudolf Grimm, Florian Schreck

Abstract: We report on an improved scheme to generate Bose-Einstein condensates (BECs) and degenerate Fermi gases of strontium. This scheme allows us to create quantum gases with higher atom number, a shorter time of the experimental cycle, or deeper quantum degeneracy than before. We create a BEC of 84-Sr exceeding 10^7 atoms, which is a 30-fold improvement over previously reported experiments. We increase… ▽ More We report on an improved scheme to generate Bose-Einstein condensates (BECs) and degenerate Fermi gases of strontium. This scheme allows us to create quantum gases with higher atom number, a shorter time of the experimental cycle, or deeper quantum degeneracy than before. We create a BEC of 84-Sr exceeding 10^7 atoms, which is a 30-fold improvement over previously reported experiments. We increase the atom number of 86-Sr BECs to 2.5x10^4 (a fivefold improvement), and refine the generation of attractively interacting 88-Sr BECs. We present a scheme to generate 84-Sr BECs with a cycle time of 2s, which, to the best of our knowledge, is the shortest cycle time of BEC experiments ever reported. We create deeply-degenerate 87-Sr Fermi gases with T/T_F as low as 0.10(1), where the number of populated nuclear spin states can be set to any value between one and ten. Furthermore, we report on a total of five different double-degenerate Bose-Bose and Bose-Fermi mixtures. These studies prepare an excellent starting point for applications of strontium quantum gases anticipated in the near future. △ Less

Submitted 11 December, 2012; originally announced December 2012.

Comments: 18 pages, 10 figures, title music by Daft Punk

Journal ref: Phys. Rev. A 87, 013611 (2013)

Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition

Authors: Meng Khoon Tey, Leonid A. Sidorenkov, Edmundo R. Sánchez Guajardo, Rudolf Grimm, Mark J. H. Ku, Martin W. Zwierlein, Yan-Hua Hou, Lev Pitaevskii, Sandro Stringari

Abstract: We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher nodal excitati… ▽ More We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state. The experimental results agree with high accuracy with the predictions of theory and provide the first evidence for the temperature dependence of the collective frequencies near the superfluid phase transition. △ Less

Submitted 1 February, 2013; v1 submitted 12 November, 2012; originally announced November 2012.

Comments: 5 pages, 2 figures

Journal ref: Phys. Rev. Lett. 110, 055303 (2013)

Creation of ultracold Sr2 molecules in the electronic ground state

Authors: Simon Stellmer, Benjamin Pasquiou, Rudolf Grimm, Florian Schreck

Abstract: We report on the creation of ultracold 84Sr2 molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain 4x10^4 molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow 1S0-3P1 intercombinati… ▽ More We report on the creation of ultracold 84Sr2 molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain 4x10^4 molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow 1S0-3P1 intercombination transition, using a vibrational level of the 0u potential as intermediate state. In preparation of our molecule association scheme, we have determined the binding energies of the last vibrational levels of the 0u, 1u excited-state, and the 1Σ_g^+ ground-state potentials. Our work overcomes the previous limitation of STIRAP schemes to systems with Feshbach resonances, thereby establishing a route that is applicable to many systems beyond bi-alkalis. △ Less

Submitted 21 May, 2012; originally announced May 2012.

Comments: 7 pages, 7 figures, 3 tables

Journal ref: Phys. Rev. Lett. 109, 115302 (2012)

Bose-Einstein Condensation of Erbium

Authors: K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, F. Ferlaino

Abstract: We report on the achievement of Bose-Einstein condensation of erbium atoms and on the observation of magnetic Feshbach resonances at low magnetic field. By means of evaporative cooling in an optical dipole trap, we produce pure condensates of $^{168}$Er, containing up to $7 \times 10^{4}$ atoms. Feshbach spectroscopy reveals an extraordinary rich loss spectrum with six loss resonances already in a… ▽ More We report on the achievement of Bose-Einstein condensation of erbium atoms and on the observation of magnetic Feshbach resonances at low magnetic field. By means of evaporative cooling in an optical dipole trap, we produce pure condensates of $^{168}$Er, containing up to $7 \times 10^{4}$ atoms. Feshbach spectroscopy reveals an extraordinary rich loss spectrum with six loss resonances already in a narrow magnetic-field range up to 3 G. Finally, we demonstrate the application of a low-field Feshbach resonance to produce a tunable dipolar Bose-Einstein condensate and we observe its characteristic d-wave collapse. △ Less

Submitted 21 May, 2012; v1 submitted 8 April, 2012; originally announced April 2012.

Comments: 4 pages, 3 figures

Journal ref: Phys. Rev. Lett. 108, 210401 (2012)

Narrow-line magneto-optical trap for erbium

Authors: A. Frisch, K. Aikawa, M. Mark, A. Rietzler, J. Schindler, E. Zupanic, R. Grimm, F. Ferlaino

Abstract: We report on the experimental realization of a robust and efficient magneto-optical trap for erbium atoms, based on a narrow cooling transition at 583nm. We observe up to $N=2 \times 10^{8}$ atoms at a temperature of about $T=15 μK$. This simple scheme provides better starting conditions for direct loading of dipole traps as compared to approaches based on the strong cooling transition alone, or o… ▽ More We report on the experimental realization of a robust and efficient magneto-optical trap for erbium atoms, based on a narrow cooling transition at 583nm. We observe up to $N=2 \times 10^{8}$ atoms at a temperature of about $T=15 μK$. This simple scheme provides better starting conditions for direct loading of dipole traps as compared to approaches based on the strong cooling transition alone, or on a combination of a strong and a narrow kHz transition. Our results on Er point to a general, simple and efficient approach to laser cool samples of other lanthanide atoms (Ho, Dy, and Tm) for the production of quantum-degenerate samples. △ Less

Submitted 16 May, 2012; v1 submitted 7 March, 2012; originally announced March 2012.

Journal ref: Phys. Rev. A 85, 051401(R) (2012)

Towards the production of ultracold ground-state RbCs molecules: Feshbach resonances, weakly bound states, and coupled-channel model

Authors: Tetsu Takekoshi, Markus Debatin, Raffael Rameshan, Francesca Ferlaino, Rudolf Grimm, Hanns-Christoph Nägerl, C. Ruth Le Sueur, Jeremy M. Hutson, Paul S. Julienne, Svetlana Kotochigova, Eberhard Tiemann

Abstract: We have studied interspecies scattering in an ultracold mixture of $^{87}$Rb and $^{133}$Cs atoms, both in their lowest-energy spin states. The three-body loss signatures of 30 incoming s- and p-wave magnetic Feshbach resonances over the range 0 to 667 G have been catalogued. Magnetic field modulation spectroscopy was used to observe molecular states bound by up to 2.5 MHz$\times h$. Magnetic mome… ▽ More We have studied interspecies scattering in an ultracold mixture of $^{87}$Rb and $^{133}$Cs atoms, both in their lowest-energy spin states. The three-body loss signatures of 30 incoming s- and p-wave magnetic Feshbach resonances over the range 0 to 667 G have been catalogued. Magnetic field modulation spectroscopy was used to observe molecular states bound by up to 2.5 MHz$\times h$. Magnetic moment spectroscopy along the magneto-association pathway from 197 to 182 G gives results consistent with the observed and calculated dependence of the binding energy on magnetic field strength. We have created RbCs Feshbach molecules using two of the resonances. We have set up a coupled-channel model of the interaction and have used direct least-squares fitting to refine its parameters to fit the experimental results from the Feshbach molecules, in addition to the Feshbach resonance positions and the spectroscopic results for deeply bound levels. The final model gives a good description of all the experimental results and predicts a large resonance near 790 G, which may be useful for tuning the interspecies scattering properties. Quantum numbers and vibrational wavefunctions from the model can also be used to choose optimal initial states of Feshbach molecules for their transfer to the rovibronic ground state using stimulated Raman adiabatic passage (STIRAP). △ Less

Submitted 7 March, 2012; v1 submitted 6 January, 2012; originally announced January 2012.

Comments: 16 pages, 11 figures, submitted to PRA

Journal ref: Phys. Rev. A 85, 032506 (2012)

Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium

Authors: M. Berninger, A. Zenesini, B. Huang, W. Harm, H. -C. Nägerl, F. Ferlaino, R. Grimm, P. S. Julienne, J. M. Hutson

Abstract: We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few… ▽ More We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and in particular to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that stays essentially constant. △ Less

Submitted 14 September, 2011; v1 submitted 20 June, 2011; originally announced June 2011.

Comments: 4 pages, 3 figures

Journal ref: Phys. Rev. Lett. 107, 120401 (2011)

Molecular spectroscopy for ground-state transfer of ultracold RbCs molecules

Authors: Markus Debatin, Tetsu Takekoshi, Raffael Rameshan, Lukas Reichsöllner, Francesca Ferlaino, Rudolf Grimm, Romain Vexiau, Nadia Bouloufa, Olivier Dulieu, Hanns-Christoph Naegerl

Abstract: We perform one- and two-photon high resolution spectroscopy on ultracold samples of RbCs Feshbach molecules with the aim to identify a suitable route for efficient ground-state transfer in the quantum-gas regime to produce quantum gases of dipolar RbCs ground-state molecules. One-photon loss spectroscopy allows us to probe deeply bound rovibrational levels of the mixed excited (A1Σ+ - b3Π0) 0+ mol… ▽ More We perform one- and two-photon high resolution spectroscopy on ultracold samples of RbCs Feshbach molecules with the aim to identify a suitable route for efficient ground-state transfer in the quantum-gas regime to produce quantum gases of dipolar RbCs ground-state molecules. One-photon loss spectroscopy allows us to probe deeply bound rovibrational levels of the mixed excited (A1Σ+ - b3Π0) 0+ molecular states. Two-photon dark state spectroscopy connects the initial Feshbach state to the rovibronic ground state. We determine the binding energy of the lowest rovibrational level |v"=0,J"=0> of the X1Σ+ ground state to be DX 0 = 3811.5755(16) 1/cm, a 300-fold improvement in accuracy with respect to previous data. We are now in the position to perform stimulated two-photon Raman transfer to the rovibronic ground state. △ Less

Submitted 1 June, 2011; originally announced June 2011.

Comments: Submitted to PCCP themed issue: Physics and Chemistry of Cold Molecules

Hyperfine, rotational, and vibrational structure of the triplet ground state of Rb molecules

Authors: Christoph Strauss, Tetsu Takekoshi, Florian Lang, Klaus Winkler, Rudolf Grimm, Johannes Hecker Denschlag, Eberhard Tiemann

Abstract: We have performed high-resolution two-photon dark-state spectroscopy of an ultracold gas of Rb molecules in the triplet ground state at a magnetic field of about 1000 G. The vibrational ladder as well as the hyperfine and low-lying rotational structure is mapped out. Energy shifts in the spectrum are observed due to singlet-triplet mixing at binding energies as deep as a few hundred GHz x h. This… ▽ More We have performed high-resolution two-photon dark-state spectroscopy of an ultracold gas of Rb molecules in the triplet ground state at a magnetic field of about 1000 G. The vibrational ladder as well as the hyperfine and low-lying rotational structure is mapped out. Energy shifts in the spectrum are observed due to singlet-triplet mixing at binding energies as deep as a few hundred GHz x h. This information together with data from other sources is used to optimize the potentials of the triplet and singlet states in a coupled-channel model. We find that the hyperfine structure depends weakly on the vibrational level. This provides a possible explanation for inaccuracies in recent Feshbach resonance calculations. △ Less

Submitted 14 October, 2010; v1 submitted 10 September, 2010; originally announced September 2010.

Journal ref: Phys. Rev. A 82, 052514 (2010)

Magnetically Controlled Exchange Process in an Ultracold Atom-Dimer Mixture

Authors: S. Knoop, F. Ferlaino, M. Berninger, M. Mark, H. -C. Nägerl, R. Grimm, J. P. D'Incao, B. D. Esry

Abstract: We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not l… ▽ More We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrödinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states. △ Less

Submitted 10 November, 2009; originally announced November 2009.

Comments: 4 pages, 4 figures

Journal ref: Phys. Rev. Lett. 104, 053201 (2010)

Observation of an Efimov resonance in an ultracold mixture of atoms and weakly bound dimers

Authors: S. Knoop, F. Ferlaino, M. Berninger, M. Mark, H. -C. Nägerl, R. Grimm

Abstract: We discuss our recent observation of an atom-dimer Efimov resonance in an ultracold mixture of Cs atoms and Cs_2 Feshbach molecules [Nature Phys. 5, 227 (2009)]. We review our experimental procedure and present additional data involving a non-universal g-wave dimer state, to contrast our previous results on the universal s-wave dimer. We resolve a seeming discrepancy when quantitatively comparin… ▽ More We discuss our recent observation of an atom-dimer Efimov resonance in an ultracold mixture of Cs atoms and Cs_2 Feshbach molecules [Nature Phys. 5, 227 (2009)]. We review our experimental procedure and present additional data involving a non-universal g-wave dimer state, to contrast our previous results on the universal s-wave dimer. We resolve a seeming discrepancy when quantitatively comparing our experimental findings with theoretical results from effective field theory. △ Less

Submitted 26 July, 2009; originally announced July 2009.

Comments: Conference Proceeding ICPEAC 2009 Kalamazoo, to appear in Journal of Physics: Conference Series

Journal ref: J. Phys.: Conf. Ser. 194, 012064 (2009)

Evidence for Universal Four-Body States Tied to an Efimov Trimer

Authors: F. Ferlaino, S. Knoop, M. Berninger, W. Harm, J. P. D'Incao, H. -C. Nägerl, R. Grimm

Abstract: We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent… ▽ More We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent theoretical predictions and demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the generic three-body problem. △ Less

Submitted 9 April, 2009; v1 submitted 6 March, 2009; originally announced March 2009.

Comments: 4 pages, 4 figures

Journal ref: Phys. Rev. Lett. 102, 140401 (2009)

Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances

Authors: A. D. Lange, K. Pilch, A. Prantner, F. Ferlaino, B. Engeser, H. -C. Naegerl, R. Grimm, C. Chin

Abstract: We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectrosc… ▽ More We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectroscopy in a range where one broad and two narrow Feshbach resonances overlap. From the data we accurately determine the Cs atomic scattering length and the positions and widths of two particular resonances. △ Less

Submitted 9 April, 2009; v1 submitted 30 October, 2008; originally announced October 2008.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. A 79, 013622 (2009)

Three-body recombination at large scattering lengths in an ultracold atomic gas

Authors: Tino Weber, Jens Herbig, Michael Mark, Hanns-Christoph Naegerl, Rudolf Grimm

Abstract: We study three-body recombination in an optically trapped ultracold gas of cesium atoms with precise magnetic control of the s-wave scattering length a. At large positive values of a, we measure the dependence of the rate coefficient on a and confirm the theoretically predicted scaling proportional to a^4. Evidence of recombination heating indicates the formation of very weakly bound molecules i… ▽ More We study three-body recombination in an optically trapped ultracold gas of cesium atoms with precise magnetic control of the s-wave scattering length a. At large positive values of a, we measure the dependence of the rate coefficient on a and confirm the theoretically predicted scaling proportional to a^4. Evidence of recombination heating indicates the formation of very weakly bound molecules in the last bound energy level. △ Less

Submitted 21 July, 2003; v1 submitted 14 April, 2003; originally announced April 2003.

Journal ref: Phys. Rev. Lett. 91, 123201 (2003)

Evanescent-wave trapping and evaporative cooling of an atomic gas near two-dimensionality

Authors: M. Hammes, D. Rychtarik, B. Engeser, H. -C. Nägerl, R. Grimm

Abstract: A dense gas of cesium atoms at the crossover to two-dimensionality is prepared in a highly anisotropic surface trap that is realized with two evanescent light waves. Temperatures as low as 100nK are reached with 20.000 atoms at a phase-space density close to 0.1. The lowest quantum state in the tightly confined direction is populated by more than 60%. The system offers intriguing prospects for f… ▽ More A dense gas of cesium atoms at the crossover to two-dimensionality is prepared in a highly anisotropic surface trap that is realized with two evanescent light waves. Temperatures as low as 100nK are reached with 20.000 atoms at a phase-space density close to 0.1. The lowest quantum state in the tightly confined direction is populated by more than 60%. The system offers intriguing prospects for future experiments on degenerate quantum gases in two dimensions. △ Less

Submitted 16 August, 2002; originally announced August 2002.

Journal ref: Phys. Rev. Lett. 90, 173001 (2003)

Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms

Authors: S. Jochim, M. Bartenstein, G. Hendl, J. Hecker Denschlag, R. Grimm, A. Mosk, M. Weidemüller

Abstract: We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length that is… ▽ More We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length that is associated with a predicted Feshbach resonance at 530(3)G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime. △ Less

Submitted 24 July, 2002; originally announced July 2002.

Journal ref: Phys. Rev. Lett. 89, 273202 (2002)

Cold atom gas at very high densities in an optical surface microtrap

Authors: M. Hammes, D. Rychtarik, H. -C. Nägerl, R. Grimm

Abstract: An optical microtrap is realized on a dielectric surface by crossing a tightly focused laser beam with an horizontal evanescent-wave atom mirror. The nondissipative trap is loaded with $\sim$$10^5$ cesium atoms through elastic collisions from a cold reservoir provided by a large-volume optical surface trap. With an observed 300-fold local increase of the atomic number density approaching… ▽ More An optical microtrap is realized on a dielectric surface by crossing a tightly focused laser beam with an horizontal evanescent-wave atom mirror. The nondissipative trap is loaded with $\sim$$10^5$ cesium atoms through elastic collisions from a cold reservoir provided by a large-volume optical surface trap. With an observed 300-fold local increase of the atomic number density approaching $10^{14}{\rm cm}^{-3}$, unprecedented conditions of cold atoms close to a surface are realized. △ Less

Submitted 8 April, 2002; originally announced April 2002.

Journal ref: Phys. Rev. A 66, 051401(R) (2002)

Sympathetic Cooling with Two Atomic Species in an Optical Trap

Authors: M. Mudrich, S. Kraft, K. Singer, R. Grimm, A. Mosk, M. Weidemuller

Abstract: We simultaneously trap ultracold lithium and cesium atoms in an optical dipole trap formed by the focus of a CO$_2$ laser and study the exchange of thermal energy between the gases. The cesium gas, which is optically cooled to $20 μ$K, efficiently decreases the temperature of the lithium gas through sympathetic cooling. The measured cross section for thermalizing $^{133}$Cs-$^7$Li collisions is… ▽ More We simultaneously trap ultracold lithium and cesium atoms in an optical dipole trap formed by the focus of a CO$_2$ laser and study the exchange of thermal energy between the gases. The cesium gas, which is optically cooled to $20 μ$K, efficiently decreases the temperature of the lithium gas through sympathetic cooling. The measured cross section for thermalizing $^{133}$Cs-$^7$Li collisions is $8 \times 10^{-12}$ cm$^2$, for both species in their lowest hyperfine ground state. Besides thermalization, we observe evaporation of lithium purely through elastic cesium-lithium collisions (sympathetic evaporation). △ Less

Submitted 30 November, 2001; originally announced November 2001.

Comments: 4 pages 3 figs

Journal ref: Phys. Rev. Lett. 88, 253001 (2002).

Sympathetic Cooling of Lithium by Laser-cooled Cesium

Authors: S. Kraft, M. Mudrich, K. Singer, R. Grimm, A. Mosk, M. Weidemueller

Abstract: We present first indications of sympathetic cooling between two neutral, optically trapped atomic species. Lithium and cesium atoms are simultaneously stored in an optical dipole trap formed by the focus of a CO$_2$ laser, and allowed to interact for a given period of time. The temperature of the lithium gas is found to decrease when in thermal contact with cold cesium. The timescale of thermali… ▽ More We present first indications of sympathetic cooling between two neutral, optically trapped atomic species. Lithium and cesium atoms are simultaneously stored in an optical dipole trap formed by the focus of a CO$_2$ laser, and allowed to interact for a given period of time. The temperature of the lithium gas is found to decrease when in thermal contact with cold cesium. The timescale of thermalization yields an estimate for the Li-Cs cross-section. △ Less

Submitted 27 September, 2001; originally announced September 2001.

Comments: 4 pages, proceedings of ICOLS 2001

Mixture of ultracold lithium and cesium atoms in an optical dipole trap

Authors: A. Mosk, S. Kraft, M. Mudrich, K. Singer, W. Wohlleben, R. Grimm, M. Weidemuller

Abstract: We present the first simultaneous trapping of two different ultracold atomic species in a conservative trap. Lithium and cesium atoms are stored in an optical dipole trap formed by the focus of a CO$_2$ laser. Techniques for loading both species of atoms are discussed and observations of elastic and inelastic collisions between the two species are presented. A model for sympathetic cooling of tw… ▽ More We present the first simultaneous trapping of two different ultracold atomic species in a conservative trap. Lithium and cesium atoms are stored in an optical dipole trap formed by the focus of a CO$_2$ laser. Techniques for loading both species of atoms are discussed and observations of elastic and inelastic collisions between the two species are presented. A model for sympathetic cooling of two species with strongly different mass in the presence of slow evaporation is developed. From the observed Cs-induced evaporation of Li atoms we estimate a cross section for cold elastic Li-Cs collisions. △ Less

Submitted 31 October, 2001; v1 submitted 31 July, 2001; originally announced July 2001.

Comments: 10 pages 9 figures, submitted to Appl. Phys. B; v2: Corrected evaporation formulas and some postscript problems

Journal ref: Applied Physics B 73, p. 791 - 799 (2001).

Resonator-Enhanced Optical Dipole Trap for Fermionic Lithium Atoms

Authors: A. Mosk, S. Jochim, H. Moritz, Th. Elsaesser, M. Weidemueller, R. Grimm

Abstract: We demonstrate a novel optical dipole trap which is based on the enhancement of the optical power density of a Nd:YAG laser beam in a resonator. The trap is particularly suited for experiments with ultracold gases, as it combines a potential depth of order 1 mK with storage times of several tens of seconds. We study the interactions in a gas of fermionic lithium atoms in our trap and observe the… ▽ More We demonstrate a novel optical dipole trap which is based on the enhancement of the optical power density of a Nd:YAG laser beam in a resonator. The trap is particularly suited for experiments with ultracold gases, as it combines a potential depth of order 1 mK with storage times of several tens of seconds. We study the interactions in a gas of fermionic lithium atoms in our trap and observe the influence of spin-changing collisions and off-resonant photon scattering. A key element in reaching long storage times is an ultra-low noise laser. The dependence of the storage time on laser noise is investigated. △ Less

Submitted 17 July, 2001; v1 submitted 3 May, 2001; originally announced May 2001.

Comments: 4 pages 3 figures Revised 17.07.2001; Corrected calibration of noise measmt

Journal ref: Opt. Lett. 26, 1837 (2001).

Evaporative cooling of cesium atoms in the gravito-optical surface trap

Authors: M. Hammes, D. Rychtarik, R. Grimm

Abstract: We report on cooling of an atomic cesium gas closely above an evanescent-wave. Our first evaporation experiments show a temperature reduction from 10muK down to 300nK along with a gain in phase-space density of almost two orders of magnitude. In a series of measurements of heating and spin depolarization an incoherent background of resonant photons in the evanescent-wave diode laser light was fo… ▽ More We report on cooling of an atomic cesium gas closely above an evanescent-wave. Our first evaporation experiments show a temperature reduction from 10muK down to 300nK along with a gain in phase-space density of almost two orders of magnitude. In a series of measurements of heating and spin depolarization an incoherent background of resonant photons in the evanescent-wave diode laser light was found to be the limiting factor at this stage. △ Less

Submitted 27 December, 2000; originally announced December 2000.

Comments: Proceedings of the Euroconference on Atom Optics and Interferometry, Cargese, France, 26 - 29 July 2000, edt. by A. Aspect, P. Bouyer, and J. Dalibard

Optical and evaporative cooling of cesium atoms in the gravito-optical surface trap

Authors: M. Hammes, D. Rychtarik, V. Druzhinina, U. Moslener, I. Manek-Hönninger, R. Grimm

Abstract: We report on cooling of an atomic cesium gas closely above an evanescent-wave atom mirror. At high densitities, optical cooling based on inelastic reflections is found to be limited by a density-dependent excess temperature and trap loss due to ultracold collisions involving repulsive molecular states. Nevertheless, very good starting conditions for subsequent evaporative cooling are obtained. O… ▽ More We report on cooling of an atomic cesium gas closely above an evanescent-wave atom mirror. At high densitities, optical cooling based on inelastic reflections is found to be limited by a density-dependent excess temperature and trap loss due to ultracold collisions involving repulsive molecular states. Nevertheless, very good starting conditions for subsequent evaporative cooling are obtained. Our first evaporation experiments show a temperature reduction from 10muK down to 300nK along with a gain in phase-space density of almost two orders of magnitude. △ Less

Submitted 14 May, 2000; originally announced May 2000.

Comments: 8 pages, 6 figures, submitted to Journal of Modern Optics, special issue "Fundamentals of Quantum Optics V", edited by F. Ehlotzky

Journal ref: J. Mod. Opt. 47, 2755 (2000)