Bose-Einstein Condensation Experiments Research Articles

Bound-state signatures in quenched Bose-Einstein condensates

We investigate the dynamics of a homogenous Bose-Einstein condensate (BEC) following a sudden quench of the scattering length. Our focus is the time evolution of short-range correlations via the dynamical contact. We compute the dynamics using a combination of two- and many-body models, and we propose an intuitive connection between them that unifies their short-time, short-range predictions. Our two-body models are exactly solvable and, when properly calibrated, lead to analytic formulae for the contact dynamics. Immediately after the quench, the contact exhibits strong oscillations at the frequency of the two-body bound state. These oscillations are large in amplitude, and their time average is typically much larger than the unregularized Bogoliubov prediction. The condensate fraction shows similar oscillations, whose amplitude we are able to estimate. These results demonstrate the importance of including the bound state in descriptions of diabatically-quenched BEC experiments.

Onsager-Kraichnan condensation in decaying two-dimensional quantum turbulence.

Despite the prominence of Onsager's point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling MonteCarlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.

Pathways toward understanding Macroscopic Quantum Phenomena

Macroscopic quantum phenomena refer to quantum features in objects of 'large' sizes, systems with many components or degrees of freedom, organized in some ways where they can be identified as macroscopic objects. This emerging field is ushered in by several categories of definitive experiments in superconductivity, electromechanical systems, Bose-Einstein condensates and others. Yet this new field which is rich in open issues at the foundation of quantum and statistical physics remains little explored theoretically (with the important exception of the work of A J Leggett [1], while touched upon or implied by several groups of authors represented in this conference. Our attitude differs in that we believe in the full validity of quantum mechanics stretching from the testable micro to meso scales, with no need for the introduction of new laws of physics.) This talk summarizes our thoughts in attempting a systematic investigation into some key foundational issues of quantum macroscopic phenomena, with the goal of ultimately revealing or building a viable theoretical framework. Three major themes discussed in three intended essays are the large N expansion [2], the correlation hierarchy [3] and quantum entanglement [4]. We give a sketch of the first two themes and then discuss several key issues in the consideration of macro and quantum, namely, a) recognition that there exist many levels of structure in a composite body and only by judicious choice of an appropriate set of collective variables can one give the best description of the dynamics of a specific level of structure. Capturing the quantum features of a macroscopic object is greatly facilitated by the existence and functioning of these collective variables; b) quantum entanglement, an exclusively quantum feature [5], is known to persist to high temperatures [6] and large scales [7] under certain conditions, and may actually decrease with increased connectivity in a quantum network [8]. We use entanglement as a measure of quantumness here and pick out these somewhat counter-intuitive examples to show that there are blind spots worthy of our attention and issues which we need to analyze closer. Our purpose is to try to remove the stigma that quantum only pertains to micro, in order to make way for deeper probes into the conditions whereby quantum features of macroscopic systems manifest.

Production of quantum-degenerate strontium gases

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.

A gradient and offset compensated Ioffe–Pritchard trap for Bose–Einstein condensation experiments

The Ioffe–Pritchard trap is the workhorse of modern cold atom physics. Here, we present a novel Ioffe–Pritchard trap coil configuration based purely on circular coils. By eliminating the traditional Ioffe bars one can increase the gradient and thus the radial trapping frequency by almost a factor 2. We also present a method to achieve minimal coupling between the gradient, curvature and offset fields of the trap, thus facilitating the dynamic control of the trapping frequencies and aspect ratio.

Coherent emission of atomic soliton pairs by Feshbach-resonance tuning

We present two simple designs of matter-wave beam splitters in a trapped Bose-Einstein Condensate (BEC). In our scheme, identical pairs of atomic solitons are produced by an adequate control --- in time and/or space --- of the scattering length. Our analysis is performed by numerical integration of the Gross-Pitaevskii equation and supported by several analytic estimates. Our results show that these devices can be implemented in the frame of current BEC experiments. The system has potential applications for the construction of a soliton interferometer.

Homogeneous one-dimensional optical lattice generation using a digital micromirror device-based high-precision beam shaper

A homogeneous one-dimensional optical lattice is demonstrated by using a high-precision beam shaper based on a digital micromirror device (DMD) with an imaging system containing a pinhole low-pass filter (LPF). This system is capable of producing a high-quality flattop beam profile to form a standing-wave optical lattice with a 50×50 μm2 flattop region. The periodic potential generated by the optical lattice confines ultracold atoms in Bose-Einstein condensate experiments. We conducted beam shaping tests at several wavelengths by implementing various coherent and incoherent light sources in the visible and infrared wavelength ranges. Experiments produced flattop and other well-controlled beam profiles with 0.2% to 0.26% root-mean-square (RMS) error after applying a digital LPF and nearly flat phase. Several concerns for the system design are presented. First, the energy requirement was determined by power conversion analysis and DMD diffraction efficiency simulation. In addition, a LabVIEW program was written to accelerate the speed of the iterative process for beam profile refinement. Finally, various camera calibrations improved the measurement accuracy. We achieved a 1.25% RMS error flattop beam with diameter of 70.4 μm at the atoms' plane. Other beam profile measurements in different diagnostic planes demonstrated a good intensity uniformity of the optical lattice.

Statistical Physics of Bose-Einstein-Condensed Light in a Dye Microcavity

We theoretically analyze the temperature behavior of paraxial light in thermal equilibrium with a dye-filled optical microcavity. At low temperatures the photon gas undergoes Bose-Einstein condensation, and the photon number in the cavity ground state becomes macroscopic with respect to the total photon number. Owing to a grand-canonical excitation exchange between the photon gas and the dye molecule reservoir, a regime with unusually large fluctuations of the condensate number is predicted for this system that is not observed in present atomic physics Bose-Einstein condensation experiments.

Transition to a Bose–Einstein condensate and relaxation explosion of excitons at sub-Kelvin temperatures

Quasiparticles in quantum many-body systems have essential roles in modern physical problems. Bose–Einstein condensation (BEC) of excitons in semiconductors is one of the unobserved quantum statistical phenomena predicted in the photoexcited quasiparticles in many-body electrons. In particular, para-excitons in cuprous oxide have been studied for decades because the decoupling from the radiation field makes the coherent ensemble a purely matter-like wave. However, BEC has turned out to be hard to realize at superfluid liquid helium-4 temperatures due to a two-body inelastic collision process. It is therefore essential to set a lower critical density by further lowering the exciton temperature. Here we cool excitons to sub-Kelvin temperature and spatially confine them to realize the critical number for BEC. We show that BEC manifests itself as a relaxation explosion as has been discussed in atomic hydrogen. The results indicate that dilute excitons are purely bosonic and BEC indeed occurs.

Compression of Bright Bound Solitons in the Bose-Einstein Condensates with Exponentially Time-Dependent Atomic Scattering Length by the Feshbach Resonance

We investigate compression of the bright bound solitons in the Bose-Einstein condensates (BECs) by exponentially increasing the absolute value of the atomic scattering length. Similarity transformation and Hirota bilinear method are used to symbolically solve the one-dimensional nonlinear Schrodinger equation with the time-dependent coefficients. We present types of the bright bound solitons in compression through manipulating their initial coherence. Results show that the improved quantity of the atomic density peaks can be observed before the collapse of the solitons when their coherence is increased. Furthermore, we discuss how those compressed bound solitons are influenced by the adjacent solitons. The bound structures in our study are illustrated to exist with the parameters within the current experimental capacity (the spatial and temporal ranges of the bound solitons are less than 56 μm and 50 ms in our investigation), which suggests a future observation in the BECs experiments.

Dynamics of a cold atom cloud in an anharmonic trap

A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.

NUMERICAL SIMULATION OF QUANTUM STATE REDUCTION IN BOSE–EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS

Following an idea first proposed by Penrose in 1996 to explain the problem of quantum state reduction as a gravitational effect, Moroz, Penrose and Tod1 have shown that quantum state reduction due to gravitational interactions could take place in about one second for the case of 1011 nucleons. However, keeping 1011 nucleons together in a quantum macroscopic state does not appear to be feasible as yet. The closest physical system to such a situation is provided by Bose–Einstein condensates (BEC) with attractive interactions. We present numerical simulations of the Schrödinger–Newton equations, which show that an attractive BEC with 103 atoms would yield a decorrelation time of the order of 10-2 seconds. Hence, a "Penrose-like" reduction, induced by BEC attractive interaction instead of gravity, might be observable and possibly monitored in current BEC experiments with attractive interactions.

Quantum interference in the time-of-flight distribution

We propose a scheme to experimentally observe matter-wave interference in the time domain, specifically in the arrival time or time-of-flight (TOF) distribution for an atomic Bose–Einstein condensate (BEC) Schrödinger-cat state represented by superposition of macroscopically separated wave packets in space. This is in contrast to interference in space at a fixed time observed in the reported BEC experiments. We predict and quantify the quantum interference in the TOF distribution calculated from the modulus of the quantum probability current density (rather than the TOF distributions obtained from a purely classical or semi-classical treatment in many reported experiments). The interference and hence the coherence in the quantum TOF signal disappears in the large-mass limit. Our scheme has the potential to probe the validity of various other theoretical approaches (Muga and Leavens 2000 Phys. Rep. 338 353) of calculating the quantum arrival time distribution.

The Lieb–Liniger model in the infinite coupling constant limit

We consider the one-dimensional Lieb–Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks–Girardeau model). This model might be relevant as a description of atomic Bose gases confined in a one-dimensional geometry. It is known to have a fermionic spectrum since the N-body wavefunctions have to vanish at coinciding points, and therefore be symmetrizations of fermionic Slater wavefunctions. We argue that in the infinite coupling constant limit the model is indistinguishable from free fermions, i.e. all physically accessible observables are the same as those of free fermions. Therefore, Bose–Einstein condensate experiments under conditions that preserve the one-dimensional geometry and strong contact interactions cannot test any bosonic characteristic of such a system.

Engineering integrable nonautonomous nonlinear Schrödinger equations

We investigate Painlevé integrability of a generalized nonautonomous one-dimensional nonlinear Schrödinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painlevé analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the constraint conditions are identified. It provides an explicit way to engineer integrable nonautonomous NLS equations at least in the sense of Painlevé integrability. Furthermore analytical solutions of this class of integrable nonautonomous NLS equations can be obtained explicitly from the solutions of the standard NLS equation by a general transformation. The result provides a significant way to control coherently the soliton dynamics in the corresponding nonlinear systems, as that in Bose-Einstein condensate experiments. We analyze explicitly the soliton dynamics under the nonlinearity management and the external potentials and discuss its application in the matter-wave dynamics. Some comparisons with the previous works have also been discussed.

Number filter for matter waves

In current Bose-Einstein condensate experiments, the shot-to-shot variation of the atom number fluctuates up to 10%. In here, we present a procedure to suppress such fluctuations by using a nonlinear $p\ensuremath{-}\ensuremath{\pi}\ensuremath{-}\overline{p}$ matter wave interferometer for a Bose-Einstein condensate with two internal states and a high beam-splitter asymmetry $(p\ensuremath{\ne}0.5)$. We analyze the situation for an inhomogeneous trap within the Gross-Pitaevskii mean-field theory, as well as a quantum mechanical Josephson model, which addresses complementary aspects of the problem and agrees well otherwise.

Multi-component vortex solutions in symmetric coupled nonlinear Schrödinger equations

A Hamiltonian system of incoherently coupled nonlinear Schrodinger (NLS) equations is considered in the context of physical experiments in photorefractive crystals and Bose-Einstein condensates. Due to the incoherent coupling, the Hamiltonian system has a group of various symmetries that include symmetries with respect to gauge transformations and polarization rotations. We show that the group of rotational symmetries generates a large family of vortex solutions that generalize scalar vortices, vortex pairs with either double or hidden charge, and coupled states between solitons and vortices. Novel families of vortices with different frequencies and vortices with different charges at the same component are constructed and their linearized stability problem is block-diagonalized for numerical analysis of unstable eigenvalues.

Influence of the Radio-Frequency source properties on RF-based atom traps

We discuss the quality required for the RF source used to trap neutral atoms in RF-dressed potentials. We illustrate this discussion with experimental results obtained on a Bose-Einstein condensation experiment with different RF sources.

Active cancellation of stray magnetic fields in a Bose-Einstein condensation experiment

A method of active field cancellation is described, which greatly reduces the stray magnetic field within the trap region of a Bose-Einstein condensation experiment. An array of six single-axis magnetic sensors is used to interpolate the field at the trap center, thus avoiding the impractical requirement of placing the sensor within the trap. The system actively suppresses all frequencies from dc to approximately 3000 Hz, and the performance is superior to conventional active Helmholtz cancellation systems. A method of reducing the field gradient, by driving the six Helmholtz coils independently, is also investigated.

A double magneto-optical trap system using a slow atomic beam for atom transfer

A rubidium double magneto-optical trap(MOT) system for Bose-Einstein condensation experiments has been set up. A slow atomic beam has been obtained with a low-velocity intense source (LVIS) and used to transfer atoms into an ultra-high-vacuum (UHV) MOT. By maintaining a pressure difference of 3 orders between LVIS-MOT and UHV-MOT, a lowest pressure of 1×10-9Pa can be achieved in UHV-MOT. The flux of the slow atomic beam is 1×109/s. About 4×108 87Rb atoms can be loaded into UHV-MOT. In this paper, maximum number of atoms captured in MOTs under two typical conditions have also been discussed.