Bulletin of the American Physical Society
46th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics
Volume 60, Number 7
Monday–Friday, June 8–12, 2015; Columbus, Ohio
Session T3: Quantum Gases in Low Dimensions |
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Chair: Jason Nguyen, Rice University Room: Franklin AB |
Friday, June 12, 2015 8:00AM - 8:12AM |
T3.00001: Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential Jesper Levinsen, Pietro Massignan, Georg Bruun, Meera Parish The one-dimensional (1D) Fermi gas with repulsive short-range interactions provides an important model of strong correlations and is often amenable to exact methods. However, in the presence of confinement, no exact solution is known for an arbitrary number of strongly interacting fermions. Here, we propose a novel ansatz for generating the lowest-energy wavefunctions of the repulsive 1D Fermi gas in a harmonic potential near the Tonks-Girardeau limit of infinite interactions. We specialize to the case of a single $\downarrow$ particle interacting with $N_\uparrow$ particles, where we may derive analytic forms of the approximate wavefunctions. Comparing with exact numerics, we show that the overlap between the wavefunctions from our ansatz and the exact ones in the ground-state manifold exceeds $0.9997$ for $N_\uparrow\leq8$. Moreover, the overlap for the ground-state wavefunction at strong repulsion extrapolates to $\sim0.9999$ as $N_\uparrow\to\infty$. Thus, our ansatz is essentially indistinguishable from ``numerically exact'' results in both the few- and many-body limits. [Preview Abstract] |
Friday, June 12, 2015 8:12AM - 8:24AM |
T3.00002: Relaxation dynamics of the one-dimensional Bose gas via the coordinate Bethe ansatz Matthew Davis, Jan Zill, Tod Wright, Karen Kheruntsyan, Thomas Gasenzer Recently there has been significant progress in understanding the nature of relaxation in closed quantum systems following a disturbance. Many of the theoretical results have been obtained through the study of models that can be mapped to non-interacting systems, or via approximate numerical methods. We instead utilise the symbolic evaluation of matrix elements between the coordinate Bethe-ansatz eigenstates of the Lieb-Liniger model to simulate quenches of the one-dimensional Bose gas for up to $N=5$ particles. We consider a range of scenarios, including quenches of the interaction strength to both repulsive and attractive values, and the application of momentum kicks in analogy to the quantum Newton's cradle experiment of Kinoshita~\emph{et al.}, Nature~\textbf{440}, 900 (2006). Our approach allows us to compare the time-evolving nonequilibrium correlation functions to their diagonal-ensemble (infinite-time-average) values. We find evidence of relaxation to the diagonal ensemble following a quench to repulsive interactions, and most of our results for relaxed-state correlations agree with recent generalized thermodynamic Bethe-ansatz calculations. However, our results for local third-order correlations differ markedly from the predictions of these generalized ensembles. [Preview Abstract] |
Friday, June 12, 2015 8:24AM - 8:36AM |
T3.00003: Momentum Distributions of 1D Bose Gases Lin Xia, Joshua M. Wilson, Laura A. Zundel, Wei Xu, Marcos Rigol, David S. Weiss Although the many-body wave functions of 1D Bose gases with $\delta $-function interacting can be exactly calculated, it has been a theoretical challenge to extract their momentum distributions at intermediate coupling strengths. We will present precise measurements of 1D Bose gas momentum distributions in the strong and intermediate coupling regimes, and compare them to new theory calculations. We will emphasize our sensitivity to the predicted p$^{-4}$ tail, and the sensitivity of the results to excitations out of the many-body ground state. [Preview Abstract] |
Friday, June 12, 2015 8:36AM - 8:48AM |
T3.00004: Novel phase-space Monte-Carlo method for quench dynamics in 1D and 2D spin models Alexander Pikovski, Johannes Schachenmayer, Ana Maria Rey An important outstanding problem is the effcient numerical computation of quench dynamics in large spin systems. We propose a semiclassical method to study many-body spin dynamics in generic spin lattice models. The method, named DTWA, is based on a novel type of discrete Monte-Carlo sampling in phase-space. We demonstare the power of the technique by comparisons with analytical and numerically exact calculations. It is shown that DTWA captures the dynamics of one- and two-point correlations 1D systems. We also use DTWA to study the dynamics of correlations in 2D systems with many spins and different types of long-range couplings, in regimes where other numerical methods are generally unreliable. Computing spatial and time-dependent correlations, we find a sharp change in the speed of propagation of correlations at a critical range of interactions determined by the system dimension. The investigations are relevant for a broad range of systems including solids, atom-photon systems and ultracold gases of polar molecules, trapped ions, Rydberg, and magnetic atoms. [Preview Abstract] |
Friday, June 12, 2015 8:48AM - 9:00AM |
T3.00005: Sudden expansion of the Lieb-Liniger gas from power-law traps Karen Kheruntsyan, A.S. Campbell, D.M. Gangardt We study free expansion of an interacting one-dimensional Bose gas (described, in the uniform limit, by the integrable Lieb-Liniger model) in a confinement quench scenario of being suddenly released from the ground state of the trapping potential. We consider the general case of power-law traps and, by using the stationary phase and local density approximations, show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the thermodynamic Bethe ansatz equations. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the known scaling solutions of the hydrodynamic approach corresponding to self-similar expansion. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the shape variation of the density profile during the evolution on the trap anharmonicity. We also characterize dynamical fermionization of an expanding cloud in terms of its first- and second-order coherences describing phase and density fluctuations. [A. S. Campbell, D. M. Gangardt, and K. V. Kheruntsyan, arXiv:1501.01896]. [Preview Abstract] |
Friday, June 12, 2015 9:00AM - 9:12AM |
T3.00006: Unification of BKT and BEC Phase Transitions in a Trapped Two-Dimensional Bose Gas Richard Fletcher, Martin Robert-de-Saint-Vincent, Jay Man, Nir Navon, Robert Smith, Konrad Viebahn, Zoran Hadzibabic We study the critical point for the emergence of coherence in a harmonically trapped two-dimensional (2d) Bose gas with tuneable interactions. Over a wide range of interaction strengths we find excellent agreement with predictions based on the Berezinskii-Kosterlitz-Thouless (BKT) theory of 2d superfluidity. This allows us to quantitatively show, without any free parameters, that the interaction-driven BKT transition smoothly converges onto the purely statistical Bose-Einstein condensation (BEC) transition in the limit of vanishing interactions. [Preview Abstract] |
Friday, June 12, 2015 9:12AM - 9:24AM |
T3.00007: The Phases of an Interacting Spin-1/2 Fermi Gas as seen from a New Variational Ansatz Sangwoo Chung, Kuei Sun, Carlos Bolech Since its introduction, the continuous matrix product states (cMPS) have demonstrated success in predicting low energy properties of repulsive one-dimensional (1D) Bose gas systems. We have extended those efforts to nonrelativistic fermions and shown that the cMPS, moreover, is able to correctly describe the ground-state superfluid and magnetic properties of interacting Fermi gases in 1D. This includes the signatures of a partially polarized superfluid regime, in agreement with the large amount of theoretical and experimental work from recent years by the cold-atoms community. The new type of ansatz promises to be ideally posed to be able to describe atomic gases in optical lattices economically but without making a lattice-model (tight-binding) approximation. [Preview Abstract] |
Friday, June 12, 2015 9:24AM - 9:36AM |
T3.00008: Polaron Thermodynamics of Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases Willie Ong, Chingyun Cheng, Ilya Arakelyan, John Thomas We present the first spatial profile measurements for spin-imbalanced mixtures of atomic $^6$Li fermions in a quasi-2D geometry with tunable strong interactions. The observed minority and majority profiles are not correctly predicted by BCS theory for a true 2D system, but are reasonably well fit by a 2D-polaron model of the free energy. Density difference profiles reveal a flat center with two peaks at the edges, consistent with a fully paired core of the corresponding 2D density profiles. These features are more prominent for higher interaction strengths. Not predicted by the polaron model is an observed transition from a spin-imbalanced normal fluid phase to a spin-balanced central core above a critical imbalance. [Preview Abstract] |
Friday, June 12, 2015 9:36AM - 9:48AM |
T3.00009: Kinematics and Thermodynamics of an Interacting 2D Fermi Gas Paul Dyke, Kristian Fenech, Tyson Peppler, Marcus Lingham, Sascha Hoinka, Chris Vale Ultracold gases of fermionic atoms have become an important paradigm for studying many-body quantum phenomena. One example is a two-component 2D ultracold Fermi gas with tunable interactions that will allow the study of the Bardeen-Schrieffer-Cooper to Berzinskii-Kosterlitz-Thouless superfluid crossover. To effectively investigate this area we need to establish the conditions for which an interacting Fermi gas subject to tight transverse confinement behaves kinematically 2D. We will present results that indicate both a geometric and interaction driven departure from the 2D regime as the atom number and interaction strength are varied, allowing us to identify the regime where interacting systems are kinematically 2D. This provides the parameter range where we investigate the 2D equation of state (EoS) where all atoms are confined to the transverse ground state. We adapt a scheme previously used for the 3D unitary Fermi gas and 2D Bose gas to obtain the density EoS and other thermodynamical variables. [Preview Abstract] |
Friday, June 12, 2015 9:48AM - 10:00AM |
T3.00010: Quasi-1D Superfluids In A Spin-Imbalanced Fermi Gas Melissa C. Revelle, Ben A. Olsen, Jacob A. Fry, Randall G. Hulet We experimentally study the phases of an ultracold two-spin component gas of atomic fermions ($^{6}$Li) confined to 1D tubes formed by a 2D optical lattice. The atoms are prepared in the lowest two hyperfine sublevels where their interactions are tuned by a Feshbach resonance. We previously observed phase separation into a partially-polarized superfluid core and either fully-paired or fully-polarized wings (depending on the spin polarization).\footnote{Y.A. Liao et al., Nature 467, 567 (2010).} In 3D, the phase separation is inverted, such that the cloud center is fully paired.\footnote{G. B. Partridge et al., Science 311, 503 (2006); Y. Shin et al., Phys. Rev. Lett. 97, 030401 (2006).} We investigate the transition from a 1D to 3D gas by varying the lattice depth and interaction strength which changes the ratio of the tunneling rate between the tubes to the pair binding energy. The region of parameter space we are exploring is believed to be the most promising region for the exotic FFLO superfluid phase.\footnote{M. Parish et al., PRL 99, 250403 (2007).} [Preview Abstract] |
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