Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session A35: Low-Dimensional and Non-Equilibrium Physics in Quantum Gases |
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Sponsoring Units: DAMOP Chair: David Pekker, University of Pittsburgh Room: 210B |
Monday, March 2, 2015 8:00AM - 8:12AM |
A35.00001: Non-equilibrium dynamics of an impurity in the one-dimensional Bose gas Neil Robinson, Robert Konik In recent years, the out-of-equilibrium dynamics of interacting many-body quantum systems have attracted much attention. Integrable quantum models have played an important role in understanding the role of local conservation laws in the relaxation of observables, explaining unusual experimental observations in the one-component Bose gas [1]. We study the non-equilibrium dynamics of ``impurity'' wave packets containing a single boson propagating in the one-component Bose gas. Utilizing the integrability of the multi-component Lieb-Liniger model and recent results from the algebraic Bethe ansatz [2], we compute the time-evolution of the density profile of the ``impurity'' in the cases where the bosons is of the same or different species as the background gas. Our method, based upon numerically solving the Bethe ansatz equations and evaluating the Lehmann spectral representation for local observables, allows us to reach long times with high numerical precision. By comparing results from the two-component Lieb-Liniger model to the one-component Bose gas we can comment on the role of distinguishability in the dynamics of impurities in integrable models.\\[4pt] [1] T. Kinoshita {\it et al.}, Nature {\bf 440}, 900 (2006).\\[0pt] [2] B. Pozsgay {\it et al.}, J. Phys. A {\bf 45}, 465007 (2012). [Preview Abstract] |
Monday, March 2, 2015 8:12AM - 8:24AM |
A35.00002: Quench dynamics of one-dimensional interacting bosons in a disordered potential: Elastic dephasing and critical speeding-up of thermalization Marco Tavora, Achim Rosch, Aditi Mitra The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. On time scales before quasiparticles scatter (prethermalized regime), the dephasing from random elastic forward scattering causes all correlations to decay exponentially fast, but the system remains far from thermal equilibrium. For longer times, the combined effect of disorder and interactions gives rise to inelastic scattering and to thermalization. A novel quantum kinetic equation accounting for both disorder and interactions is employed to study the dynamics. Thermalization turns out to be most effective close to the superfluid-Bose glass critical point where nonlinearities become more and more important. The numerically obtained thermalization times are found to agree well with analytic estimates. [Preview Abstract] |
Monday, March 2, 2015 8:24AM - 8:36AM |
A35.00003: Thermalisation of a quantum system from first principles Gregoire Ithier, Florent Benaych-Georges How does a quantum system reach thermodynamical equilibrium? Answering such a question from first principles is, perhaps surprisingly, still an open issue (Popescu Nat. Phys. 2006, Goldstein PRL 2006, Genway PRL 2013). We present here a new model comprising an arbitrary quantum system interacting with a large arbitrary quantum environment, both initially prepared in a quantum pure state. We then demonstrate that thermalisation is an emergent property of the unitary evolution under a Schr\"{o}dinger equation of this large composite system. The key conceptual tool of our method is the phenomenon of ``measure concentration'' appearing with functions defined on large dimension Hilbert spaces, a phenomenon which cancels out any effect of the microscopic structure of interaction Hamiltonians. Using our model, we first characterize the transient evolution or decoherence of the system and show its universal character. We then focus on the stationary regime and recover the canonical state well known from statistical thermodynamics. This finding leads us to propose an alternative and more general definition of the canonical partition function, that includes, among other things, the possibility of describing partial thermalisation. [Preview Abstract] |
Monday, March 2, 2015 8:36AM - 8:48AM |
A35.00004: ABSTRACT WITHDRAWN |
Monday, March 2, 2015 8:48AM - 9:00AM |
A35.00005: Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit Fabian Heidrich-Meisner, Lode Pollet, Stefan Sorg, Lev Vidmar We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling [1]. The same interaction quench was realized in a recent experiment [2]. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. \newline\noindent [1] Sorg et al., PRA 90, 033606 (2014)\newline [2] Ronzheimer et al., PRL 110, 205301 (2013) [Preview Abstract] |
Monday, March 2, 2015 9:00AM - 9:12AM |
A35.00006: Measuring time-dependent Greens Functions of strongly correlated gases in optical lattices Adrian Kantian, Ulrich Schollw\"ock, Thierry Giamarchi Recent advances in single-site addressing [1] in optical-lattice confined strongly correlated ultracold gases promise to deliver entirely new capabilities for these systems to serve as quantum simulators. We show how these advances may be employed to design in-situ measurements of both local and nonlocal time-dependent Greens functions as well as higher-order correlators. Using analytics side-by-side with time-dependent DMRG we quantify the practically available resolutions of these schemes - which can be applied for practically any 1D and 2D system of lattice-confined ultracold atoms - for several examples of interest, such as the mobile impurity problem [2] and the superfluid-Mott insulator transition. \\[4pt] [1] W. S. Bakr, et. al., Nature 462, 74 (2009); J. F. Sherson, et. al. Nature 467, 68 (2010).\\[0pt] [1] T. Fukuhara, et. al., Nat. Phys. 9, 235 (2013); [1] A. Kantian et. al., Phys. Rev. Lett. 113, 070601 (2014). [Preview Abstract] |
Monday, March 2, 2015 9:12AM - 9:24AM |
A35.00007: Entanglement entropy scaling laws and eigenstate thermalization in free fermion systems Hsin-Hua Lai, Kun Yang We demonstrate that the entanglement entropy area law for free fermion ground states and the corresponding volume law for highly excited states are related by a position-momentum duality, thus of the same origin. For a typical excited state in the thermodynamic limit, we further show that the reduced density matrix of a subsystem approaches thermal density matrix, provided the subsystem's linear size is small compared to that of the whole system in all directions. This provides an explicit example of eigenstate thermalization, and reveals how statistical physics emerges from a single eigenstate by tracing out a large number of degrees of freedom. [Preview Abstract] |
Monday, March 2, 2015 9:24AM - 9:36AM |
A35.00008: Particle partition entanglement of Luttinger liquids C.M. Herdman, Adrian Del Maestro We consider the R\'enyi entanglement entropy of a Luttinger liquid under a particle bipartition. Using Luttinger liquid theory, we demonstrate that the leading finite-size scaling of the second R\'enyi particle entanglement entropy is logarithmic in the system-size with a prefactor that is the inverse Luttinger parameter. While higher order corrections depend on the short distance physics, the leading order scaling depends only on the sole dimensionless parameter that characterizes the low energy physics; this contrasts with the leading entanglement entropy scaling under a spatial bipartition, for which the scaling coefficient is universal and independent of the Luttinger parameter. Additionally, using quantum Monte Carlo calculations, we explicitly confirm the Luttinger liquid theory scaling for the Lieb-Liniger model of delta function interacting bosons in the one-dimensional spatial continuum; we find that the scaling coefficient of the 2nd R\'enyi particle entropy of the ground state of the Lieb-Linger model agrees with the Luttinger parameter determined from the Bethe ansatz. [Preview Abstract] |
Monday, March 2, 2015 9:36AM - 9:48AM |
A35.00009: ABSTRACT WITHDRAWN |
Monday, March 2, 2015 9:48AM - 10:00AM |
A35.00010: ABSTRACT MOVED TO Y35.00008 |
Monday, March 2, 2015 10:00AM - 10:12AM |
A35.00011: 2D Superexchange mediated magnetization dynamics in an optical lattice R.C. Brown, R. Wyllie, S.B. Koller, E.A. Goldschmidt, M. Foss-Feig, J.V. Porto The competition of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study non-equilibrium magnetization dynamics in an extended 2D system by loading effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered state, we quench the lattice to its final configuration, and observe relaxation dynamics governed by two well-separated rates. These rates scale with the underlying Hamiltonian parameters associated with superexchange and tunneling. Remarkably, with tunneling off-resonantly suppressed, we are able to observe superexchange dominated dynamics over two orders of magnitude in magnetic coupling strength, despite the presence of vacancies. In this regime, the measured timescales are in agreement with simple theoretical estimates, but the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques. [Preview Abstract] |
Monday, March 2, 2015 10:12AM - 10:24AM |
A35.00012: Sound-induced vortex interactions in a zero temperature two-dimensional superfluid Piotr Surowka, Andrew Lucas Recent experimental work\footnote{T. W. Neely \textit{et al}., Physical Review Letters 111 235301 (2013).}\footnote{W. J. Kwon \textit{et al}., arXiv:1403.4658.} on two-dimensional turbulent superfluids have increased the importance of resolving fundamental theoretical questions about the nature of superfluid turbulence in two dimensions. Crucial to this task is a proper understanding of the effective dynamics of vortices in the superfluid. We present a systematic calculation of the effective action of $N > 1$ superfluid vortices, assuming that the underlying continuum action is the Gross-Pitaevskii action. Our calculation is valid at next-to-leading order in the ratio of the vortex core size to intervortex spacing, and so takes into account the leading-order dressing of superfluid vortices by sound. We are able to exactly determine the action for a pair of vortices and we find that it demonstrates no instability to annihilation. This is suggestive that the inverse cascade picture of classical turbulence is qualitatively correct for a turbulent zero temperature superfluid. [Preview Abstract] |
Monday, March 2, 2015 10:24AM - 10:36AM |
A35.00013: Decay of hydrodynamic modes in dilute Bose-Einstein condensates Erich Gust, Linda Reichl We present the results of Bogoliubov mean field theory [1] applied to the hydrodynamic modes in a dilute Bose-Einstein condensate. The condensate has six hydrodynamic modes, two of which are decaying shear modes related to the viscosity, and two pairs pairs of sound modes which undergo an avoided crossing as the equilibrium temperature is varied [2]. The two pairs of sound modes decay at very different rates, except in the neighborhood of the avoided crossing, where the identity of the longest-lived mode switches. The predicted speed and lifetime of the longest-lived sound mode are consistent with recent experimental observations on sound in an $^{87}$Rb Bose-Einstein condensate. The strong depedence of the decay rates on temperature implies a possible new method for determining the temperature of Bose-Einstein condensates. [1] L. E. Reichl and Erich D. Gust, Phys. Rev. A 88, 053603 (2013) [2] Erich D. Gust and L. E. Reichl, Phys. Rev. A 90, 043615 (2014) [Preview Abstract] |
Monday, March 2, 2015 10:36AM - 10:48AM |
A35.00014: ABSTRACT WITHDRAWN |
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