Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session P50: Quenched Atomic Systems and Thermalization |
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Sponsoring Units: DAMOP Chair: Mohammad Maghrebi, Joint Quantum Institute, University of Maryland Room: Hilton Baltimore Holiday Ballroom 1 |
Wednesday, March 16, 2016 2:30PM - 2:42PM |
P50.00001: Prethermalization and exponentially slow energy absorption in periodically driven many-body systems Dmitry Abanin, Wen Wei Ho, Wojciech De Roeck, Francois Huveneers We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian $H_*$ up to time $\tau_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $t< \tau_*$, eventually heating up to an infinite-temperature state at times $t\sim \tau_*$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for cold atoms experiments which realize topological states by periodic driving. [Preview Abstract] |
Wednesday, March 16, 2016 2:42PM - 2:54PM |
P50.00002: Universal aspects of thermalization after a quantum quench James R. Garrison, Tarun Grover A very fundamental problem in quantum statistical mechanics involves whether---and how---an isolated quantum system will thermalize at long times. The Eigenstate Thermalization Hypothesis (ETH) posits that when thermalization occurs, it occurs at the level of each individual energy eigenstate. In recent work [1], we examined an isolated quantum system that obeys ETH and identified the precise class of operators for which ETH is satisfied. Here, we use similar techniques to study the more general case of a time-evolved system after a quantum quench. Given a ``typical'' initial state, we investigate the class of operators that thermalize and the associated time scales, and remark on the similarities and differences compared with a single eigenstate at finite energy density. Possible experimental implications will be discussed. [1] J. R. Garrison and T. Grover, arXiv:1503.00729. [Preview Abstract] |
Wednesday, March 16, 2016 2:54PM - 3:06PM |
P50.00003: Short- and long-time dynamics of isolated many-body quantum systems Marco Tavora, Jonathan Torres-Herrera, Lea Ferreira dos Santos We show our results for the relaxation process of isolated interacting quantum spin chains in the integrable and chaotic regimes. The dynamics of the survival probability (the probability for finding the system still in its initial state at later times) and of few-body observables are analyzed. Different time scales are considered. While the short-time evolution is determined by the shape of the weighted energy distribution of the initial state, the long-time behavior depends on the bounds of the spectrum.~ Both numerical and analytical results are presented as well as comparisons with existing rigorous mathematical derivations. We consider initial states that can be prepared in experiments with cold atoms in optical lattices. [Preview Abstract] |
Wednesday, March 16, 2016 3:06PM - 3:18PM |
P50.00004: Temperature of a small quantum system as an internal property Jiaozi Wang, Wenge Wang Equilibration of small quantum systems is a topic of current interest both theoretically and experimentally. In this work, we study the extent to which a temperature can be assigned to a small quantum (chaotic) system as an internal property, but not as a property of any large environment. Specifically, we study a total system, which is composed of an Ising chain in a nonhomogeneous transverse field and an additional spin coupled to one of the spins in the chain. The additional spin can be used as a probe to detect local temperature of the chain. The total system lies in a pure state under unitary evolution and initial state of the chain is prepared in a typical state within an energy shell. Our numerical simulations show that the reduced density matrix of the probe spin approaches canonical states with similar temperatures at different locations of the chain beyond a relaxation time, and the results are close to the theoretical prediction given by the statistical mechanics in the thermodynamic limit, namely $\beta=\frac{\partial\ln\rho(E)}{\partial E}$ with $\rho(E)$ being the density of states. We also study effects due to finite size of the chain, including the dependence on initial state of the probe and difference of numerically-obtain temperature from theoretical results. [Preview Abstract] |
Wednesday, March 16, 2016 3:18PM - 3:30PM |
P50.00005: Temporal fluctuations after a quantum quench: Many-particle dephasing Florian Marquardt, Thomas Kiendl After a quantum quench, the expectation values of observables continue to fluctuate in time. In the thermodynamic limit, one expects such fluctuations to decrease to zero, in order for standard statistical physics to hold. However, it is a challenge to determine analytically how the fluctuations decay as a function of system size. So far, there have been analytical predictions for integrable models (which are, naturally, somewhat special), analytical bounds for arbitrary systems, and numerical results for moderate-size systems. We have discovered a dynamical regime where the decrease of fluctuations is driven by many-particle dephasing, instead of a redistribution of occupation numbers. On the basis of this insight, we are able to provide exact analytical expressions for a model with weak integrability breaking (transverse Ising chain with additional terms). These predictions explicitly show how fluctuations are exponentially suppressed with system size. [Preview Abstract] |
Wednesday, March 16, 2016 3:30PM - 3:42PM |
P50.00006: Persistent Hall response after a quantum quench in Dirac systems Justin Wilson, Justin Song, Gil Refael The geometry and topology of quantum states play a central role in producing novel types of responses, such as the quantum anomalous Hall effect. These have featured prominently in topological materials in equilibrium as well as driven systems in the steady state. Here we unveil how quantum geometry yields radically new types of responses in systems far from equilibrium such as that realized in a quantum quench. To illustrate this, we consider quenches of two-band systems with spin-orbit coupling (e.g. Dirac systems). We find that quenching a time-reversal broken gap gives a Hall-type response that persists even at long times. Intimately tied to the quantum geometry of the underlying Hilbert space, the unconventional persistent Hall response yield clear signatures in quench protocols that can be implemented in cold atoms set-ups. [Preview Abstract] |
Wednesday, March 16, 2016 3:42PM - 3:54PM |
P50.00007: Quantum Quenches in Arrays of Coupled Luttinger Liquids Andrew James, Andrew Hallam, Robert Konik, Andrew Green Cold atom realisations of one dimensional interacting bosonic models are typically formed as large arrays of decoupled tubes. A low energy description of the individual tubes (including the Lieb-Liniger case) is provided by Luttinger liquid theory. Using matrix product state methods combined with integrability, we study the time evolution of an infinite array of coupled Luttinger Liquids, after a quantum quench in which \emph{interchain} tunnelling is switched on to form a 2D system. We extract the time dependence of the density, bosonic modes, the Loschmidt echo and the entanglement entropy and consider possible implications for phase transitions in the coupled chain system. Our results are compared to perturbation theory and contrasted with simulations for coupled arrays of massive chains. [Preview Abstract] |
Wednesday, March 16, 2016 3:54PM - 4:06PM |
P50.00008: Melting of a spin domain wall in the context of recent experiments with ultracold atoms Lev Vidmar, Deepak Iyer, Marcos Rigol When a one-dimensional spin domain wall of the form \textbar up \textellipsis up up down down \textellipsis down\textgreater is melting, transverse spin correlations in the XX model exhibit a power-law decay in the melted region. This model can be mapped to hard-core bosons via Jordan-Wigner transformation. For hard-core bosons, these emerging power-law correlations correspond to singularities in the quasimomentum distribution at finite quasimomenta $+$/- pi/2, resulting in a dynamical quasicondensation with the emerging phase order different from the ground-state order. This phenomenon has been recently observed experimentally with ultracold bosons in optical lattices [1]. Here we study the emergence of correlations in melting domain walls for hard-core bosons, spinless fermions and the Fermi-Hubbard model at infinite onsite repulsion. In all cases, the density dynamics exhibit identical ballistic expansion, while the correlations show strikingly different features. References: [1] Vidmar et al, PRL 115, 175301 (2015) [Preview Abstract] |
Wednesday, March 16, 2016 4:06PM - 4:18PM |
P50.00009: Spatio-temporal correlations after a quantum quench in the Bose-Hubbard model Matthew Fitzpatrick, Malcolm Kennett The quench dynamics of the Bose-Hubbard model (BHM) has received considerable attention in recent years. Theoretically, it has proven challenging to study spatio-temporal correlations in the BHM in dimensions higher than one. We use the Schwinger-Keldysh technique and a strong-coupling expansion to develop a two-particle irreducible formalism that allows the study of spatio-temporal correlations in both the superfluid (SF) and Mott-insulating (MI) regimes during a quantum quench for dimensions higher than one. In this talk, we focus on quenches from the SF to the MI regime and present our numerical results for the evolution of two-time correlation functions. We relate our results to recent cold-atom experiments. [Preview Abstract] |
Wednesday, March 16, 2016 4:18PM - 4:30PM |
P50.00010: Entanglement dynamics after a quantum quench in the O(N) model Yonah Lemonik, Aditi Mitra The entanglement properties of quenched quantum systems is an active area of study, however results in dimensions other than $d=1$ are generally lacking. We remedy this by investigating the entanglement properties after a critical quench in the bosonic O(N) model in $d=3$, comparing our results to the free massless theory. We find that the evolution of the entanglement entropy for the free and interacting systems is nearly identical, as expected from a "quasi-particle" picture. However, the low-lying entanglement spectrum is controlled by the different non-equilibrium critical exponents of these two systems. Therefore we demonstrate that these critical exponents can be extracted by studying purely the entanglement in the system. [Preview Abstract] |
Wednesday, March 16, 2016 4:30PM - 4:42PM |
P50.00011: Quench dynamics of 1D spin-imbalanced Fermi-Hubbard model Xiao Yin, Leo Radzihovsky We study a non-equilibrium dynamics of a 1D spin-imbalanced Fermi-Hubbard model following a quantum quench of on-site interaction, using bosonization and exact analysis. By focusing on the evolution of singlet-, triplet-, density and magnetization correlation functions, we find that the evolution and the final state display a strong dependence on the initial state. Thus, we demonstrate that such quantum quench may be used as a new approach to identify and probe the 1D gapless analogue of the elusive FFLO state. [Preview Abstract] |
Wednesday, March 16, 2016 4:42PM - 4:54PM |
P50.00012: Quenched dynamics of superconducting Dirac fermions on honeycomb lattice Ming Lu, X. C. Xie We study the BCS paring dynamics for the superconducting Dirac fermions on honeycomb lattice after a sudden quench of pairing strength. We observe two distinct phases, one is the synchronized phase with undamped oscillations of paring amplitude; the other phase has the paring amplitude oscillates from positive to negative. The exact phase transition point is given by investigating the integrability of the system. Different from the previous work on normal superconducting fermions, which has three distinct phases, our results shows the absence of the Landau damped phase and over damped phase. Moreover, we present a linear analysis in the weakly quenched regime, showing that in a rather long time scale, the dynamics can be approximated as the periodic oscillation with $2\Delta_\infty$ angular frequency along with the logarithmic decay of the pairing amplitude, in contrast of the $t^{-1/2}$ decay for the normal fermions, namely the Landau damped phase. [Preview Abstract] |
Wednesday, March 16, 2016 4:54PM - 5:06PM |
P50.00013: Preparation of Bose Einstein condensates in realistc trapping potentials for precision atom interferometry Katerine Posso Trujillo, Ernst M. Rasel, Naceur Gaaloul Preparation of Bose Einstein condensates in realistc trapping potentials for precision atom interferometry Theoretical studies of the ground state and the dynamical properties of Bose Einstein condensates (BECs) are typically realized by considering the ensemble as being initiaally trapped by a harmonic potential. Dramatic discrepancies were found by comparing numerical results of the long-time expansion of BECs after being released from the harmonic trap, and measurements of the free evolution and delta-kick cooling (DKC) of a $^{87}$Rb BEC on large timescales of up to 2 s in micro-gravity (micro-g) environment such as those performed in the QUANTUS project from our group [1]. The modification in the dynamics of a $^{87}$Rb BEC with the application of DKC by using experimentally implemented trapping geometries and the effect of gravity have been studied. Three different configurations have been considered: atom chip-based potential, dipole trap and the time-averaged orbiting potential. Such discrepancies may be crucial in high precision atom interferometry experiments in micro-g and zero-g platforms in which the implementation of DKC is mandatory to achieve the long-expansion times required. [1] H. Müntinga et al., Phys. Rev. Lett. vol. 110 093602 (2013). [Preview Abstract] |
Wednesday, March 16, 2016 5:06PM - 5:18PM |
P50.00014: Memory effects in noninteracting isolated systems from dynamical geometry transformations in ultracold quantum gases Chen-Yen Lai, Chin-Chun Chien Memory effects have been of broad interest and particularly relevant in condensate matter systems where dynamical properties depend on history. Here we explore possibilities of observing memory effects in simple isolated quantum systems undergoing geometry transformations. By transforming into lattices supporting flat-bands consisting of localized states, memory effects could be observed in ultracold atoms in optical lattices due to different time scales of localized and mobile atoms. As an optical lattice is continuously transformed from a triangular lattice into a kagome or square lattice, the system reach a non-thermal quasi-steady state. In the absence of interactions and dissipations, the emergence of steady states are highly nontrivial and crucial in identifying memory effects unambiguously. Moreover, when the lattices transform from a triangular lattice into a kagome lattice with a flat band, history-dependent density distributions even in noninteracting systems can be observed in fermionic as well as bosonic systems. Rapid growth of cold atom technology and possibilities of various mechanisms for inducing memory effect promise interesting applications of novel quantum devices utilizing memory effect, especially in the thriving field of atomtronics. (arXiv:1510.08978) [Preview Abstract] |
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