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arXiv:1809.03532 · Physical Review A

Memory effects in a quasiperiodic Fermi lattice

F. Cosco, Sabrina Maniscalco

Published Nov 5, 2018• 11 citations
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Abstract

We investigate a system of fermions trapped in a quasiperiodic potential from an open quantum system theory perspective, designing a protocol in which an impurity atom (a two-level system) is coupled to a trapped fermionic cloud described by the noninteracting Aubry-Andr\'e model. The Fermi system is prepared in a charge-density-wave state before it starts its relaxation. In this work we focus our attention on the time evolution of the impurity in such an out-of-equilibrium environment and study whether the induced dynamics can be classified as Markovian or non-Markovian. We find how the localized phase of the Aubry-Andr\'e model displays evidence of strong and stable memory effects and can be considered as a controllable and robust non-Markovian environment.

DOI
10.1103/physreva.98.053608

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We investigate a system of fermions trapped in a quasiperiodic potential from an open quantum system theory perspective, designing a protocol in which an impurity atom (a two-level system) is coupled to a trapped fermionic cloud described by the noninteracting Aubry-Andr'e model. The Fermi system is prepared in a charge-density-wave state before it starts its relaxation. In this work we focus our attention on the time evolution of the impurity in such an out-of-equilibrium environment and study whether the induced dynamics can be classified as Markovian or non-Markovian. We find how the localized phase of the Aubry-Andr'e model displays evidence of strong and stable memory effects and can be considered as a controllable and robust non-Markovian environment.
In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andr\'e model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.
The dynamics of a one-dimensional two-component Fermi gas in the presence of a quasiperiodic optical lattice (OL) is investigated by means of a density functional theory approach. Inspired by the protocol implemented in recent cold-atom experiments---designed to identify the many-body localization transition---we analyze the relaxation of an initially prepared imbalance between the occupation number of odd and of even sites. For quasidisorder strength beyond the Anderson localization transition, the imbalance survives for long times, indicating the inability of the system to reach local equilibrium. The late-time value of the imbalance diminishes for increasing interaction strength. Close to the critical quasidisorder strength corresponding to the noninteracting (Anderson) transition, the interacting system displays an extremely slow relaxation dynamics, consistent with subdiffusive behavior. The amplitude of the imbalance fluctuations around its running average is found to decrease with time, and such damping is more effective with increasing interaction strengths. While our study addresses the setup with two equally intense OLs, very similar effects due to interactions have been observed also in recent cold-atom experiments performed in the tight-binding regime, i.e., where one of the two OLs is very deep and the other is much weaker.
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing one to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realizable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of a superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.
We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.
The Fermi-edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and to the degree of the non-Markovian nature of its dynamics.