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arXiv:1203.4540 · Physical Review Letters

Interaction-Induced Impeding of Decoherence and Anomalous Diffusion

Dario Poletti, Jean-Sébastien Bernier, Antoine Georges, Corinna Kollath

Published Jul 24, 2012• 125 citations
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Abstract

We study how the interplay of dissipation and interactions affects the dynamics of a bosonic many-body quantum system. In the presence of both dissipation and strongly repulsive interactions, observables such as the coherence and the density fluctuations display three dynamical regimes: an initial exponential variation followed by a power-law regime, and finally a slow exponential convergence to their asymptotic values. These very long-time scales arise as dissipation forces the population of states disfavored by interactions. The long-time, strong coupling dynamics are understood by performing a mapping onto a classical diffusion process displaying non-Brownian behavior. While both dissipation and strong interactions tend to suppress coherence when acting separately, we find that strong interaction impedes the decoherence process generated by the dissipation.

DOI
10.1103/physrevlett.109.045302

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We study how the interplay of dissipation and interactions affects the dynamics of a bosonic many-body quantum system. In the presence of both dissipation and strongly repulsive interactions, observables such as the coherence and the density fluctuations display three dynamical regimes: an initial exponential variation followed by a power-law regime, and finally a slow exponential convergence to their asymptotic values. These very long-time scales arise as dissipation forces the population of states disfavored by interactions. The long-time, strong coupling dynamics are understood by performing a mapping onto a classical diffusion process displaying non-Brownian behavior. While both dissipation and strong interactions tend to suppress coherence when acting separately, we find that strong interaction impedes the decoherence process generated by the dissipation.
We study the dynamics of bosonic atoms in a double well potential under the influence of dissipation. The main effect of dissipation is to destroy quantum coherence and to drive the system towards a unique steady state. We study how the atom-atom interaction affects the decoherence process. We use a systematic approach considering different atomic densities. We show that, for two atoms, the interaction already strongly suppresses decoherence: a phenomenon we refer to as "interaction impeded decoherence". For many atoms, thanks to the increased complexity of the system, the nature of the decoherence process is dramatically altered giving rise to an algebraic instead of exponential decay.
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular, we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are due here to strong interactions. This complex two-stage dynamics reveals information on the level structure of the strongly interacting gas.
Recent experimental and theoretical efforts have focused on the effect of dissipation on quantum many-body systems in their many-body localized (MBL) phase. While in the presence of dephasing noise such systems reach a unique ergodic state, their dynamics is characterized by slow relaxation manifested in nonexponential decay of self-correlations. Here we shed light on a currently much debated issue, namely, the role of interactions for this relaxation dynamics. We focus on the experimentally relevant situation of the evolution from an initial charge density wave in the presence of strong dephasing noise. We find a crossover from a regime dominated by disorder to a regime dominated by interactions, with an accompanying change of time correlators from stretched exponential to compressed exponential form. The strongly interacting regime can be explained in terms of nucleation and growth dynamics of relaxing regions---reminiscent of the kinetics of crystallization in soft matter systems---and should be observable experimentally. This interaction-driven crossover suggests that the competition between interactions and noise gives rise to a much richer structure of the MBL phase than anticipated so far.
We use two-time correlation functions to study the complex dynamics of dissipative many-body quantum systems. In order to measure, understand, and categorize these correlations we extend the framework of the adiabatic elimination method. We show that, for the same parameters and times, two-time correlations can display two distinct behaviors depending on the observable considered: a fast exponential decay or a much slower dynamics. We exemplify these findings by studying strongly interacting bosons in a double well subjected to phase noise. While the single-particle correlations decay exponentially fast with time, the density-density correlations display slow aging dynamics. We also show that this slow relaxation regime is robust against particle losses. Additionally, we use the developed framework to show that the dynamic properties of dissipatively engineered states can be drastically different from their Hamiltonian counterparts.
We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.