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arXiv:1405.4163 · Physical Review A

Quantum diffusion and thermalization at resonant tunneling

Carlos A. Parra-Murillo, Javier Madroñero, Sandro Wimberger

Published May 9, 2014• 19 citations
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Abstract

Nonequilibrium dynamics and effective thermalization are studied in a resonant tunneling scenario via multilevel Landau-Zener crossings. Our realistic many-body system, composed of two energy bands, naturally allows a separation of degrees of freedom. This gives access to an effective temperature and single- and two-body observables to characterize the delocalization of eigenstates and the nonequilibrium dynamics of our paradigmatic complex quantum system.

DOI
10.1103/physreva.89.053610

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Nonequilibrium dynamics and effective thermalization are studied in a resonant tunneling scenario via multilevel Landau-Zener crossings. Our realistic many-body system, composed of two energy bands, naturally allows a separation of degrees of freedom. This gives access to an effective temperature and single- and two-body observables to characterize the delocalization of eigenstates and the nonequilibrium dynamics of our paradigmatic complex quantum system.
We study an experimentally realizable paradigm of a complex many-body quantum system, a twoband Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A clean cross-over between regular to quantum chaotic spectra is found within the many-level avoided crossings at resonant tunneling conditions. The spectral properties determine the evolution of states across a cascade of Landau-Zener events, which can be used to study diffusion and to dynamically prepare target states interesting for experimental applications.
A two‐band Bose‐Hubbard model is presented which is shown to be minimal in the necessary coupling terms at resonant tunneling conditions. The dynamics of the many‐body problem is studied by sweeping the system across an avoided level crossing. The linear sweep generalizes Landau‐Zener transitions from single‐particle to many‐body realizations. The temporal evolution of single‐ and two‐body observables along the sweeps is investigated in order to characterize the non‐equilibrium dynamics in our complex quantum system. image
We study the dynamical melting of hot one-dimensional quantum glasses. We focus on quantum glasses that emerge at strong disorder: specifically, many-body localized systems and their critical variants. The latter category includes disordered Ising, Potts, and anyonic chains whose excited-state properties and dynamics can be accessed via real-space renormalization group methods. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into a classical thermal liquid. By accounting for resonant tunneling of energy, we derive and solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport, crossing over to ordinary classical diffusion at asymptotically long length scales for critical glasses. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. For non-critical, many-body localized glasses, the crossover scale diverges and subdiffusion persists to the thermodynamic limit. Our approach provides a firm microscopic basis for understanding the generic structure of many-body delocalization transitions in one dimension, and also reveals a general scaling relation among the critical exponents of the transition.
Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.
We study stationary and dynamical properties of the many-body Landau-Zener dynamics of a Bose quantum fluid confined in two coupled one-dimensional chains by using a many-body generalization recently reported Chen et al. [Nature Phys. 7, 61 (2011)], within the decoupling approximation and the one-level band scheme. The energy spectrum shows evidence of the structure of the avoided level crossings as a function of the onsite interparticle interaction strength. On the dynamical side, a phase diagram of the transfer efficiency across ground-state and inverse sweeps is presented. A totally different scenario with respect to the original single-particle Landau-Zener scheme is found for ground-state sweeps, in which a breakdown of the adiabatic region emerges as the sweep rate decreases. On the contrary, the transfer efficiency across inverse sweeps reveals consistent results with the single-particle Landau-Zener predictions. In the strong-coupling regime, we find that there is a critical value of the onsite interaction for which the transfer of particles starts to vanish independently of the sweep rate. Our results are in qualitative agreement with those of the experimental counterpart.
Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model-in one and two dimensions-for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the nonequilibrium relaxation to it.