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arXiv:1511.02690 · Annalen der Physik

Chaotic level mixing in a two‐band Bose‐Hubbard model

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

Published Feb 10, 2015• 2 citations
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Abstract

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

DOI
10.1002/andp.201400200

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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 an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A crossover between regular and quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the nonequilibrium dynamics of our many-body system in different parameter regimes.
We study a model for ultracold, spinless atoms in quasi-one-dimensional optical lattices and subjected to a tunable tilting force. Statistical tests are employed to quantitatively characterize the spectrum of the Floquet-Bloch operator of the system along the transition from the regular to the quantum chaotic regime. Moreover, we perturbatively include the coupling of the one-band model to the second energy band. This allows us to study the Landau-Zener interband tunneling within a truly many-body description of ultracold atoms. The distributions of the computed tunneling rates provide an independent and experimentally accessible signature of the regular-chaotic transition.
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.
We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the \npossibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analyzed in a \nframework of three-level model. We compute Landau–Zener probabilities for a linear sweep of the gate charge \nand investigate Rabi oscillations in a periodically driven three-level system under in- and off-resonance conditions. It was shown that the Landau–Zener probabilities reveal two different patterns: “step”- and “beats”-like \nbehaviors associated with the quantum interference effects. Control on these two regimes is provided by change \nof the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and finetuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels \nis forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. \nThis effect can be observed by measuring a population difference slowly varying in time between the states of \nthe Cooper-pair box characterized by the same parity
We present a cluster Gutzwiller mean-field study for ground states and time-evolution dynamics in the Bose-Hubbard ladder (BHL), which can be realized by loading Bose atoms in double-well optical lattices. In our cluster mean-field approach, we treat each double-well unit of two lattice sites as a coherent whole for composing the cluster Gutzwiller ansatz, which may remain some residual correlations in each two-site unit. For an unbiased BHL, in addition to conventional superfluid phase and integer Mott insulator phases, we find that there are exotic fractional insulator phases if the interchain tunneling is much stronger than the intrachain one. The fractional insulator phases cannot be found by using a conventional mean-field treatment based upon the single-site Gutzwiller ansatz. For a biased BHL, we find there appear single-atom tunneling and interaction blockade if the system is dominated by the interplay between the on-site interaction and the interchain bias. In the many-body Landau-Zener process, in which the interchain bias is linearly swept from negative to positive or vice versa, our numerical results are qualitatively consistent with the experimental observation [Nat. Phys. 7, 61 (2011)]. Our cluster bosonic Gutzwiller treatment is of promising perspectives in exploring exotic quantum phases and time-evolution dynamics of bosonic particles in superlattices.