Two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system

Abstract

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 LandauZener processes can be engineered. A cross-over between regular to 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 non-equilibrium dynamics of our many-body system in different parameter regimes.

Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

“…Theoretical models based on Floquet's theorem are being developed to simulate systems in regimes otherwise inaccessible in conventional condensed matter materials [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . Experimentally, cold atoms' unique controllability was employed to observe dynamical localisation and phase-coherence in strongly shaken bosonic systems [19][20][21][22][23][24] .…”

Generation of robust entangled states in a non-Hermitian periodically driven two-band Bose-Hubbard system

“…The Hamiltonian might be seen as an infinite collection of tilted single-band Bose-Hubbard Hamiltonians, plus additional coupling terms between them. The coupling is mainly induced by the external force F , but also by the interparticle interaction characterized by the constant g [15]. Clearly, the force breaks the translational invariance of the flat lattice, therefore the Bloch band picture interpretation strictly speaking fails.…”

“…Following Ref. [15], we can argue, that in a doubly periodic optical lattice, we obtain situations in which the two lowest (mini)bands are sufficiently isolated from the upper bands, such that the assumptions just discussed are indeed fulfilled. Furthermore, we assume that only the upper band is effectively coupled to the higher bands.…”

“…1) and an entire zoo of single-and many-body processes to be identified and investigated in detail, see e.g. [13][14][15][16].…”

“…The effect of many-body interactions on the interband coupling was studied theoretically to great detail, in the weakly interacting limit [13] as well as in the context of strongly correlated Bose-Hubbard models [14][15][16]. The latter many-body models, however, restricted to two bands only and neglected the opening of the system arising from the coupling to higher lying energy bands.…”