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arXiv:1610.06867 · Physical Review A

Quench-induced resonant tunneling mechanisms of bosons in an optical lattice with harmonic confinement

Georgios M. Koutentakis, S. I. Mistakidis, Peter Schmelcher

Published Jan 18, 2017• 37 citations
arXivHTMLPDF

Abstract

The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.

DOI
10.1103/physreva.95.013617

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The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.
We unravel the correlated nonequilibrium dynamics of a mass balanced Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong to weak confinement. Regarding the system's ground state, the competition between the inter- and intraspecies interaction strength gives rise to the immiscible and miscible phases characterized by negligible and complete overlap of the constituting atomic clouds, respectively. The resulting dynamical response depends strongly on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. For varying quench amplitude and referring to a fixed phase, a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels.
Abstract The nonequilibrium quantum dynamics of few boson ensembles which experience a spatially modulated interaction strength and are confined in finite optical lattices is investigated. We utilize a cosinusoidal spatially modulated effective interaction strength which is characterized by its wavevector, inhomogeneity amplitude, interaction offset and a phase. Performing quenches either on the wavevector or the phase of the interaction profile an enhanced imbalance of the interatomic repulsion between distinct spatial regions of the lattice is induced. Following both quench protocols triggers various tunneling channels and a rich excitation dynamics consisting of a breathing and a cradle mode. All modes are shown to be amplified for increasing inhomogeneity amplitude of the interaction strength. Especially the phase quench induces a directional transport enabling us to discern energetically, otherwise, degenerate tunneling pathways. Moreover, a periodic population transfer between distinct momenta for quenches of increasing wavevector is observed, while a directed occupation of higher momenta can be achieved following a phase quench. Finally, during the evolution regions of partial coherence are revealed between the predominantly occupied wells.
The correlated non-equilibrium dynamics of few-boson systems in one-dimensional finite lattices is investigated. Starting from weak interactions we perform a sudden interaction quench and employ the numerically exact multi-layer multi-configuration time-dependent Hartree method for bosons to obtain the resulting quantum dynamics. Focusing on the low-lying modes of the finite lattice we observe the emergence of density-wave tunneling, breathing and cradle-like processes. In particular, the tunneling induced by the quench leads to a 'global' density-wave oscillation. The resulting breathing and cradle modes are inherent to the local intrawell dynamics and connected to excited-band states. Moreover, the interaction quenches couple the density-wave and the cradle modes allowing for resonance phenomena. These are associated with an avoided-crossing in the respective frequency spectrum and lead to a beating dynamics for the cradle. Finally, complementing the numerical studies, an effective Hamiltonian in terms of the relevant Fock states is derived for the description of the spectral properties and the related resonant dynamics.
The correlated nonequilibrium quantum dynamics following a multiple interaction quench protocol for few-bosonic ensembles confined in finite optical lattices is investigated. The quenches give rise to an interwell tunneling and excite the cradle and a breathing mode. Several tunneling pathways open during the time interval of increased interactions, while only a few occur when the system is quenched back to its original interaction strength. The cradle mode, however, persists during and in between the quenches, while the breathing mode possesses distinct frequencies. The occupation of excited bands is explored in detail revealing a monotonic behavior with increasing quench amplitude and a nonlinear dependence on the duration of the application of the quenched interaction strength. Finally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Our results open the possibility to dynamically manipulate various excited modes of the bosonic system.
The nonequilibrium dynamics following a quench of strongly repulsive bosonic ensembles in one-dimensional finite lattices is investigated by employing interaction quenches and/or a ramp of the lattice potential. Both sudden and time-dependent quenches are analyzed in detail. For the case of interaction quenches we address the transition from the strong repulsive to the weakly interacting regime, suppressing in this manner the heating of the system. The excitation modes such as the cradle process and the local breathing mode are examined via local density observables. In particular, the cradle mode is inherently related to the initial delocalization and, following a negative interaction quench, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a negative quench of the lattice depth which favors the spatial delocalization is used to access the cradle mode for setups with filling smaller than unity. Our results shed light on possible schemes to control the cradle and the breathing modes. Finally, employing the notion of fidelity we study the dynamical response of the system after a diabatic or adiabatic parameter modulation for short and long evolution times. The evolution of the system is obtained numerically using the ab initio multilayer multiconfiguration time-dependent Hartree method for bosons, which permits us to follow nonequilibrium dynamics including the corresponding investigation of higher-band effects.
We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing-mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low-energy eigenspectrum of the trapped many-boson system and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a ``free-boson'' limit and a ``free-fermion'' limit, in which the Bose-Hubbard breathing-mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.