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arXiv:1412.8275 · Physical Review A

Sudden death of particle-pair Bloch oscillation and unidirectional propagation in a one-dimensional driven optical lattice

S. Lin, X. Z. Zhang, Z. Song

Published Dec 2, 2014• 16 citations
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Abstract

We study the dynamics of bound pairs in the extended Hubbard model driven by a linear external field. It is shown that two interacting bosons or singlet fermions with nonzero on-site and nearest-neighbor interaction strengths can always form bound pairs in the absence of an external field. There are two bands of bound pairs, one of which may have incomplete wave vectors when it has an overlap with the scattering band, referred to as an imperfect band. In the presence of the external field, the dynamics of the bound pair in the perfect band exhibits distinct Bloch-Zener oscillation (BZO), while in the imperfect band the oscillation presents a sudden death. The pair becomes uncorrelated after the sudden death and the BZO never comes back. Such dynamical behaviors are robust even for the weak-coupling regime and thus can be used to characterize the phase diagram of the bound states.

DOI
10.1103/physreva.90.063411

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Variational solutions of the Boltzmann equation usually rely on the concept of linear response. We extend the variational approach for tight-binding models at high entropies to a regime far beyond linear response. We analyze both weakly interacting fermions and incoherent bosons on a lattice. We consider a case where the particles are driven by a constant force, leading to the well-known Bloch oscillations, and we consider interactions that are weak enough not to overdamp these oscillations. This regime is computationally demanding and relevant for ultracold atoms in optical lattices. We derive a simple theory in terms of coupled dynamic equations for the particle density, energy density, current, and heat current, allowing for analytic solutions. As an application, we identify damping coefficients for Bloch oscillations in the Hubbard model at weak interactions and compute them for a one-dimensional toy model. We also approximately solve the long-time dynamics of a weakly interacting, strongly Bloch-oscillating cloud of fermionic particles in a tilted lattice, leading to a subdiffusive scaling exponent.
We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schrödinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.
The coherent dynamics of two strongly interacting electrons hopping on a one-dimensional lattice and driven by combined dc-ac fields is theoretically investigated in the framework of the Hubbard model. It is shown that, under appropriate forcing conditions in the strong-field regime, super-Bloch oscillations (SBOs) can be observed for the bound particle state, but not for unpaired electrons that remain frozen in the lattice. As compared to single-particle SBOs, SBOs of correlated particles are generally quasiperiodic.