Dynamics and symmetries of a repulsively bound atom pair in an infinite optical lattice

Abstract

We investigate the dynamics of two bosons trapped in an infinite one-dimensional optical lattice potential within the framework of the Bose-Hubbard model and derive an exact expression for the wave function at finite time. As initial condition we chose localized atoms that are separated by a distance of d lattice sites and carry a center-of-mass quasimomentum. An initially localized pair (d = 0) is found to be more stable as quantified by the pair probability (probability to find two atoms at the same lattice site) when the interaction and/or the center-of-mass quasimomentum is increased. For initially separated atoms (d = 0) there exists an optimal interaction strength for pair formation. Simple expressions for the wave function, the pair probability, and the optimal interaction strength for pair formation are computed in the limit of infinite time. Whereas the time-dependent wave function differs for values of the interaction strength that differ only by the sign, important observables such as the density and the pair probability do not. With a symmetry analysis this behavior is shown to extend to the N -particle level and to fermionic systems. Our results provide a complementary understanding of the recently observed [Winkler et al., Nature (London) 441, 853 (2006)] dynamical stability of atom pairs in a repulsively interacting lattice gas.

Creation and dynamics of remote spin-entangled pairs in the expansion of strongly correlated fermions in an optical lattice

“…This is a direct consequence of a transformation property of the (spin-or density-) correlators and of the initial state under time reversal and π -boost (translation of all momenta by π). This dynamical U → −U symmetry in the Hubbard model is discussed in more detail in [6,41].…”

Ultracold bosons with short-range interaction in regular optical lattices

“…[211][212][213] analytically and numerically for negative U but the result can be easily generalized to arbitrary U . Later it was discussed in the context of ultracold atoms [214][215][216][217][218][219][220]. The energy spectrum consists of the scattering states of a pair of asymptotically free particles and the bound state.…”

“…The corresponding eigenstates (187) are described by the coefficients and the normalization has been discussed in Ref. [220]. In the limit L → ∞, the bound state is given by…”

Spin-1 quantum walks

“…7b) around U 2 = 0 makes it difficult to observe the spin-mixing. Finally, all results discussed in this section are completely applicable when the U 0 sign changes while maintaining the ratio U 2 /U 0 , because of the symmetry of the dynamics governed by the 1D spinless BH model [50].…”