Nonperturbative theoretical description of two atoms in an optical lattice with time-dependent perturbations

Abstract

A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. Rev. A 84, 062710 (2011)]. It allows presently to treat any time-dependent external perturbation of the lattice potential up to quadratic order. Example calculations of the experimentally relevant cases of an acceleration of the lattice and the turning-on of an additional harmonic confinement are presented.

Two cold atoms in a time‐dependent harmonic trap in one dimension

“…In the absence of the interaction, the behavior of this system is well-understood [10,11]. In the presence of the interaction, however, the two-body dynamics requires a thorough investigation [12,13]. The main objective of our work is to study this dynamics for two representative scenarios.…”

Two-channel Bose-Hubbard model of atoms at a Feshbach resonance

“…In order to do so an approach described in [21] is used, which allows for finding the stationary solutions of the two-body problem with arbitrary isotropic single-channel interaction potentials. On the basis of the stationary solutions the method described in [22] is used to determine the time-dependent wavefunction during a perturbation of the lattice potential.…”

“…is considered, which corresponds to an increasing acceleration of the lattice [22]. The dynamical behavior due toV pert is governed mainly by two effects: (i) The linear perturbation leads to a coupling between Wannier functions of odd and even symmetry, i.e.…”

“…However, we show that one can largely simplify the problem by introducing a square-well interaction potential that realistically mimics the behavior at a FR. Using this single-channel interaction potential we apply an approach introduced in [21,22] in order to obtain the correct energies and wave functions of two atoms in a small OL at a FR. The correct stationary and dynamic behavior of two atoms in a double-well potential is compared with the results of the introduced BH model.…”