Dynamics of spin-1 bosons in an optical lattice: spin mixing, quantum phase revival spectroscopy and effective three-body interactions

TL;DR

This paper investigates the non-equilibrium dynamics of spin-1 bosons in optical lattices, revealing how spin mixing, quantum revivals, and effective multi-body interactions inform about the initial state and underlying interactions.

Contribution

It derives effective three-body interaction parameters for spin-1 atoms and analyzes their impact on spin-mixing and observable dynamics in optical lattices.

Findings

Collapse-and-revival oscillations reveal superfluid and magnetic properties.

Interaction strengths can be deduced from observed oscillations.

Effective multi-body interactions significantly influence spin dynamics.

Abstract

We study the dynamics of spin-1 atoms in a periodic optical-lattice potential and an external magnetic field in a quantum quench scenario where we start from a superfluid ground state in a shallow lattice potential and suddenly raise the lattice depth. The time evolution of the non-equilibrium state, thus created, shows collective collapse-and-revival oscillations of matter-wave coherence as well as oscillations in the spin populations. We show that the complex pattern of these two types of oscillations reveals details about the superfluid and magnetic properties of the initial many-body ground state. Furthermore, we show that the strengths of the spin-dependent and spin-independent atom-atom interactions can be deduced from the observations. The Hamiltonian that describes the physics of the final deep lattice not only contains two-body interactions but also effective multi-body interactions, which arise due to virtual excitations to higher bands. We derive these effective spin-dependent three-body interaction parameters for spin-1 atoms and describe how spin-mixing is affected. Spinor atoms are unique in the sense that multi-body interactions are directly evident in the in-situ number densities in addition to the momentum distributions. We treat both antiferromagnetic (e.g. $^{23}$Na atoms) and ferromagnetic (e.g. $^{87}$Rb and $^{41}$K) condensates.