Strongly Interacting Quantum Gases in One-Dimensional Traps

TL;DR

This paper develops an effective spin-chain model for strongly interacting one-dimensional quantum gases with arbitrary spin, revealing a transition between ferromagnetic and antiferromagnetic states and proposing methods to distinguish these states.

Contribution

It introduces a super-exchange based spin-chain Hamiltonian for arbitrary spin particles in 1D traps, connecting strongly interacting regimes to well-known magnetic models.

Findings

Transition between AFM and FM states with interaction tuning.

Distinct responses of FM and AFM states to magnetic gradients.

Validation of the spin-chain model against unbiased computational methods.

Abstract

Under the second-order degenerate perturbation theory, we show that the physics of $N$ particles with arbitrary spin confined in a one dimensional trap in the strongly interacting regime can be described by super-exchange interaction. An effective spin-chain Hamiltonian (non-translational-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translational-invariant Heisenberg model, where a transition between Heisenberg anti-ferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished in two different methods: the first is based on their distinct response to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distribution. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques