Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases

TL;DR

This paper analyzes the momentum distributions of strongly interacting one-dimensional spinor gases, revealing how spin order influences these distributions and introducing efficient numerical methods for large systems with complex potentials.

Contribution

It provides new insights into the momentum distributions related to spin order and introduces scalable numerical techniques for large, strongly interacting spinor gases.

Findings

Momentum distributions resemble noninteracting systems with high-momentum tails.

Spin order, especially antiferromagnetic, can be inferred from momentum data.

Numerical methods enable analysis of systems with over 20 particles in complex potentials.

Abstract

One-dimensional spinor gases with strong delta interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain---in particular antiferromagnetic spin order---may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.