Feshbach Resonance in a Synthetic Non-Abelian Gauge Field

TL;DR

This paper investigates how a synthetic non-Abelian gauge field influences Feshbach resonances in spin-1/2 particles, revealing momentum-dependent resonance conditions and the potential for bound states, with implications for many-body quantum states.

Contribution

It develops a renormalizable quantum field theory incorporating gauge fields and shows how Feshbach resonance properties are modified by spin-orbit coupling effects.

Findings

Feshbach magnetic field depends on the particles' center of mass momentum.

Supports two bound states over a range of magnetic fields for certain gauge fields.

Broad resonances are favorable for realizing rashbon condensates.

Abstract

We study the Feshbach resonance of spin-1/2 particles in the presence of a uniform synthetic non-Abelian gauge field that produces spin orbit coupling along with constant spin potentials. We develop a renormalizable quantum field theory that includes the closed channel boson which engenders the Feshbach resonance, in the presence of the gauge field. By a study of the scattering of two particles in the presence of the gauge field, we show that the Feshbach magnetic field, where the apparent low energy scattering length diverges, depends on the conserved centre of mass momentum of the two particles. For high symmetry gauge fields, such as the one which produces an isotropic Rashba spin orbit coupling, we show that the system supports two bound states over a regime of magnetic fields for a negative background scattering length and resonance width comparable to the energy scale of the spin orbit coupling. We discuss the consequences of these findings for the many body setting, and point out that a broad resonance (width larger than spin orbit coupling energy scale) is most favourable for the realization of the rashbon condensate.