Abstract
In this work, we study the BCS-BEC crossover and quantum phase transition in a Fermi gas under Rashba spin-orbit coupling close to a Feshbach resonance. By adopting a two-channel model, we take into account the closed-channel molecules, and show that combined with spin-orbit coupling, a finite background scattering in the open channel can lead to two branches of solution for both the two-body and the many-body ground states. The branching of the two-body bound-state solution originates from the avoided crossing between bound states in the open and the closed channels, respectively. For the many-body states, we identify a quantum phase transition in the upper branch regardless of the sign of the background scattering length, which is in clear contrast to the case without spin-orbit coupling. For systems with negative background scattering length in particular, we show that the bound state in the open channel, and hence the quantum phase transition in the upper branch, are induced by spin-orbit coupling. We then characterize the critical detuning of the quantum phase transition for both positive and negative background scattering lengths, and demonstrate the optimal parameters for the critical point to be probed experimentally.
Highlights
Synthetic spin-orbit coupling (SOC), a recent addition to the toolbox available for quantum simulation in ultracold atomic gases, can give rise to interesting twobody and many-body properties by modifying the singleparticle dispersion spectrum of the underlying system [1,2,3,4,5]
For systems with negative background scattering length in particular, we show that the bound state in the open channel, and the quantum phase transition in the upper branch, are induced by spin-orbit coupling
We have studied a spin-orbit coupled ultracold Fermi gas near a Feshbach resonance by using a two-channel model
Summary
Synthetic spin-orbit coupling (SOC), a recent addition to the toolbox available for quantum simulation in ultracold atomic gases, can give rise to interesting twobody and many-body properties by modifying the singleparticle dispersion spectrum of the underlying system [1,2,3,4,5]. While it has been reported before that in the absence of SOC, two branches of bound state can be found near a Feshbach resonance for a Fermi gas with positive background scattering length, the extra bound state under negative background scattering length is purely induced by SOC The existence of this new two-body bound state should leave signatures on the many-body level. For a Fermi gas without SOC, a quantum phase transition exists for a positive background scattering length, which is intimately connected with the corresponding two-body bound state [45]. With a negative background scattering length, the upper branch emerges from the scattering threshold on the low-field-side of the Feshbach resonance via a quantum phase transition for any finite SOC. With the recent experimental implementation of Feshbach resonance in spin-orbit coupled degenerate Fermi gases [4, 5], we expect that the SOC-induced quantum phase transition reported here can be experimentally probed in the future.
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