Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

Zhang, Caixia; Peng, Sijia; Jiang, Kaijun

doi:10.1103/physreva.101.043616

Cited by 9 publications

(13 citation statements)

References 65 publications

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“…These complications dramatically affect the theoretical description of interactions between cold atoms, and especially modify the asymptotic behavior of the many-body wave function when two atoms get close [41]. Then new scattering parameters need to be introduced by SO coupling besides the well-known scattering length and effective range [42,43]. Consequently, Tan's universal relations, governed by the short-range behavior of the two-body physics, are also amended by SO-coupling.…”

Section: Introductionmentioning

confidence: 99%

Universal scattering phase shift in the presence of spin-orbit coupling

Zhang,

Peng

2022

Preprint

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Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the scattering phase shifts for cold atoms in the presence of spin-orbit coupling. We first construct the asymptotic form of the two-body wave function when two fermions get as close as the interaction range, and consider perturbatively the correction of the spin-orbit coupling up to the second order, in which new scattering parameters are introduced. Then for elastic collisions, the scattering phase shifts are defined according to the unitary scattering S matrix. We show how the low-energy behavior of the scattering phase shifts is modified by these new scattering parameters introduced by spin-orbit coupling. The universality of the scattering phase shifts is manifested as the independence of the specific form of the interatomic potential. The explicit forms of the new scattering parameters are analytically derived within a model of the spherical-square-well potential. Our method provides a unified description of the low-energy properties of scattering phase shifts in the presence of spin-orbit coupling.

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Section: Introductionmentioning

confidence: 99%

Universal scattering phase shift in the presence of spin-orbit coupling

Zhang,

Peng

2022

Preprint

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“…At the same time, the universal relations for the three-dimensional ultracold gases with an arbitrary type of SOC have been investigated [67,68]. Furthermore, the universal relations for spin-orbit-coupled Fermi gases in two dimensions have been derived [69]. However, the one-dimensional (1D) Fermi gases with SOC has not been studied.…”

Section: Introductionmentioning

confidence: 99%

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

2020

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We study the contacts, large-momentum tail, radio-frequency spectroscopy, and some other universal relations for an ultracold one-dimensional (1D) two-component Fermi gas with spin-orbit coupling (SOC). Different from previous studies, we find that the q −8 tail in the spin-mixing (off-diagonal) terms of the momentum distribution matrix is dependent on the two SOC parameters in the laboratory frame for 1D systems, where q is the relative momentum. This tail can be observed through time-of-flight measurement as a direct manifestation of the SOC effects on the many-body level. Besides the traditional 1D even-wave scattering length, we find that two new physical quantities must be introduced due to the SOC. Consequently, two new adiabatic energy relations with respect to the two SOC parameters are obtained. Furthermore, we derive the pressure relation and virial theorem at short distances for this system. To find how the SOC modifies the large-momentum behavior, we take the SOC parameters as perturbations since the strength of the SOC should be much smaller than the corresponding strength scale of the interatomic interactions. In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the q −8 order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters. We also find that the momentum distribution matrix shows spin-dependent and anisotropic features. Furthermore, we calculate the momentum distribution matrix in the laboratory frame for the experimental implication. In addition, we calculate the high-frequency tail of the radio-frequency spectroscopy and find that the presence of the contact related to the center-of-mass momentum in the radio-frequency spectral is due to the SOC effects. This paper paves the way for exploring the profound properties of many-body quantum systems with SOC in one dimension.

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“…Recent experimental realization of the spin-orbital coupling (SOC) in ultracold gases [37][38][39][40][41] also leads to interesting few-and many-body physics [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. In particular, the universal relations for the spin-orbital-coupled Fermi gases attract much attention [59][60][61][62][63]. Since the SOC breaks the rotational symmetry, it would mix different partial waves at the two-body level.…”

Section: Introductionmentioning

confidence: 99%

Universal relations for hybridized s - and p -wave interactions from spin-orbital coupling

Qin

Zhang

2020

Phys. Rev. A

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In this work, we study the universal relations for one-dimensional spin-orbital-coupled fermions near both s-and p-wave resonances using effective field theory. Since the spin-orbital coupling mixes different partial waves, a contact matrix is introduced to capture the nontrivial correlation between dimers. We find the signature of the spin-orbital coupling appears at the leading order for the off-diagonal components of the momentum distribution matrix, which is proportional to 1/q 3 (q is the relative momentum). We further derive the large frequency behavior of the Raman spectroscopy, which serves as an independent measurable quantity for contacts. Finally, we give an explicit example of contacts by considering a two-body problem.

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Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

Cited by 9 publications

References 65 publications

Universal scattering phase shift in the presence of spin-orbit coupling

Universal scattering phase shift in the presence of spin-orbit coupling

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

Universal relations for hybridized s - and p -wave interactions from spin-orbital coupling

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