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

Qin, Fang and Zhang, Pengfei and Zhao, Peng-Lu (2020) Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling. Physical Review A, 101 (6). Art. No. 063619. ISSN 2469-9926. https://resolver.caltech.edu/CaltechAUTHORS:20200615-132514406

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.101.063619DOIArticle
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.101.063619PublisherArticle
https://arxiv.org/abs/2004.11095arXivDiscussion Paper
ORCID:
AuthorORCID
Qin, Fang0000-0002-6386-8056
Zhang, Pengfei0000-0002-7408-0918
Zhao, Peng-Lu0000-0002-9729-2163
Alternate Title:Large-momentun tail of 1D Fermi gases with spin-orbit coupling
Additional Information:© 2020 American Physical Society. Received 1 May 2020; accepted 19 May 2020; published 15 June 2020. We acknowledge helpful discussions with Wei Yi, Xiaoling Cui, and Lianyi He. This work was supported by the National Natural Science Foundation of China (Grant No. 11404106). F.Q. acknowledges support from the project funded by the China Postdoctoral Science Foundation (Grant No. 2019M662150) and SUSTech Presidential Postdoctoral Fellowship.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of China11404106
China Postdoctoral Science Foundation2019M662150
Southern University of Science and Technology (SUSTech)UNSPECIFIED
Issue or Number:6
Record Number:CaltechAUTHORS:20200615-132514406
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200615-132514406
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103923
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:15 Jun 2020 20:34
Last Modified:15 Jun 2020 20:34

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