Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions
| Autor: | Zhang, Cai-Xia, Peng, Shi-Guo, Jiang, Kaijun |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. A 101, 043616 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.101.043616 |
| Popis: | We present a comprehensive derivation of a set of universal relations for spin-orbit-coupled Fermi gases in three or two dimension, which follow from the short-range behavior of the two-body physics. Besides the adiabatic energy relations, the large-momentum distribution, the grand canonical potential and pressure relation derived in our previous work for three-dimensional systems {[}Phys. Rev. Lett. 120, 060408 (2018){]}, we further derive high-frequency tail of the radio-frequency spectroscopy and the short-range behavior of the pair correlation function. In addition, we also extend the derivation to two-dimensional systems with Rashba type of spin-orbit coupling. To simply demonstrate how the spin-orbit-coupling effect modifies the two-body short-range behavior, we solve the two-body problem in the sub-Hilbert space of zero center-of-mass momentum and zero total angular momentum, and perturbatively take the spin-orbit-coupling effect into account at short distance, since the strength of the spin-orbit coupling should be much smaller than the corresponding scale of the finite range of interatomic interactions. The universal asymptotic forms of the two-body wave function at short distance are then derived, which do not depend on the short-range details of interatomic potentials. We find that new scattering parameters need to be introduced because of spin-orbit coupling, besides the traditional $s$- and $p$-wave scattering length (volume) and effective ranges. This is a general and unique feature for spin-orbit-coupled systems. We show how these two-body parameters characterize the universal relations in the presence of spin-orbit coupling. This work probably shed light for understanding the profound properties of the many-body quantum systems in the presence of the spin-orbit coupling. Comment: 17 pages |
| Databáze: | arXiv |
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