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arXiv:1605.05653 · Physical Review A

Effective theory and universal relations for Fermi gases near a d -wave-interaction resonance

Pengfei Zhang, Shizhong Zhang, Zhenhua Yu

Published Apr 10, 2017• 20 citations
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Abstract

In this work, we present an effective-field theory to describe a two-component Fermi gas near a $d$-wave-interaction resonance. The effective-field theory is renormalizable by matching with the low-energy $d$-wave scattering phase shift. Based on the effective-field theory, we derive universal properties of the Fermi gas by the operator-product-expansion method. We find that beyond the contacts defined by adiabatic theorems, the asymptotic expressions of the momentum distribution and the Raman spectroscopy involve two extra contacts which provide additional information on correlations of the system. Our formalism sets the stage for further explorations of many-body effects in a $d$-wave resonant Fermi gas. Finally, we generalize our effective-field theory for interaction resonances of arbitrary higher partial waves.

DOI
10.1103/physreva.95.043609

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The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact was extended to higher partial waves; in particular, the ppp-wave contacts have been experimentally probed in recent experiments. So far, discussions on ppp-wave contacts have been limited to three dimensions. In this paper, we generalize the ppp-wave contacts to two dimensions and derive a series of universal relations, including the adiabatic relations, high-momentum distribution, virial theorem, and pressure relation. At the high-temperature and low-density limit, we calculate the ppp-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing-mode frequency and the ppp-wave contacts is given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three- and two-dimensional Fermi gases and discuss possible experimental realization of a two-dimensional Fermi gas with ppp-wave interactions.
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In this work, we study the universal relations for one-dimensional spin-orbital-coupled fermions near both sss- and ppp-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/q31/{q}^{3}1/q3 (qqq 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.