Universal relations for a spin-polarized Fermi gas in two dimensions

Abstract

We derive the full set of universal relations for spin-polarized Fermi gases with $p$-wave interaction in two dimensions, simply using the short-range asymptotic behavior of fermion-pair wave functions. For $p$-wave interactions, an additional contact related to the effective range needs to be introduced, besides the one related to the scattering volume. Since the subleading tail ($k^{-4}$) of the large-momentum distribution cannot fully be captured by the contacts defined by the adiabatic relations, an extra term resulted from the center-of-mass motions of the pairs gives rise to an additional divergence in the kinetic energy of the system, besides those related to the contacts defined. We show in Tan's energy theorem that if only two-body correlations are taken into account, all these divergences are reasonably removed, leading to a finite internal energy of the system. In addition, we find that all the other universal relations, such as the high-frequency behavior of the radio-frequency response, short-range behavior of the pair correlation function, generalized virial theorem, and pressure relation, remain unaffected by the center-of-mass motions of the pairs, and are fully governed by the contacts defined by the adiabatic relations. Our results confirm the feasibility of generalizing the contact theory for higher-partial-wave scatterings, and could readily be confirmed in current experiments with ultracold ${}^{40}$K and ${}^6$Li atoms.

15 pages

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Verification of universal relations in a strongly interacting Fermi gas
• p-wave Feshbach molecules
• Universal Properties of the Ultra-Cold Fermi Gas
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Theory of RF-spectroscopy of strongly interacting Fermions
• Anisotropic Fermi Superfluid via p-wave Feshbach Resonance
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance
• Static structure factor of a strongly correlated Fermi gas at large momenta
• Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode
• Large-momentum distribution of a polarized Fermi gas and p-wave contacts
• High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap
• Sigature of the universal super Efimov Effect: three-body contact in two dimensional Fermi gases
• Contact theory for spin-orbit-coupled Fermi gases
• Two-body state with p-wave interaction in one-dimensional waveguides under transversely anisotropic confinement

Cited by in corpus (4)

• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Universal scattering phase shift in the presence of spin-orbit coupling