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.
We investigate the properties of a spinless Fermi gas close to a p-wave interaction resonance. We show that the effects of interaction near a p-wave resonance are captured by two contacts, which are related to the variation of energy with the p-wave scattering volume v and with the effective range R in two adiabatic theorems. Exact pressure and virial relations are derived. We show how the two contacts determine the leading and subleading asymptotic behavior of the momentum distribution (∼1/k^{2} and ∼1/k^{4}) and how they can be measured experimentally by radio-frequency and photoassociation spectroscopies. Finally, we evaluate the two contacts at high temperature with a virial expansion.
We investigate theoretically strong-coupling and finite-temperature effects on the
p-wave contacts, as well as the asymptotic behavior of the momentum distribution in the large-momentum region in a one-component Fermi gas with a tunable
p-wave interaction. Including
p-wave pairing fluctuations within a strong-coupling theory, we calculate the
p-wave contacts above the superfluid transition temperature
Tc from the adiabatic energy relations. We show that, while the
p-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the
p-wave interaction with increasing effective range. We also analyze the asymptotic form of the momentum distribution in the large-momentum region. In contrast to the conventional
s-wave case, we show that the asymptotic behavior cannot be completely described by only the
p-wave contacts, and the extra terms, which are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement by including the effects of a harmonic trap potential within the local density approximation. We show that, while our model qualitatively explains the dependence on the interaction strength of the
p-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the
p-wave contact related to the effective range. Since the
p-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.
In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], it has been shown that center-of-mass-momentum-dependent two-body interactions can be generated and tuned by Raman coupling the closed-channel bound states in a magnetic Feshbach resonance. Here we investigate the universal relations in a three-dimensional Fermi gas near such a laser modulated
s-wave Feshbach resonance. Using the operator-product expansion approach, we find that to fully describe the high-momentum tail of the density distribution up to ${q}^{\ensuremath{-}6}$ (
q is the relative momentum), four center-of-mass-momentum-dependent parameters are required, which we identify as contacts. These contacts appear in various universal relations connecting microscopic and thermodynamic properties. One contact is related to the variation of energy with respect to the inverse scattering length and determines the leading ${q}^{\ensuremath{-}4}$ tail of the high-momentum distribution. Another vector contact appears in the subleading ${q}^{\ensuremath{-}5}$ tail, which is related to the velocity of closed-channel molecules. The other two contacts emerge in the ${q}^{\ensuremath{-}6}$ tail and are respectively related to the variation of energy with respect to the range parameter and to the kinetic energy of closed-channel molecules. Particularly, we find that the ${q}^{\ensuremath{-}5}$ tail and part of the ${q}^{\ensuremath{-}6}$ tail of the momentum distribution show anisotropic features. We derive the universal relations and, as a concrete example, estimate the contacts for the zero-temperature superfluid ground state of the system using a mean-field approach.
We investigate universal relations in a spinless Fermi gas near a p-wave Feshbach resonance, and show that the momentum distribution n_{k} has an asymptote proportional to k^{-2} with the proportionality constant-the p-wave contact-scaling with the number of closed-channel molecules. We prove the adiabatic sweep theorem for a p-wave resonance which reveals the thermodynamic implication of the p-wave contact. In contrast to the unitary Fermi gas in which Tan's contact is universal, the p-wave contact depends on the short-range details of the interaction.
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.