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.
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
p-wave contacts have been experimentally probed in recent experiments. So far, discussions on
p-wave contacts have been limited to three dimensions. In this paper, we generalize the
p-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
p-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing-mode frequency and the
p-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
p-wave interactions.
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.
We present a derivation of the adiabatic energy relations as well as the large momentum distribution of a polarized Fermi gas near
p-wave Feshbach resonances. The leading asymptotic behavior ${k}^{\ensuremath{-}2}$ and subleading behavior ${k}^{\ensuremath{-}4}$ of the large momentum distribution have recently been predicted by Z. Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by M. Y. He et al. [Phys. Rev. Lett. 116, 045301 (2016)] using two different approaches. Here, we show that the subleading asymptotic behavior ($\ensuremath{\sim}{k}^{\ensuremath{-}4}$) cannot fully be captured by the contact defined from the adiabatic energy relation related to the
p-wave effective range, and there should be an extra term resulting from the center-of-mass motion of the pairs. The omission of this extra term is perhaps a reasonable approximation at zero temperature. However, it should be taken into account at finite temperature and should have significant importance to understand the recently measured momentum distribution in a resonant
p-wave Fermi gas of ultracold
40K atoms [C. Luciuk et al., Nat. Phys. 12, 599 (2016)].
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.
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.