We study the dependence of the p-wave contact on the Fermi temperature T_{F} and reduced temperature T/T_{F} based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow m=0 and m=±1 dipolar splitting of the p-wave Feshbach resonance in ^{6}Li, enabling the independent determination of the contact for all three m components. For each component, we identify a near-resonant scaling with sqrt[T_{F}], indicating the contribution of the normalized effective range k_{F}R_{e}. In addition, we show that the peak contacts observed near resonance increase as T/T_{F} is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the p-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced p-wave Fermi gases.
The length scale separation in dilute quantum gases in quasi-one-dimensional or quasi-two-dimensional traps has spatially divided the system into two distinct regimes. Whereas universal relations defined in strict one or two dimensions apply in a scale that is much larger than the characteristic length of the transverse confinements, physical observables in the short distances are inevitably governed by three-dimensional contacts. Here, we show that
p-wave contacts defined in different length scales are intrinsically connected by a universal relation, which depends on a simple geometric factor of the transverse confinements. While this universal relation is derived for one of the
p-wave contacts, it establishes a concrete example of how dimensional crossover interplays with contacts and universal relations for arbitrary partial wave scatterings.
In a recent experiment [Peng et al., Phys. Rev. A 97, 012702 (2018)], it has been shown that the
p-wave Feshbach resonance can be shifted toward the
s-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting
s- and
p-wave interactions under optical control of a
p-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for
40K atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the
p-wave channel can be probed by measuring the
s-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.