Large-momentum distribution of a polarized Fermi gas and p -wave contacts

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-2 and subleading behavior k-4 of the large momentum distribution have recently been predicted by Z. Yu et al. [Phys. Rev. Lett. 115, 135304 (2015) PRLTAO0031-900710.1103/PhysRevLett.115.135304] and by M. Y. He et al. [Phys. Rev. Lett. 116, 045301 (2016) PRLTAO0031-900710.1103/PhysRevLett.116.045301] using two different approaches. Here, we show that the subleading asymptotic behavior (∼k-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 K40 atoms [C. Luciuk et al., Nat. Phys. 12, 599 (2016)1745-247310.1038/nphys3670].