Many-body $\mathit{\text{T}}$-matrix theory of a strongly interacting spin-orbit coupled Fermi gas: Momentum-resolved radio-frequency spectroscopy and fermionic pairing

Interacting Fermi gases with spin-orbit coupling are responsible for many intriguing phenomena such as topological superfluids and Majorana fermions. Here we characterize theoretically fermionic pairing in a strongly interacting spin-orbit coupled Fermi gas, by using momentum-resolved radio-frequency spectroscopy. We develop a strong-coupling $T$-matrix theory and present a phase diagram near the unitary resonance limit. A smooth transition from atomic to molecular responses in the momentum-resolved spectroscopy is predicted, with a clear signature of anisotropic pairing at and below resonance. Our prediction with many-body pairing can be directly tested in a spin-orbit coupled Fermi gas of ${}^{40}$K or ${}^6$Li atoms near broad Feshbach resonances.