Non-Hermitian p -wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas

We theoretically investigate non-Hermitian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>p</a:mi></a:math>-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Eagles-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>p</b:mi></b:math>-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>p</c:mi></c:math>-wave interaction is crucial for reaching the non-Hermitian <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>p</d:mi></d:math>-wave Fermi superfluid state. Moreover, our theoretical framework for many-body systems with the three-body loss, which is inevitable in ultracold atoms, would promote further progress in non-Hermitian cold-atomic physics.