Odd-frequency pair correlations in the trapped fermionic Tonks-Girardeau gas

Abstract

The fermionic Tonks-Girardeau gas is an exactly solvable model realizing a conventional macroscopic condensate of p-wave Cooper pairs. Here we demonstrate that, when confined by a trapping potential, it also hosts unconventional odd-frequency pairing, i.e., pair correlations with s-wave symmetry that are only present with a finite time delay t between fermions forming a pair. Quantitative results for fixed particle number are obtained using a generalization of Yang's theory of off-diagonal long-range order to define a t-dependent order parameter that is antisymmetric under combined t inversion and exchange of fermion-pair indices. Odd-frequency pairing in the fermionic Tonks-Girardeau gas is found to be a mesoscopic effect, localized at the system's boundary and therefore nonextensive thermodynamically. Our results show that this elusive hidden order is accessible in systems having fixed particle number, suggesting new avenues towards its experimental realization and further detailed study.