Pair excitations in the ground state of a two-dimensional attractive Fermi gas

Abstract

Crossover of the pair excitation spectrum in the ground state of a dilute two-dimensional Fermi gas is studied as a function of the attraction strength $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$, where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy. It is shown that at $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\simeq}\frac{1}{4}$ the spectrum changes its character from the continuous one in the strong-coupling, or "Bose-gas," limit ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\gg}1$) to that which consists of two different types of excitations in the weak-coupling ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\ll}1$) regime: (i) long-wavelength soundlike mode with the cutoff at momentum ${q}_{c}\ensuremath{\sim}\frac{1}{{\ensuremath{\xi}}_{0}}$, and (ii) pair excitations with $q\ensuremath{\ge}\sqrt{8m\ensuremath{\mu}}$.