Bound States in a Quasi-Two-Dimensional Fermi Gas

Abstract

We consider the problem of N identical fermions of mass m(↑) and one distinguishable particle of mass m(↓) interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For N=2 and mass ratios m(↑)/m(↓)<13.6, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the N+1 system can be approximated by an effective two-channel model. We use this approximation to solve the 3+1 problem and we find that a bound tetramer can exist for mass ratios m(↑)/m(↓) as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions.