Bound States in a Quasi-Two-Dimensional Fermi Gas

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.