## Energy as a function of dimensionless spin–orbit coupling parameter β for the case where the oscillator potential is deformed

**Figure 2.** Energy as a function of dimensionless spin–orbit coupling parameter β for the case where the oscillator potential is deformed. The left panel has \gamma =\frac{\omega _x}{\omega _y} = 2 and the right panel has γ = 3.

**Abstract**

We consider a spin–orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin–orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation imply that the few- and many-body physics of spin–orbit coupled systems can be manipulated by variation of these parameters.