## Single-particle density of states as a function of energy for the spherical γ = 1 case (upper panel) and deformed cases with the frequency ratios γ = 2 (middle panel) and γ = 1.57 (lower panel)

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**Figure 5.** Single-particle density of states as a function of energy for the spherical γ = 1 case (upper panel) and deformed cases with the frequency ratios γ = 2 (middle panel) and γ = 1.57 (lower panel). The smearing parameter δ and the dimensionless Rashba coupling parameters β are given in the panels. Here we set ω = ω_{y}.

**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.