%0 DATA
%A O, V Marchukov
%A A, G Volosniev
%A D, V Fedorov
%A A, S Jensen
%A N, T Zinner
%D 2013
%T The critical coupling constant *G*_{c} (in units of ω_{y}) as a function of the chemical potential μ 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)
%U https://iop.figshare.com/articles/_The_critical_coupling_constant_em_G_sub_c_sub_em_in_units_of_img_src_http_ej_iop_org_icons_Entities/1012065
%R 10.6084/m9.figshare.1012065.v1
%2 https://iop.figshare.com/ndownloader/files/1479887
%K Rashba interaction
%K 0.5
%K strength
%K parameter
%K deformation
%K function
%K variation
%K panel
%X **Figure 6.** The critical coupling constant *G*_{c} (in units of ω_{y}) as a function of the chemical potential μ 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 parameter β are given in the panels. The notation in the legend indicates that G_\Sigma is obtained by doing summation over levels, while *G*_{0.5} and *G*_{1} indicate that we have used smeared distribution with δ = 0.5 and δ = 1 respectively. 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.