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

<p><strong>Figure 2.</strong> 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.</p> <p><strong>Abstract</strong></p> <p>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.</p

Same as figures 2 and 3 for γ = 5 (left panel) and γ = 10 (right panel)

<p><strong>Figure 4.</strong> Same as figures <a href="http://iopscience.iop.org/0953-4075/46/13/134012/article#jpb467366f2" target="_blank">2</a> and <a href="http://iopscience.iop.org/0953-4075/46/13/134012/article#jpb467366f3" target="_blank">3</a> for γ = 5 (left panel) and γ = 10 (right panel). These results approach the limit of an effective one-dimensional system, i.e. γ 1.</p> <p><strong>Abstract</strong></p> <p>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.</p

Energy as a function of the dimensionless spin–orbit coupling parameter β for the case of equal frequencies ω = ω_<em>x</em> = ω_<em>y</em> with no Zeeman shift (left panel) and including a Zeeman shift of magnitude μ<em>B</em> = ω

<p><strong>Figure 1.</strong> Energy as a function of the dimensionless spin–orbit coupling parameter β for the case of equal frequencies ω = ω_<em>x</em> = ω_<em>y</em> with no Zeeman shift (left panel) and including a Zeeman shift of magnitude μ<em>B</em> = ω.</p> <p><strong>Abstract</strong></p> <p>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.</p