Cavity-Mediated Strong Matter Wave Bistability in a Spin-1 Condensate

We study matter-wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields is accomplished via spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter-wave nonlinearity, making matter-wave bistability in a cavity at the single-photon level achievable.

Figure 1

Schematic diagram of the system.

Figure 2

Phase diagram in the parameter space of ${\overline{\delta }}_c$ and ${\eta }^2$ for different types of solutions: (a) $\theta =0$; (b) $\theta =\pi$. Different regions are differentiated by their colors and are labeled with the numbers of corresponding solutions. In the black region, no physical phase-dependent solutions can be found. The dimensionless parameters are estimated to be ${\overline{\lambda }}_a={10}^{-3}$, $\overline{q}=2{\overline{\lambda }}_a$, and ${\overline{U}}_0=-5$ [29], the other parameters are set as $m=0$ and $N=1000$. The red-dashed line in (a) correspond to ${\eta }^2=0.8$.

Figure 3

Upper panel: Mean intracavity photon number $|\alpha {|}^2$ and the normalized spin-0 population $x$ versus cavity-pump detuning ${\overline{\delta }}_c$ for the steady-state solutions with ${\eta }^2=0.8$, corresponding to the red-dashed line in Fig. 2a. The ones represented by the red dotted lines correspond to dynamically unstable solutions. Lower panel: From left to right, the phase-space contour plot of $H$ corresponding to different values of ${\overline{\delta }}_c$ marked in the upper panel as a, b and c, respectively.

Figure 4

Quantum and mean-field energy levels with $N=20$, $m=0.2$, and ${\eta }^2=0.02$; the other parameters are the same as before. The solid lines are quantum energy levels, the black dots refer to the mean-field energy levels with $\theta =\pi$, while the white dots refer to those with $\theta =0$.