Multistability in an optomechanical system with a two-component Bose-Einstein condensate

We investigate a system consisting of a two-component Bose-Einstein condensate interacting dispersively with a Fabry-Perot optical cavity where the two components of the condensate are resonantly coupled to each other by another classical field. The key feature of this system is that the atomic motional degrees of freedom and the internal pseudospin degrees of freedom are coupled to the cavity field simultaneously, hence an effective spin-orbital coupling within the condensate is induced by the cavity. The interplay among the atomic center-of-mass motion, the atomic collective spin, and the cavity field leads to a strong nonlinearity, resulting in multistable behavior in both matter wave and light wave at the few-photon level.

Figure 1

(a) Schematic diagram of the system. The cavity is pumped at rate $\eta$ and the cavity photon decays at rate $\kappa$. (b) Atomic level diagram: The two stable atomic hyperfine ground states $|a\rangle$ and $|b\rangle$ are coupled by a classical field with coupling strength $J$. In addition, they interact with the cavity dispersively, resulting to an energy shift $U_a$ and $U_b$, respectively.

Figure 2

Phase diagram for different types of solutions with $\theta =0$ in the parameter space of ${\mathrm{\eta ̄}}^2$ and ${\mathrm{\Delta ̄}}_c$. Different regions are differentiated by their colors. The digits labeled in each region denote the numbers of corresponding solutions. The dimensionless parameters are taken to be ${\mathrm{Ū}}_a=50$, ${\mathrm{Ū}}_b=200$, $\mathrm{\omega ̄}=400$, $\mathrm{J̄}=-1$. The total number of atoms are set as $N={10}^5$. The red dashed line corresponds to ${\mathrm{\eta ̄}}^2=7$.

Figure 3

Mean intracavity photon number $N_c$ (upper panel) and normalized collective spin $m$ (lower panel) vs cavity-pump detuning ${\mathrm{\Delta ̄}}_c$ for the steady-state solutions with ${\mathrm{\eta ̄}}^2=7$, corresponding to the red-dashed line in Fig. 2. The branches represented by the blue (darker) lines correspond to the dynamically stable solutions (the solid parts denote the ground state and the dashed parts denote stable but not the ground state), and the ones represent by the red (lighter) dot-dashed lines correspond to the dynamically unstable solutions.