Controllable optical switch using a Bose-Einstein condensate in an optical cavity

The optical bistability of an ultracold atomic ensemble located in a small-volume ultrahigh-finesse optical cavity is investigated. We find that a transverse pumping field can be used to control the bistable behavior of the intracavity photons induced by the input pumping along the cavity axis. This phenomenon can be used as a controllable optical switch.

Figure 1

The considered setup of a BEC in a cavity, driven by two pump fields. The transverse pump field is reflected by a mirror indicated in the top of the figure, leading to a standing wave. The characteristics of the pump fields control whether or not the cavity-BEC system exhibits optical bistability.

Figure 2

The cavity photon number as a function of the input pump along the cavity axis. For (a) to (c), the parameters are $N=4.8\times {10}^4$, ${\mathrm{Ũ}}_0=0.25$, ${\mathrm{\delta ̃}}_c=1.2\times {10}^3$, $\mathrm{\kappa ̃}=0.4\times {10}^3$, and (a) ${\mathrm{\eta ̃}}_{\perp }=0$, (b) ${\mathrm{\eta ̃}}_{\perp }=0.1$, (c) ${\mathrm{\eta ̃}}_{\perp }=0.5$. For (d) to (f), the parameters are $N=1\times {10}^4$, ${\mathrm{Ũ}}_0=0.5$, ${\mathrm{\delta ̃}}_c=1.1\times {10}^3$, $\mathrm{\kappa ̃}=0.2\times {10}^3$, and (a) ${\mathrm{\eta ̃}}_{\perp }=0$, (b) ${\mathrm{\eta ̃}}_{\perp }=0.4$, (c) ${\mathrm{\eta ̃}}_{\perp }=1$. In all cases, we neglect the atom-atom interaction to allow for a direct comparison with the DMA method. The red dotted lines are added to guide the eye.

Figure 3

The cavity photon number as a function of the input pump along the cavity axis by the three-level DMA method. The parameters are $N=4.8\times {10}^4$, ${\mathrm{Ũ}}_0=0.25$, ${\mathrm{\delta ̃}}_c=1.2\times {10}^3$, $\mathrm{\kappa ̃}=0.4\times {10}^3$, and (a) ${\mathrm{\eta ̃}}_{\perp }=0$, (b) ${\mathrm{\eta ̃}}_{\perp }=0.1$, (c) ${\mathrm{\eta ̃}}_{\perp }=0.5.$

Figure 4

The cavity photon number as a function of the input pump along the cavity axis. The parameters are $N=4.8\times {10}^4$, ${\mathrm{Ũ}}_0=0.25$, ${\mathrm{\delta ̃}}_c=1.2\times {10}^3$, $\mathrm{\kappa ̃}=0.4\times {10}^3$, and (a) ${\mathrm{\eta ̃}}_{\perp }=0$, (b) ${\mathrm{\eta ̃}}_{\perp }=0.1$, (c) ${\mathrm{\eta ̃}}_{\perp }=0.5.$

Figure 5

(a) and (c) The cavity output photon number $n_{\mathrm{out}}$ as a function of the trial input photon number $n_{\mathit{tr}}$. (b) and (d) Plots of $\langle \cos (2\mathit{kx})\rangle$ as a function of the parallel pumping strength. The parameters are $N=4.8\times {10}^4$, ${\mathrm{Ũ}}_0=0.25$, ${\mathrm{\delta ̃}}_c=1.2\times {10}^3$, $\mathrm{\kappa ̃}=0.4\times {10}^3$, and (a) and (b) ${\mathrm{\eta ̃}}_{\perp }=0$ and (c) and (d) ${\mathrm{\eta ̃}}_{\perp }=0.5$. The curves in (a) and (c) correspond to ${\mathrm{\eta ̃}}_{\parallel }=(0.5,0.9,1.2,1.4,1.6)\times {10}^3$, respectively.

Figure 6

The influence of atom-atom interactions on the bistability. Two lines each with the same line style correspond to the two branches of the bistable behavior for a given value of ${\mathit{Ng}}_c=0$, $10$, $20$, $30$, $40$, $50$, and $60$, in units of ${\omega }_r\lambda /2\pi$ from bottom to top. Other parameters are $N=4.8\times {10}^4$, ${\mathrm{Ũ}}_0=0.25$, $\mathrm{\kappa ̃}=0.4\times {10}^3$, ${\mathrm{\eta ̃}}_{\perp }=0$, and ${\mathrm{\delta ̃}}_c=1.1\times {10}^3$.

Figure 7

The cavity photon number as a function of the input pump perpendicular to the cavity axis. The parameters are $N=1\times {10}^4$, ${\mathrm{Ũ}}_0=0.5$, ${\mathrm{\delta ̃}}_c=1.1\times {10}^3$, $\mathrm{\kappa ̃}=0.2\times {10}^3$, ${\mathit{Ng}}_c=0$, and (a) ${\mathrm{\eta ̃}}_{\parallel }=0$, (b) ${\mathrm{\eta ̃}}_{\parallel }=50$, (c) ${\mathrm{\eta ̃}}_{\parallel }=1\times {10}^3$, and (d) ${\mathrm{\eta ̃}}_{\parallel }=1.5\times {10}^3$.

Figure 8

The regions of lower branch, bistability, and upper branch of the cavity photon number. The parameters are $N=1\times {10}^4$, ${\mathrm{Ũ}}_0=0.5$, ${\mathrm{\delta ̃}}_c=1.1\times {10}^3$, $\mathrm{\kappa ̃}=0.2\times {10}^3$, and ${\mathit{Ng}}_c=0$.