Motion-induced enhancement of Rabi coupling between atomic ensembles in cavity optomechanics

We propose a scheme of enhancement of Rabi coupling between two identical atomic ensembles trapped inside an optical cavity in a membrane-in-the-middle setup. The cavity modes dispersively interact with the ensembles and the effective interaction between the ensembles is governed by the tunneling rate of the cavity modes through the oscillating membrane. We have shown that this interaction can be made large enough such that the Rabi oscillation occurs in a time scale much smaller than the relevant decay time scales of the cavity modes and of the membrane. We present the detailed analytical and numerical results and assess the feasibility of the scheme using currently available technology.

Figure 1

Schematic diagram of two trapped atomic ensembles in a hybrid optomechanical cavity.

Figure 2

Temporal variation of the expectation values $|\langle \delta c_L\rangle {|}^2, |\langle \delta c_R\rangle {|}^2$ (left $y$ axis), $|\langle \delta a_L\rangle {|}^2$, and $|\langle \delta a_R\rangle {|}^2$ (right $y$ axis) with time, normalized with respect to $2\pi \times 1$ MHz. The parameters chosen are ${\gamma }_L={\gamma }_R={\gamma }_c=2\pi \times 10$ MHz, ${\gamma }_1={\gamma }_2={\gamma }_{\mathrm{at}}=2\pi \times 10$ kHz, ${\gamma }_m=2\pi \times 1$ kHz, ${\delta }_L^{\prime }=-{\delta }_R^{\prime }=-2\pi \times 100$ MHz, ${\omega }_m=2J=2\pi \times 1$ GHz, $g_1=2\pi \times 1$ MHz, ${\mathrm{\Delta }}_L={\mathrm{\Delta }}_R=2\pi \times 10$ MHz, ${\alpha }_L={\alpha }_R=\alpha =1$, and $\overline{g}\sqrt{N}=2\pi \times 10$ MHz. The initial condition is chosen as $\langle \delta c_L\rangle =1$, while all the other expectation values are zero.