Adiabatic transfer of energy fluctuations between membranes inside an optical cavity

A scheme is presented for the adiabatic transfer of average fluctuations in the phonon number between two membranes in an optical cavity. We show that by driving the cavity modes with external time-delayed pulses, one can obtain an effect analogous to stimulated Raman adiabatic passage in the atomic systems. The adiabatic transfer of fluctuations from one membrane to the other is attained through a “dark” mode, which is robust against decay of the mediating cavity mode. The results are supported with analytical and numerical calculations with experimentally feasible parameters.

Figure 1

Three-level $\lambda$ system.

Figure 2

Schematic diagram of two membranes inside an optical cavity.

Figure 3

Time variation of the eigenvalues (44) of the matrix $M$ and the time-dependent optomechanical couplings (42) and (43). The inset displays the time variation of the first-order shift of the eigenvalue ${\lambda }_1=0$, in the presence of decay. All the parameters are normalized with respect to 1 MHz. Parameters are $A=350$, ${\mathrm{\Delta }}_j^{\prime }={\omega }_{mk}=1$, $g_k=0.001$, $J_k=1/2$, $T=3$, $\tau =1$, ${\gamma }_j=0$, and ${\gamma }_{mk}=0$, for all $j\in \text{L},\text{M},\text{R}$ and $k\in 1,2$.

Figure 4

Time evolution of the average excitation fluctuations of the two membranes and the three subcavity modes. We have chosen initial average excitation fluctuations of the first membrane as $\langle \delta b_1^{†}\delta b_1\rangle =1$. We have chosen ${\gamma }_j=0.4$ and ${\gamma }_{mk}=0.0001$. All the other parameters are the same as in Fig. 3.