Continuous Optical-to-Mechanical Quantum State Transfer in the Unresolved Sideband Regime

Optical-to-mechanical quantum state transfer is an important capability for future quantum networks, quantum communication, and distributed quantum sensing. However, existing continuous state transfer protocols operate in the resolved sideband regime, necessitating a high-quality optical cavity and a high mechanical resonance frequency. Here, we propose a continuous protocol that operates in the unresolved sideband regime. The protocol is based on feedback cooling, can be implemented with current technology, and is able to transfer non-Gaussian quantum states with high fidelity. Our protocol significantly expands the kinds of optomechanical devices for which continuous optical-to-mechanical state transfer is possible, paving the way toward quantum technological applications and the preparation of macroscopic superpositions to test the fundamentals of quantum science.

Figure 1

Schematic optomechanical system with feedback. Light is coupled into an optomechanical cavity. The reflected light is measured through homodyne detection. The detected photocurrent [$Y_{\mathrm{out}}(t)$] is convolved with a filter $f(t)$ and directly fed back to the momentum of the mechanical resonator.

Figure 2

Transfer gain $(\sqrt{g_X{g}_Y},\mathrm{red})$ and squeezing $(g_X/g_Y,\mathrm{blue})$ as a function of the feedback strength by cooperativity ($G/C$). The dashed line indicates $\mathrm{G}=1$ and the full gray line indicates the optimal gain $(G=8C)$, where $g_X/g_Y=1$. The dots are numerically obtained, and the lines are using the analytic expressions derived in the high-quality factor limit.

Figure 3

(a) Contributions to the variance as a function of interaction strength of mechanical noise (blue), optical signal (yellow), and two contributions of optical noise: mode mismatch on $Q$ (black), and inefficiency (red). The size of the points correspond to the inefficiency ($\eta =0.9$, 0.75, and 0.5 for small, medium, and large points, respectively). (b) The transfer fidelity $(\mathcal{F})$ as a function of interaction strength for a coherent state (black), cat state (green) ($\alpha =2$), and single photon Fock state (dark blue). Inset shows $\mathcal{F}$ as a function of $\eta$ for the coherent state, at a fixed value of $C/n_{\mathrm{th}}=10$ corresponding, for our parameters, to an optomechanical cooperativity of $C\sim 6200$. (c) Corresponding plots of the Wigner distributions for a coherent state (top row), cat state (middle row), and Fock state (bottom row) at the interaction strengths indicated by the gray lines connected to subplot (b). The black dotted circle in the top right indicates the length scale of the contour of the ground state. The orientation of the plots is indicated by the black arrows in the top right plot.