Mechanically Mediated Microwave Frequency Conversion in the Quantum Regime

We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than ${10}^{12}\text{photons}/\mathrm{s}$ with a 95% efficiency and a 14 kHz bandwidth. With less than ${10}^{-1}\text{photons}·{\mathrm{s}}^{-1}·{\mathrm{Hz}}^{-1}$ of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.

Figure 1

Device description and experimental setup. (a) The device, placed in a cryogenic refrigerator, consists of two inductor-capacitor cavities whose resonance frequencies are tuned by the motion of a mechanically compliant capacitor. Microwave drives are inductively coupled to both cavities via a single port. The reflected signals and the noise emitted by the cavities are amplified and demodulated at room temperature. (b) False-color optical micrograph of the aluminum device on a sapphire substrate (blue). (c) False-color scanning electron micrograph of the mechanically compliant vacuum gap capacitor. (d) Diagram of the density of states (DoS) as a function of frequency. Except for the mechanical linewidth, all the frequencies and linewidths are to scale. The red dashed lines indicate the two parametric drive frequencies, at the lower mechanical sidebands of each cavity, ${\omega }_{1,2}^{-}={\omega }_{1,2}-{\mathrm{\Omega }}_m$.

Figure 2

Conversion efficiency. (a) Magnitude of the transmission (orange) and reflection (bright and dark blue) coefficients on resonance, as a function of the total cooperativity $C_1+C_2$. The photon-phonon conversion rate for each cavity is balanced so that $C_1=C_2$. The solid lines are the theoretical predictions from Eqs. (1) and ((2)). The dotted line is the inferred internal transmission efficiency ${|t|}^2/{\eta }_1{\eta }_2$. The FWHM of the conversion, $\mathrm{\Gamma }\approx {\mathrm{\Gamma }}_m(C_1+C_2)$, is shown on the top $x$ axis. (b) Magnitude of the transmission (orange) and reflection (bright and dark blue) coefficients as a function of the probe detuning with respect to the cavity frequencies, for $C_1+C_2=156$, showing a clear Lorentzian shape of width $\mathrm{\Gamma }$.

Figure 3

Noise performance. (a) Noise spectrum emitted by cavity 1, around ${\omega }_1={\omega }_1^{-}+{\mathrm{\Omega }}_m$, for $C_1+C_2=40$, 160, and 2520 (with $C_1=C_2$). The measurement noise floor corresponds to a system noise temperature of $T_{\mathit{N}}[{\omega }_1]=9.5\mathrm{K}$. The noise added by the frequency converter appears as a Lorentzian of width $\mathrm{\Gamma }$ and peak amplitude $n_2^{\mathrm{add}}$. (b) Noise added by the frequency conversion as a function of the total cooperativity $C_1+C_2$. The solid line is the theoretical prediction for an equilibrium mechanical thermal occupancy of $n_m^{\mathrm{th}}=60$. The right $y$ axis is the corresponding mechanical occupancy, following Eq. (2). The yellow, green, and blue dots correspond to the spectra shown in (a).

Figure 4

Tunable beam splitter. The magnitude of the transmission (orange) and reflection (bright and dark blue) coefficients on resonance, as a function of the ratio $C_2/C_1$ for a fixed $C_1=400$. The solid lines are the theoretical predictions from Eqs. (1) and (2). The device can be tuned from a near-ideal mirror ($C_2/C_1\ll 1$) to fully transparent ($C_2=C_1$), and for $C_2/C_1\approx 0.2$ one realizes a 50:50 beam splitter.