Spatially Adiabatic Frequency Conversion in Optoelectromechanical Arrays

Faithful conversion of quantum signals between microwave and optical frequency domains is crucial for building quantum networks based on superconducting circuits. Optoelectromechanical systems, in which microwave and optical cavity modes are coupled to a common mechanical oscillator, are a promising route towards this goal. In these systems, efficient, low-noise conversion is possible using a mechanically dark mode of the fields, but the conversion bandwidth is limited to a fraction of the cavity linewidth. Here, we show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that the mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. Finally, we demonstrate that the bandwidth enhancement is, surprisingly, largest for small arrays; this feature makes our scheme particularly attractive for state-of-the-art experimental setups.

Figure 1

(a) Basic optoelectromechanical transducer formed by coupling an optical cavity and a microwave resonator to a common mechanical oscillator (the yellow membrane in the middle of the optical cavity). (b) Schematic representation of the transducer, including waveguides for input and output fields. (c) Transducer array for spatially adiabatic frequency conversion. The transducers are directionally coupled; signals propagate from left to right. (d) Continuous model for frequency conversion where the propagating fields are coupled via a spatially extended mechanical mode $b(z)$.

Figure 2

(a) Energy conversion spectrum for different array sizes. From dark colors to light, the array size is $N=1$, 10, 50, 200. The inset shows the phase of the conversion coefficient versus frequency for array sizes $N=5$ (solid blue line) and $N=20$ (dashed red line). (b) Transducer bandwidth [full-width half-maximum of the energy conversion coefficient $|T_{21}(\omega ){|}^2$] versus array size. The solid blue line shows results of numerical simulations; the dashed red line represents the analytical result (4) and the dot-dashed green line the linear fit $4g^{2}N/\kappa$. With the thin black line, we plot the bandwidth for an asymmetric transducer with ${\kappa }_1=\kappa ={\kappa }_2/10$. For both panels (and following discussion), we use $g=0.08\kappa$.

Figure 3

(a) Conversion efficiency (on resonance) versus array size for transmission loss between neighboring transducers 0.1% (solid blue line), 1% (dashed green line), and 5% (dot-dashed red line). (b) Conversion spectrum (its positive-frequency part) for $N=10$ transducers with backscattering rates (from dark to light) ${\kappa }_L/{\kappa }_R=0$, 0.1, 0.2, 0.5, 0.9.