Laser Cooling and Optical Detection of Excitations in a $LC$ Electrical Circuit

We explore a method for laser cooling and optical detection of excitations in a room temperature $LC$ electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the $LC$ and at the same time interacting with light via an optomechanical force is shown to provide strong electromechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an “optical loud speaker” are outlined.

Figure 1

(Left) Schematic of a Fabry-Perot cavity with a nanomechanical membrane inserted in the waist of the cavity; the membrane, in turn, is part of a parametric capacitor. (Right) Equivalent circuit with a dc voltage bias describing the coupled electromechanical system.

Figure 2

Coupling of capacitor and membrane. (a) Schematic of the considered setup (left). A capacitor is made of a plate of area $A$ separated from a set of wires by a distance $D$. The wires have thickness $t$ and width $r$ and are separated by a distance $d$. A membrane of thickness $h$ is separated from the wires by a distance $x_m$. To find the capacitance we perform finite element method simulations over a cross section of the capacitor (right). The gray scale indicates the simulated electric potential with $r=D/4$, $d=3D/4$, $t=D/4$, $h=D/20$, and $ϵ=7.6$. (b) Ratio of capacitance with the membrane to a parallel plate geometry without membrane, $c$ (full curve, left axis), and characteristic length $-\zeta =C/(dC/dx)$ (dashed curve, right axis) for the same parameters as in (a).