Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath

Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

Figure 1

Schematic of the coupled harmonic oscillator system, with optomechanical cooling on oscillator $b$. We are interested in the regime where $a$ couples weakly to its heat bath, which means ${\gamma }_a\ll \lambda ,{\gamma }_b$.

Figure 2

(a) Rescaled position fluctuation spectrum for different values of optomechanical cooperativity ${\mathcal{C}}_{\mathrm{OM}}$, with the mechanical oscillator cooperativity chosen as ${\mathcal{C}}_{ab}=8$. (b) Rescaled effective temperature as a function of ${\mathcal{C}}_{\mathrm{OM}}$ for ${\mathcal{C}}_{ab}=50$ and different values of $|({\omega }_a-{\omega }_b)|/{\gamma }_b$.

Figure 3

(a) Optomechanical design consisting of two similar quarter-wave beam resonators, nominal length $L_0$, coupled through a center support region, width $w$, containing a photonic crystal optical structure that supports two optical modes $c$ and $d$. (b) Simulated symmetric (top) and antisymmetric (bottom) eigenmodes, $\epsilon \approx 0$. Insets show the strain deformation of a single photonic defect (envisioned as part of a “zipper” photonic crystal resonator) that would lead to a strong strain-induced optomechanical coupling only between optical and mechanical modes of the same parity. (c),(d) As the asymmetry $\epsilon$ is increased, the antisymmetric and symmetric modes are increasingly coupled, shifting the simulated eigenfrequencies and clamping losses (red squares and blue circles, respectively), consistent with fits to the theoretical model of Eq. (1) (black lines). Simulation parameters are $L_0=20\mu \mathrm{m}$, $h=0.3\mu \mathrm{m}$, and $w=0.5\mu \mathrm{m}$, corresponding to ${\omega }_0=2\pi \times 1.102\mathrm{MHz}$ and ${\gamma }_b/2=2\pi \times 70\mathrm{Hz}$ clamping loss for an individual arm fabricated from silicon nitride.