Cryogenic properties of optomechanical silica microcavities

We report the study of the optical and mechanical properties of high-$Q$ fused silica microtoroidal resonators at cryogenic temperatures (down to 1.6 K). A thermally induced optical multistability is observed and theoretically described, originating from the reverse thermally induced optical frequency shift. Moreover the influence of structural defect states (two level fluctuators) on their mechanical properties is observed and probed at an unprecedentedly achieved low phonon number. The resulting implications for cavity optomechanics and studies of mechanical decoherence are also discussed.

Figure 1

(Color online) (a) Experimental setup. FPC: fiber polarization controller and EDFA: erbium doped fiber amplifier. (b) Typical displacement noise spectrum obtained at low temperature (1.6 K, 4 mbar) for the radial breathing mode of a $30\text{−}\mu \text{m}$-radius toroid oscillating at 63 MHz. The rms amplitude of its Brownian motion (approximately 4 fm) serves as measure of the toroid temperature, proving its proper thermalization ensured by the exchange gas. (c) Optical resonance frequency ${\nu }_o\left(T\right)$ vs temperature. The solid line represents a polynomial fit of the data. (d) Relative optical frequency shift with temperature; i: $\frac{-1}{{\nu }_o}\frac{d{\nu }_o}{dT}$; ii: silica’s thermal expansion coefficient $\alpha$ [14]; iii: inferred effective refractive index contribution, $\frac{1}{n_{\text{eff}}}\frac{d{n}_{\text{eff}}}{dT}=-\frac{1}{{\nu }_o}\frac{d{\nu }_o}{dT}-\alpha$; iv: measured contribution of silica’s refractive index, from Ref. [15], and extrapolation to lower temperatures.

Figure 2

(Color online) Optical multistability at cryogenic temperatures. Above: normalized intracavity intensity $\tilde{I}$ versus normalized laser detuning ${\phi }_l$ for increasing input powers (13, 131, and $260\mu \text{W}$) presenting a multistable behavior (finesse: $44000$, optical linewidth $2{\Omega }_{\text{c}}/2\pi =28\text{MHz}$ critically coupled, $T_0=2.3\text{K}$). Below: results of the simulations for corresponding $\mu$ parameter (0.8, 8.4, and 16.7).

Figure 3

(Color online) (a) Laser detuning of the four turning points for varying input powers (${10}^5$ finesse, 4 K, and $R=30\mu \text{m}$). Their relative position defines the different observable regimes, reported in panel (b) for varying cavity finesse: (i): monostability; (ii): “red side” bistability; (iii): “blue side” bistability; (iv) and (v): tristability; and (vi) double bistability. (c) Typical transmission curve obtained for a lower exchange gas pressure (0.5 mbar, $P_{\text{in}}=280\mu \text{W}$, and $\mathcal{F}=31000$) presenting a double bistable behavior (region vi). (d) Optical resonance frequency shift inversion observed at higher exchange gas pressure (20 mbar), revealing the deposition of a superfluid film on the toroid.

Figure 4

(Color online) Mechanical damping $Q^{-1}$ and relative frequency shift $\delta {\Omega }_{\text{m}}/{\Omega }_{\text{m}}$ versus temperature for 36 MHz (red circles) and 63 MHz (black squares) resonators. The temperature dependence observed reveal the phonon coupling to structural defects states of glass, modelized by an assembly of TLS. The solid line is a fit of the thermally activated regime (above 10 K) according to [22]. The dotted line corresponds to an acoustic wave attenuation experiment, driven at 40 MHz [23].