Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator

When an optical field is reflected from a compliant mirror, its intensity and phase become quantum-correlated due to radiation pressure. These correlations form a valuable resource: the mirror may be viewed as an effective Kerr medium generating squeezed states of light, or the correlations may be used to erase backaction from an interferometric measurement of the mirror’s position. To date, optomechanical quantum correlations have been observed in only a handful of cryogenic experiments, owing to the challenge of distilling them from thermomechanical noise. Accessing them at room temperature, however, would significantly extend their practical impact, with applications ranging from gravitational wave detection to chip-scale accelerometry. Here, we observe broadband quantum correlations developed in an optical field due to its interaction with a room-temperature nanomechanical oscillator, taking advantage of its high-cooperativity near-field coupling to an optical microcavity. The correlations manifest as a reduction in the fluctuations of a rotated quadrature of the field, in a frequency window spanning more than an octave below mechanical resonance. This is due to coherent cancellation of the two sources of quantum noise contaminating the measured quadrature—backaction and imprecision. Supplanting the backaction force with an off-resonant test force, we demonstrate the working principle behind a quantum-enhanced “variational” force measurement.

Popular Summary

In the realm of quantum mechanics, it is impossible to make a measurement (the position of a particle, for example) without influencing the outcome of that measurement—an effect known as measurement-induced backaction. When light is reflected off a mirror to infer its displacement, for example, measurement backaction is due to quantum fluctuations of radiation pressure. Observing the effects of backaction on a macroscopic object under ambient temperature conditions has remained an elusive goal. We observe measurement backaction vis-à-vis the correlations created between the probe light and the motion of a room-temperature mechanical oscillator. We also demonstrate how these quantum correlations can be used to cancel measurement backaction and thus be used to improve the signal-to-noise ratio in force measurements.

Our experimental setup consists of a glass nanostring coupled to a circular optical cavity that supports standing electromagnetic waves around its edge known as “whispering gallery modes.” The system is held in a vacuum chamber at room temperature, and the cavity is probed with a laser. The vibration of the nanostring, acting as an effective nonlinear optical medium, creates correlations between the amplitude and phase of the laser light. We detect these quantum correlations, at the level of 10%, over frequencies of more than an octave around mechanical resonance. In addition, we use these in situ generated correlations to enhance the ability to detect an external force.

This measurement heralds the rise of optomechanical systems as a room-temperature platform for quantum-enhanced metrology and paves the road for the generation of squeezed light inside room-temperature interferometers.

Figure 1

Optomechanical quantum correlations. (a) Schematic of the experiment: The optomechanical system is formed by a ${\mathrm{Si}}_3{\mathrm{N}}_4$ nanobeam oscillator (red) evanescently coupled to ${\mathrm{SiO}}_2$ microdisk cavity (blue). Both are maintained at room temperature $(T\approx 300\mathrm{K})$ in a low-pressure ($\approx {10}^{-7}\mathrm{mbar}$) vacuum chamber. The cavity is probed on resonance with 780-nm light from a Ti:sapphire laser. The transmitted field is read out with a homodyne detector with variable local oscillator phase $\theta$. Amplitude and phase fluctuations of the light field are correlated after passing through the cavity, represented as squashing in a phase space cartoon. (b) Model of the homodyne photocurrent spectrum [normalized to vacuum noise, Eq. (9)] for detection near the amplitude quadrature ($\theta \approx 0°$). The signal (red line) has a symmetric part (blue line) due to physical motion and an asymmetric part (green line) due to quantum correlations.

Figure 2

Asymmetry in homodyne spectrum. (a) Resonant magnitude of the photocurrent signal ${\overline{S}}_{II}^{\theta }[{\mathrm{\Omega }}_m]$ (normalized to shot noise) as a function of the homodyne angle $\theta$. Blue points are measurements. Red line is a fit to Eq. (11). 40-dB suppression of the signal is achieved on the amplitude quadrature, limited by residual fluctuations in the homodyne angle (${\theta }_{\mathrm{rms}}<0.57°$). (b) Example spectra taken near the phase (green) and amplitude (blue) quadratures. Also plotted is the background with the meter laser blocked (gray), dominated by LO shot noise (detector electronic noise is 10 dB below shot noise). For all measurements, feedback is used to stabilize the mechanical mode, as discussed in the main text. Note that the sharp peak at 3.5 MHz is due to thermal motion of the fundamental in-plane beam mode. (c) Magnified image of the spectrum at two quadratures, $\theta =\pm 13°$, highlighted with vertical lines in (a) (blue is $+13°$, yellow is $-13°$). The $\sim 10\%$ asymmetry between the two spectra at Fourier frequency detunings away from mechanical resonance (${\mathrm{\Omega }}_m\approx 2\pi \times 3.5\mathrm{MHz}$) arises due to quantum correlations [last term in Eq. (11)]. Larger asymmetry is observed at Fourier frequencies farther from mechanical resonance, as predicted by Eq. (12). The spectra are measured at an injected power of $P_{\mathrm{in}}=280\mu \mathrm{W}$.

Figure 3

Asymmetry in spectrum as a function of homodyne angle. Each plot shows asymmetry of the homodyne spectra, $R_{\theta }$ [Eq. (14)], as a function of homodyne angle. From top to bottom, $R_{\theta }$ is plotted as the probe power (mean intracavity photon number) is increased: $P_{\mathrm{in}}=1.5,9,113.4\mu \mathrm{W}$ ($n_c\approx 0.3\times {10}^4,2.1\times {10}^4,58\times {10}^4$). Red lines are a model employing only quantum noises and independently inferred values of the effective single-photon cooperativity $\eta C_0$; gray band shows interval corresponding to uncertainties in either parameter.

Figure 4

Visibility of quantum correlations versus laser power. Blue points are measurement of $\mathrm{\Delta }R$ [Eq. (16)] as a function of laser power (referred to optomechanical cooperativity $C$). At each value of the injected power, the various blue points show $\mathrm{\Delta }R$ inferred from various choices of the detuning $\delta$. The red line is a prediction based on Eq. (16), with a notably square-root dependence on power. The gray line is a linear fit to the data, which would apply if the correlations were entirely due to classical amplitude noise in the laser [see Eq. (17)].

Figure 5

Quantum-enhanced force estimation. (a) Inset: Green shows homodyne photocurrent spectrum near phase quadrature showing the two balanced forces applied on the mechanical oscillator via radiation pressure from the auxiliary laser; gray is the shot-noise background. Main: Red line (blue line) shows the signal-to-noise ratio of the force $F_{+}$ ($F_{-}$) normalized to its value for phase quadrature detection, i.e., ${\mathrm{SN}}_{+(-)}^{\theta }/{\mathrm{SN}}_{+(-)}^{\pi /2}$. The asymmetry between the two traces at $\theta \approx \pm 10°$ is due to quantum-noise cancellation. Here, the laser input power is $P_{\mathrm{in}}=100\mu \mathrm{W}$. (b) Blue shows ${\mathrm{SN}}_{+}^{\theta }/{\mathrm{SN}}_{-}^{\theta }$, extracted as a ratio of the blue and red traces in (a). For a force balanced in intensity and frequency offset from resonance, Eq. (22) predicts that ${\mathrm{SN}}_{+}^{\theta }/{\mathrm{SN}}_{-}^{\theta }\propto R_{\theta }$. The solid red line is a prediction based on Eq. (22) in conjunction with Eq. (14), while red dashed line shows the same model excluding the contribution from quantum correlations.