Strong Optomechanical Squeezing of Light

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation-pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of $1.7\pm 0.2\mathrm{dB}$ below the shot-noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.

Popular Summary

Light interferometry is an important tool for sensing small displacements and forces that is widely used in astrophysics, biology, engineering, and many other disciplines. The sensitivity of a typical interferometer is limited by shot noise, which results from the discrete particle nature of photons. To improve the sensitivity of interferometers, researchers have therefore proposed using “squeezed” light. These are quantum states of light with reduced quantum fluctuations in one parameter (such as phase) at the price of increased fluctuations in another (such as amplitude). Methods for generating squeezed states generally couple the amplitude of a light beam to its phase, which has, for example, been accomplished using nonlinear optical media. Another promising possibility is optomechanical or “ponderomotive” squeezing, which involves coupling the quantum fluctuations in a light field to the mechanical motion of an oscillator. Optomechanical squeezing has the potential to be tunable to mechanical frequencies of interest and to be low loss, but so far, few experiments have been able to substantially squeeze light in this way.

Here, we show that controlling the interaction between a coherent light beam and a solid mechanical object can be used to prepare squeezed light at a level 32% below shot noise, which is the highest level of squeezing achieved to date with an optomechanical method. The experiment consists of transmitting light through a Fabry-Perot interferometer containing a small, vibrating dielectric membrane that is cooled to about 1 mK to reduce thermal noise. The highest level of squeezing occurs at frequencies close to the 1.5-MHz resonant frequency of the membrane.

The output of the optomechanical setup could be used in future interferometry experiments to perform continuous position measurements below the shot-noise limit. Interferometers that take advantage of the lower noise levels in squeezed states could soon be important for precision measurements in biology and the detection of gravitational waves.

Figure 1

Experimental diagram for optomechanical squeezing. (a) The signal beam (blue arrows) enters the optomechanical cavity as a coherent state. After the optomechanical interaction, a squeezed state emerges. The signal beam is detected either with balanced direct photodetection or with balanced homodyne detection by mixing with an optical local oscillator (LO) (green arrow). A weaker damping beam (red arrows) orthogonally polarized to the signal beam is also injected into the cavity. The two beams are combined before the cavity and separated after the cavity with polarizing beam splitters (PBS) and detected with photodetectors (PD). (b) Signal- and damping-beam detunings from the cavity resonance. (c) Representative $\delta X_I-\delta X_Q$ phase-space distributions of the signal beam for real and imaginary values of $r$, the Kerr parameter. The dashed circle represents the variance of the Gaussian noise distribution of the vacuum state. Distributions inside the dashed circle represent squeezed states. (d) Simulated signal-beam quadrature spectrum for $\Delta =0$ in the idealized case of zero temperature and no optical loss. Otherwise, Heisenberg-Langevin simulation parameters are set to experimental values: $\kappa /2\pi =1.7\mathrm{MHz}$, ${\Gamma }_0^{\mathrm{eff}}/2\pi =2.6\mathrm{kHz}$, ${\omega }_m/2\pi =1.53\mathrm{MHz}$, and $\sqrt{\overline{N}}{g}_0/2\pi =350\mathrm{kHz}$. The spectrum is displayed on a logarithmic scale. The region between the white contours is squeezed.

Figure 2

Quantum intensity noise suppression. (a) Directly detected optical intensity noise signal-beam spectra for several signal-beam detunings. Also displayed are the measured shot-noise level (gray curves) and the theoretical predictions (black curves). A 200-Hz bandwidth is used. The ratio of RPSN relative to thermal drive $R$ is fixed at 5.1. The damping beam provides ${\Gamma }_0^{\mathrm{eff}}/2\pi =2.7\mathrm{kHz}$ and ${\omega }_m^{\mathrm{eff}}/2\pi =1.524\mathrm{MHz}$. However, the total mechanical damping rate and resonance frequency change with the signal-beam detuning $\Delta$. (b) The minimum value of $S_I$ for spectra as displayed in (a) (blue circles). Statistical error bars indicate the standard deviation. The frequency where the minimum occurs ${\omega }_{\mathrm{opt}}$ shifts with $\Delta$ because of the optical spring effect. Also displayed are the mechanical thermal noise floor for our current parameters $1/R$ (dashed green line), the limit set by finite detection efficiency $1-ϵ$ (dot-dashed green line), the sum of the thermal and detection efficiency limits (dot-dot-dashed green line), and expected squeezing in the absence of optical loss and thermal motion (dotted gray line). (c) The directly detected optical intensity noise signal-beam spectrum with intentionally added white, classical amplitude noise (red curve), theoretical prediction (black curve), and level of added amplitude noise (gray line). (d) The mechanical displacement spectrum inferred from the damping-beam transmission spectrum (orange region) and Lorentzian fit (dotted black line). The detection noise floor is also shown (dotted gray line). One additional peak due to excess noise is visible in the bottom panel of (a) and in (d) at frequencies of approximately $1.545\mathrm{MHz}$ due to a thermally occupied mechanical mode of the cavity support structure.

Figure 3

Optical quadrature spectrum. (a) Color map of $S_{\varphi }$. The white contour is at the shot-noise level, and the region inside this contour is squeezed. Several additional noise peaks are evident at frequencies away from the mechanical resonance, due to motion of thermally occupied modes of the support structure. The inset shows the squeezed region in more detail and also includes a theoretical prediction (dashed black curves) of the expected shot-noise contour. The experimental parameters are the same as in Fig. 2, except $\Delta /2\pi =-42\mathrm{kHz}$. (b) Cuts through quadrature phase at three different frequencies 1.517 MHz (blue circles), 1.526 MHz (green stars), and 1.535 MHz (red triangles), averaged over a 1-kHz bandwidth, and corresponding to zero-free-parameter theoretical models (colored solid curves).

Figure 4

Calculated homodyne spectrum for finite signal-beam detuning. Homodyne transmission spectra $S_{\varphi }$ are calculated for three signal-beam-cavity detunings: (a) $\Delta /2\pi =0$, (b) $\Delta /2\pi =-42\mathrm{kHz}$, and (c) $\Delta /2\pi =-100\mathrm{kHz}$. The other parameters used are $g/2\pi =33\mathrm{Hz}$, $m=6.75\times {10}^{-12}\mathrm{kg}$, ${\omega }_m^{\mathrm{eff}}/2\pi =1.5243\mathrm{MHz}$, ${\Gamma }_0^{\mathrm{eff}}/2\pi =2560\mathrm{Hz}$, $T^{\mathrm{eff}}=3.8\times {10}^{-4}\mathrm{K}$, ${ϵ}_{\mathrm{ext}}=0.55$, $\kappa /2\pi =1.7\mathrm{MHz}$, ${\kappa }_R=0.6\kappa$, $\overline{N}=1.1\times {10}^8$, and ${ϵ}_{\mathrm{ext}}|{\overline{a}}_{\mathrm{out}}{|}^2/|{\overline{a}}_{\mathrm{LO}}{|}^2=0.1$. The parameters of (b) match the parameters of the measured spectrum presented in Fig. 3. With those parameters, the mechanical damping from the signal beam is 6 kHz. Calculated spectra are displayed on a logarithmic scale. The region between the white 0-dB contours is squeezed.