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Room-temperature optomechanical squeezing

Abstract

Squeezed light—light with quantum noise lower than shot noise in some quadratures and higher in others—can be used to improve the sensitivity of precision measurements. In particular, squeezed light sources based on nonlinear optical crystals are being used to improve the sensitivity of gravitational wave detectors. In optomechanical squeezers, the radiation-pressure-driven interaction of a coherent light field with a mechanical oscillator induces correlations between the amplitude and phase quadratures of the light, which induce the squeezing. However, thermally driven fluctuations of the mechanical oscillator’s position make it difficult to observe the quantum correlations at room temperature and at low frequencies. Here, we present a measurement of optomechanically squeezed light, performed at room temperature in a broad band near the audio-frequency regions relevant to gravitational wave detectors. We observe sub-Poissonian quantum noise in a frequency band of 30–70 kHz with a maximum reduction of 0.7 ± 0.1 dB below shot noise at 45 kHz. We present two independent methods of measuring this squeezing, one of which does not rely on the calibration of shot noise.

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Fig. 1: An overview of the main subsystems in the experiment.
Fig. 2: Measured spectrum and modelled noise budget at 12° quadrature.
Fig. 3: Measured and budgeted noises on PDsqz at 14 different quadratures, distributed more densely near the squeezing quadrature and sparsely elsewhere.
Fig. 4: Calibration of squeezing by using correlations instead of measuring shot noise.

Data availability

Source Data are provided with this paper. All other data that support the plots within this paper and other findings of this study are referenced under https://doi.org/10.5281/zenodo.3694290.

Code availability

All code that support the plots within this paper and other findings of this study is referenced under https://doi.org/10.5281/zenodo.3694290. It can be downloaded from GitLab at https://git.ligo.org/nancy.aggarwal/room-temperature-optomechanical-squeezing.git and from GitHub at https://github.com/nancy-aggarwal/room-temperature-optomechanical-squeezing_github.git.

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Acknowledgements

This work was supported by National Science Foundation grants PHY-1707840, PHY-1404245, PHY-1806634 and PHY-1150531. We are particularly grateful to V. Sudhir, L. McCuller and M.J. Yap for valuable discussions and for their detailed comments on this manuscript. The microresonator manufacturing was carried out at the UCSB Nanofabrication Facility. We also thank MathWorks for their computing support.

Author information

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Authors

Contributions

N.A. led the work, with this being the major focus of her doctoral thesis. She also conducted a theoretical study to optimize the experimental parameters being used in this experiment. J.C. and T.C. built the optomechanical cavity and the vacuum system at LSU, where the measurements were performed. J.C., N.A. and T.C. built the detection system for this measurement. T.J.C., N.A. and T.C. made the measurements and performed the data analysis. N.A. wrote the manuscript with help from T.C., T.J.C., J.C., R.L. and N.M. N.A., J.C., A.L., R.L. and T.C. designed the mechanical oscillator used in this experiment. P.H., D.F. and G.D.C. fabricated the mechanical oscillators used in this experiment. T.C. and N.M. supervised the whole project.

Corresponding authors

Correspondence to Nancy Aggarwal, Thomas Corbitt or Nergis Mavalvala.

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The authors declare no competing interests.

Additional information

Peer review statement Nature Physics thanks Ryutaro Takahashi, Andre Xuereb and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Expected squeezing with lower detection loss and in the absence of technical noises.

The differential phase noise masks the squeezing at low frequencies, whereas the noise injected by the cavity feedback electronics degrades the high frequency side of the correlations. Once these technical noises have been suppressed, and the optical losses have been lowered, we would expect to see about 1.5 dB of squeezing from this system. This limit comes from a combination of escape efficiency and thermal noise (N. Aggarwal et al., in preparation).

Extended Data Fig. 2 Noise budget: contributing noise sources compared to the measurement as a function of quadrature, averaged over a 1 kHz bin.

Note that a 20 dB offset has been added to the differential phase noise in order to be visible on the same axis. Measured noise is shown in orange. Also shown are the contributions from quantum noise (with excess loss) in purple, thermal noise in red, differential phase noise in brown, and cavity-feedback noise in pink. The quadrature sum of all these contributions is shown in dashed green. All noises are relative to shot noise and are shown in dBs.

Extended Data Fig. 3 Noise budget: contributing noise sources compared to the measurement as a function of frequency at the squeezing quadrature, 12.

Measured noise is shown in orange. Also shown are the contributions from quantum noise (with excess loss) in purple, thermal noise in red, differential phase noise in brown, and cavity-feedback noise in pink. The quadrature sum of all these contributions is shown in dashed green. All noises are relative to shot noise and are shown in dBs.

Extended Data Fig. 4 Classical laser intensity noise and dark noise, shown relative to shot noise.

Since we always keep the total detected power on PDsqz constant (and just change the local oscillator (LO) power to change the measurement quadrature), the relative dark noise and classical laser intensity noise can just be scaled to that power.

Extended Data Fig. 5 A phasor diagram showing how the tunable homodyne detector selects the measurement quadrature.

The sum of the local oscillator (LO) field (blue) and the signal field (red) selects the quadrature that is being measured (green). In the entire manuscript, we report this angle θs as the measurement quadrature. We determine the quadrature by knowing the power in all the three fields, and the visibility. The dashed green circle represents a contour of constant detection power. In order to keep the shot noise reference unchanged, we choose to always lock PDsqz with a constant total detected power, and vary the LO power to change the measurement quadrature. This has the effect of changing the angle θ of the LO.

Extended Data Fig. 6 Measurement of the open loop transfer function of the homodyne locking loop around the squeezing frequency band.

Since this loop is designed only to suppress large path length fluctuations between the local oscillator and the signal at low frequencies (< 1 kHz), this loop has close to zero gain at our measurement frequencies.

Source data

Source Data Fig. 2

Data for Fig. 2: contains shot-noise measurement, shot-noise average, total measured noise and total budgeted noise as a function of frequency, and shows the total noise dips as low as 0.7 dB below shot noise between 30 kHz and 60 kHz.

Source Data Fig. 3

Data for Fig. 3: contains total measured and budgeted noise as a function of frequency and measurement quadrature. Data for each panel comprise 15 columns each, panel a being the first 15 columns and panel b the last 15 columns. In each dataset, the first column is measurement frequency and the rest are measurement quadratures.

Source Data Fig. 4

Data for Fig. 4: normalized correlation factor C, shot-noise-calibrated squeezing and correlation-calibrated squeezing, all as a function of frequency.

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Aggarwal, N., Cullen, T.J., Cripe, J. et al. Room-temperature optomechanical squeezing. Nat. Phys. 16, 784–788 (2020). https://doi.org/10.1038/s41567-020-0877-x

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