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Sideband cooling beyond the quantum backaction limit with squeezed light

Nature volume 541, pages 191–195 (2017)Cite this article

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Abstract

Quantum fluctuations of the electromagnetic vacuum produce measurable physical effects such as Casimir forces and the Lamb shift1. They also impose an observable limit—known as the quantum backaction limit—on the lowest temperatures that can be reached using conventional laser cooling techniques2,3. As laser cooling experiments continue to bring massive mechanical systems to unprecedentedly low temperatures4,5, this seemingly fundamental limit is increasingly important in the laboratory6. Fortunately, vacuum fluctuations are not immutable and can be ‘squeezed’, reducing amplitude fluctuations at the expense of phase fluctuations. Here we propose and experimentally demonstrate that squeezed light can be used to cool the motion of a macroscopic mechanical object below the quantum backaction limit. We first cool a microwave cavity optomechanical system using a coherent state of light to within 15 per cent of this limit. We then cool the system to more than two decibels below the quantum backaction limit using a squeezed microwave field generated by a Josephson parametric amplifier. From heterodyne spectroscopy of the mechanical sidebands, we measure a minimum thermal occupancy of 0.19 ± 0.01 phonons. With our technique, even low-frequency mechanical oscillators can in principle be cooled arbitrarily close to the motional ground state, enabling the exploration of quantum physics in larger, more massive systems.

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Figure 1: Experimental set-up.
Figure 2: Theoretical mechanical bath temperature in the presence of squeezed light.
Figure 3: Experimentally measured power spectral densities of the upper and lower mechanical sidebands.
Figure 4: Observed cooling enhancement with squeezed light.

References

  1. Milonni, P. W. The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, 1993)

  2. Marquardt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007)

    Article  ADS  Google Scholar 

  3. Wilson-Rae, I., Nooshi, N., Zwerger, W. & Kippenberg, T. J. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett. 99, 093901 (2007)

    Article  ADS  CAS  Google Scholar 

  4. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011)

    Article  ADS  CAS  Google Scholar 

  5. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011)

    Article  ADS  CAS  Google Scholar 

  6. Peterson, R. et al. Laser cooling of a micromechanical membrane to the quantum backaction limit. Phys. Rev. Lett. 116, 063601 (2016)

    Article  ADS  CAS  Google Scholar 

  7. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014)

    Article  ADS  Google Scholar 

  8. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010)

    Article  ADS  Google Scholar 

  9. Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016)

    Article  ADS  CAS  Google Scholar 

  10. Wilson, D. J. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015)

    Article  ADS  CAS  Google Scholar 

  11. Phillips, W. D. Nobel lecture: Laser cooling and trapping of neutral atoms. Rev. Mod. Phys. 70, 721–741 (1998)

    Article  ADS  CAS  Google Scholar 

  12. Wineland, D. J. Nobel lecture: Superposition, entanglement, and raising Schrodinger’s cat. Rev. Mod. Phys. 85, 1103–1114 (2013)

    Article  ADS  CAS  Google Scholar 

  13. Vanner, M. R. et al. Pulsed quantum optomechanics. Proc. Natl Acad. Sci. USA 108, 16182–16187 (2011)

    Article  ADS  CAS  Google Scholar 

  14. Liu, Y.-C., Xiao, Y.-F., Luan, X. & Wong, C. W. Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics. Phys. Rev. Lett. 110, 153606 (2013)

    Article  ADS  Google Scholar 

  15. Elste, F., Girvin, S. M. & Clerk, A. A. Quantum noise interference and backaction cooling in cavity nanomechanics. Phys. Rev. Lett. 102, 207209 (2009)

    Article  ADS  Google Scholar 

  16. Ojanen, T. & Børkje, K. Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency. Phys. Rev. A 90, 013824 (2014)

    Article  ADS  Google Scholar 

  17. Huang, S. & Agarwal, G. S. Enhancement of cavity cooling of a micromechanical mirror using parametric interactions. Phys. Rev. A 79, 013821 (2009)

    Article  ADS  Google Scholar 

  18. Lü, X.-Y. et al. Squeezed optomechanics with phase-matched amplification and dissipation. Phys. Rev. Lett. 114, 093602 (2015)

    Article  ADS  Google Scholar 

  19. Cirac, J. I. & Zoller, P. Laser cooling of trapped ions in a squeezed vacuum. Phys. Rev. A 47, 2191–2195 (1993)

    Article  ADS  CAS  Google Scholar 

  20. Graham, R., Walls, D. F. & Zhang, W. Laser cooling in a squeezed vacuum. Phys. Rev. A 44, 7777–7784 (1991)

    Article  ADS  CAS  Google Scholar 

  21. Shevy, Y. Laser cooling of atoms in squeezed vacuum. Phys. Rev. Lett. 64, 2905–2908 (1990)

    Article  ADS  CAS  Google Scholar 

  22. Loudon, R. & Knight, P. L. Squeezed light. J. Mod. Opt. 34, 709–759 (1987)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981)

    Article  ADS  Google Scholar 

  24. Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator. Nat. Phys. 12, 683–687 (2016)

    Article  CAS  Google Scholar 

  25. Paris, M. G. A., Illuminati, F., Serafini, A. & De Siena, S. Purity of Gaussian states: measurement schemes and time evolution in noisy channels. Phys. Rev. A 68, 012314 (2003)

    Article  ADS  Google Scholar 

  26. Cicak, K. et al. Low-loss superconducting resonant circuits using vacuum-gap-based microwave components. Appl. Phys. Lett. 96, 093502 (2010)

    Article  ADS  Google Scholar 

  27. Safavi-Naeini, A. H. et al. Laser noise in cavity-optomechanical cooling and thermometry. New J. Phys. 15, 035007 (2013)

    Article  ADS  Google Scholar 

  28. Purdy, T. P. et al. Optomechanical Raman-ratio thermometry. Phys. Rev. A 92, 031802 (2015)

    Article  ADS  Google Scholar 

  29. Underwood, M. et al. Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime. Phys. Rev. A 92, 061801 (2015)

    Article  ADS  Google Scholar 

  30. Vahlbruch, H., Mehmet, M., Danzmann, K. & Schnabel, R. Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency. Phys. Rev. Lett. 117, 110801 (2016)

    Article  ADS  Google Scholar 

  31. Harlow, J. Microwave Electromechanics: Measuring and Manipulating the Quantum State of a Macroscopic Mechanical Oscillator. PhD thesis, Univ. Colorado, Boulder (2013)

  32. Fabre, C. et al. Quantum-noise reduction using a cavity with a movable mirror. Phys. Rev. A 49, 1337–1343 (1994)

    Article  ADS  CAS  Google Scholar 

  33. Mancini, S. & Tombesi, P. Quantum noise reduction by radiation pressure. Phys. Rev. A 49, 4055–4065 (1994)

    Article  ADS  CAS  Google Scholar 

  34. Brooks, D. W. C. et al. Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012)

    Article  ADS  CAS  Google Scholar 

  35. Purdy, T. P., Yu, P.-L., Peterson, R. W., Kampel, N. S. & Regal, C. A. Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013)

    Google Scholar 

  36. Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013)

    Article  ADS  CAS  Google Scholar 

  37. Dobrindt, J. M., Wilson-Rae, I. & Kippenberg, T. J. Parametric normal-mode splitting in cavity optomechanics. Phys. Rev. Lett. 101, 263602 (2008)

    Article  ADS  CAS  Google Scholar 

  38. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011)

    Article  ADS  CAS  Google Scholar 

  39. Verhagen, E., Delglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

This work was financially supported by NIST and the DARPA QuASAR program. J.B.C. acknowledges the NIST National Research Council Postdoctoral Research Associateship Program for its financial support. Contribution of the US government, not subject to copyright.

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Authors and Affiliations

  1. National Institute of Standards and Technology, Boulder, 80305, Colorado, USA

    Jeremy B. Clark, Florent Lecocq, Raymond W. Simmonds, José Aumentado & John D. Teufel

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  1. Jeremy B. Clark
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  2. Florent Lecocq
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  3. Raymond W. Simmonds
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  4. José Aumentado
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  5. John D. Teufel
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Contributions

J.B.C. and J.D.T. conceived and designed the experiment. F.L. fabricated the optomechanical circuit and contributed technical input for the experimental set-up. J.B.C. performed the measurements and data analysis, and developed the theory with assistance from J.D.T. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to John D. Teufel.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks P. Tombesi and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Cryogenic measurement set-up.

LPF, low-pass filter; JPA, Josephson parametric amplifier; OM, optomechanical; HEMT, high-electron-mobility transistor amplifier; μ-wave, microwave. The components shaded in grey signify broadband microwave attenuators. The rectangular components shaded red indicate directional couplers.

Extended Data Figure 2 Calculated power spectral density of the ponderomotive squeezing and antisqueezing that would be detected by an ideal homodyne receiver.

The solid lines indicate pondermotive squeezing and the dashed lines antisqueezing. SNL denotes the shot-noise limit (vacuum fluctuations). The indicated mechanical resonance frequency Ω includes optical springing effects. The colour of each curve denotes the resultant power spectral density produced by either of two coherent-state pump detunings satisfying (Δ/Δ0) ± 1 = constant. Here, Δ0 denotes the traditional optimal drive detuning when sideband cooling with coherent states (equation (31)). All curves assume a mechanical quality factor Qm = 5 × 105, a constant (and strong) optical damping rate Γopt = Γ+ − Γ− = 103Γ, a lossless optomechanical cavity and zero temperature. Additionally, a normalized cavity linewidth κ/Ω ≈ 2.85 has been assumed, which yields −10 dB of ponderomotive squeezing when Δ = Δ0 (see equation (30)).

Extended Data Figure 3 Calculated power spectral density (PSD) of the reflected drive field as would be detected by an ideal homodyne receiver.

The field quadrature being plotted is that which is maximally squeezed (ponderomotively). SNL denotes the shot-noise limit (vacuum fluctuations). All panels assume the same conditions as for Fig. 2, with the exception of a constant drive detuning (Δ = Δ0) and a constant drive cooperativity C = 4g2/(κΓ ) = 5,000. Each panel assumes a different level of injected squeezing, although the optimal squeezing phase θ = θ0 (equation (11)) is assumed throughout. The strength of the injected squeezing is parameterized by r, expressed in units of the critical squeezing parameter rc. The critical squeezing for this cavity is −5 dB.

Extended Data Figure 4 Modelling the impurity of the squeezing.

a, A pure squeezed state (with squeezing strength parameterized by rin) is subject to loss via a beamsplitter of transmittance ηin. Although the loss is to vacuum, the resulting squeezed state is impure and does not obey the minimum uncertainty relation: . b, Amplitude variance of a pure −10 dB squeezed state subject to loss as the squeezing phase θ is rotated (see inset). c, The Gaussian state in the right-hand panel of a can be equivalently represented with nl and r. The impurity is captured by the uncertainty product , which is maintained in the presence of an ideal entropy-preserving squeezing operation (parameterized by r). The dashed circles denote the standard vacuum fluctuations for reference. d, e, Computed values of r (d) and nl (e) given various values of input squeezing rin and ηin (see equations (39) and (40)).

Extended Data Figure 5 Numerically computed effective mechanical bath occupancy plotted against the normalized coupling rate g/κ for various pure squeezed states.

By numerically computing the full bath occupancy , we account for the role of ‘strong coupling’ physics discussed elsewhere. Various squeezing parameters r were considered (expressed in units of the critical squeezing parameter rc in equation (5)). All curves assume drive detuning Δ = Δ0 (equation (31)) and squeezing phase θ = θ0 (equation (11)). The optomechanical system is assumed to be deep in the resolved sideband cooling limit (κ/Ω = 0.1). The grey dashed line shows the strong coupling limit to the squeezing-enhanced cooling, which scales as (g/Ω)2.

Extended Data Figure 6 Comparison of the mechanical bath temperature with squeezed and unsqueenzed light in the presence of internal cavity loss.

The solid and dashed lines correspond to the mechanical bath temperature with squeezed (; equation (42)) and unsqueezed (; equation (2)) light, respectively. The bath occupancies are plotted as a function of the external coupling rate κext normalized by the internal loss rate of the cavity κ0. Each colour corresponds to a different value of κ0. All curves assume a drive detuning Δ0 (equation (31)) from cavity resonance and the corresponding optimal squeezing phase θ0 (equation (11)). and approach the same limit (equation (44)) as κext/κ0 → 0, indicating that internal cavity loss limits the coldest temperatures that can be reached when sideband cooling with any Gaussian state. For , diverges (equation (46)) whereas asymptotically approaches the ratio κ0/(4Ω) (equation (45)).

Extended Data Table 1 Summary of notation
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Clark, J., Lecocq, F., Simmonds, R. et al. Sideband cooling beyond the quantum backaction limit with squeezed light. Nature 541, 191–195 (2017). https://doi.org/10.1038/nature20604

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