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Squeezed Light from a Silicon Micromechanical Resonator LETTER doi:10.1038/nature12307 Squeezed light from a silicon micromechanical resonator Amir H. Safavi-Naeini1,2*, Simon Gro¨blacher1,2*, Jeff T. Hill1,2*, Jasper Chan1, Markus Aspelmeyer3 & Oskar Painter1,2,4 Monitoring a mechanical object’s motion, even with the gentle electromechanical elements20, solid-state mechanical elements21–23 and touch of light, fundamentally alters its dynamics. The experimental ultracold gas-phase atoms6,24 integrated with or comprising Fabry–Pe´rot manifestation of this basic principle of quantum mechanics, its cavities, and on-chip nanophotonic cavities sensitive to mechanical link to the quantum nature of light and the extension of quantum deformations25,26. measurement to the macroscopic realm have all received extensive The canonical cavity-optomechanical system consists of an optical attention over the past half-century1,2. The use of squeezed light, with cavity resonance that is dispersively coupled to the position of a mech- quantum fluctuations below that of the vacuum field, was proposed anical resonance. The Hamiltonian describing the interaction between 3 ~ { ~ ^{z^ nearly three decades ago as a means of reducing the optical read-out light and mechanics is Hint Bgp0a^ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia^^x xzpf , where ^x xzpf (b b) is noise in precision force measurements. Conversely, it has also been the mechanical position, xzpf ~ B=2meff vm is the zero-point fluc- proposed that a continuous measurement of a mirror’s position with tuation amplitude, vm is the mechanical resonance frequency, meff is light may itself give rise to squeezed light4,5. Such squeezed-light the effective motional mass of the resonator, g0 is the frequency shift of generation has recently been demonstrated in a system of ultracold the optical resonance for a mechanical amplitude of x , B is Planck’s 6 zpf gas-phase atoms whose centre-of-mass motion is analogous to the constant divided by 2p, a^ and ^a{ are respectively the annihilation and motion of a mirror. Here we describe the continuous position mea- creation operators for optical excitations, and ^b and ^b{ are the analog- surement of a solid-state, optomechanical system fabricated from a ous operators for mechanical excitations. The optical cavity decay rate, silicon microchip and comprising a micromechanical resonator k, is the loss rate of photons from the cavity and the rate at which coupled to a nanophotonic cavity. Laser light sent into the cavity is optical vacuum fluctuations are coupled into the optical resonance27. used to measure the fluctuations in the position of the mechanical Similarly, the mechanical damping rate, ci, is the rate at which thermal resonator at a measurement rate comparable to its resonance fre- bath fluctuations couple to the mechanical system. In all experimental quency and greater than its thermal decoherence rate. Despite the realizations of solid-state optomechanics so far, including that pre- mechanical resonator’s highly excited thermal state (104 phonons), sented here, the optomechanical coupling rate, g0, has been much we observe, through homodyne detection, squeezing of the reflected smaller than k. As such, without a strong coherent drive, the inter- light’s fluctuation spectrum at a level 4.5 6 0.2 per cent below that of action of the vacuum fluctuations with the mechanics is negligible. vacuum noise over a bandwidth of a few megahertz around the Under the effect of a coherent laser drive, the cavity is populated with mechanical resonance frequency of 28 megahertz. With further a mean intracavity photon number Æncæ, and wep considerffiffiffiffiffiffiffiffi the optical fluc- device improvements, on-chip squeezing at significant levels should tuations about the classical steady state, ^a? hnciza^. This modifies be possible, making such integrated microscale devices well suited the optomechanical interaction, resulting in a linear coupling between for precision metrology applications. { the fluctuations of the intracavity optical field, X^0~^aza^ , and the The generation of states of light with fluctuations below that position fluctuations of the mechanical system, ^x: H ~BGX^ ^x x . 3,7–9 int 0 zpf of vacuum has been of great theoretical interest since the 1970s . Thep parametricffiffiffiffiffiffiffiffi linear coupling occurs at an effective interaction rate of Early experimental work demonstrated squeezing of a few per cent G: hncig0, and the mechanical motion is coupled to the intracavity below the vacuum noise level in a large variety of different nonlinear optical field at a rate of C ; 4G2/k. Through this interaction, the 10 11 meas systems, such as neutral atoms in a cavity , optical fibres and crystals intensity fluctuations of the vacuum field, X^ (in) (t), entering the cavity 12,13 h~0 with bulk optical nonlinearities . Modern experiments demonstrate impart a force on the mechanical system: squeezing of almost 13 dB (ref. 14). Initial research was mainly pursued pffiffiffiffiffiffiffiffiffiffiffi B C as a strategy to mitigate the effects of shot-noise, the manifestation ^ ~ meas ^ (in) FBA(t) Xh~0(t) ð1Þ of vacuum noise in the intensity detection of light, given the possi- xzpf bility of improved optical communication7 and better sensitivity in This radiation-pressure shot-noise (RPSN) force has previously been gravitational-wave detectors3,8. In recent years, in addition to being measured in an ultracold atomic gas24 and, more recently, on a mac- used in gravitational-wave detectors15, squeezed light has enhanced roscopic silicon nitride nanomembrane28. The mechanical motion is in metrology in more applied settings16,17. turn recorded in the phase of the light leaving the cavity: The vacuum fluctuations arising from the quantum nature of light pffiffiffiffiffiffiffiffiffiffiffi C determine our ability to resolve mechanical motion optically, and set ^ (out) ~{^ (in) { meas 18 Xh (t) Xh (t) 2 ^x(t) sin (h) ð2Þ limits on the perturbation caused by the act of measurement .A xzpf system well suited to studying quantum measurement experimentally ^ (j)~ {ihz { ih is that of cavity optomechanics, in which an optical cavity’s resonance Here Xh ^aje ^aj e , a^in and ^aout are respectively the operators of frequency is designed to be sensitive to the position of a mechanical the input and reflected optical fields from the cavity, and h is the quad- system. By monitoring the phase and intensity of the reflected light rature angle with h 5 0 and h 5 p/2 corresponding respectively to the from such a cavity, a continuous measurement of mechanical displace- intensity and phase quadratures. In such a measurement, the optical ment can be made. Systems operating on this simple principle have cavity has the role of the position detector, measuring the observable ^x been realized in a variety of experimental settings, such as in large-scale at a rate Cmeas, and the RPSN imposes a measurement back-action force laser gravitational-wave interferometers19, microwave circuits with on the mechanical system2. In addition to this back-action noise, thermal 1Kavli Nanoscience Institute and Thomas J. Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA. 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA. 3Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, A-1090 Wien, Austria. 4Max Planck Institute for the Science of Light, Gu¨ nther-Scharowsky-Straße 1/Bldg 24, D-91058 Erlangen, Germany. *These authors contributed equally to this work. 8 AUGUST 2013 | VOL 500 | NATURE | 185 ©2013 Macmillan Publishers Limited. All rights reserved RESEARCH LETTER fluctuations from the bath also drive the mechanical motion, with motion of the zipper cavity. A wavelength scan of the reflected signal their magnitudes becoming comparable as Cmeas approaches the ther- from the cavity is plotted in Fig. 2b, showing an optical resonance malization rate, Cthermal(v):cin(v),wheren(v) is the thermal bath with a linewidth k/2p 5 3.42 GHz at a wavelength of lc 5 1,540 nm. occupancy. Inefficiencies in the collection and detection of light result in addi- Formally, the output noise power spectral density (PSD) of the tional uncorrelated shot-noise in the measured signal and can reduce homodyne detector photocurrent, I, normalized to the shot-noise level the squeezing to undetectable levels. For the device studied here, the is found by taking the Fourier transform of the autocorrelation of cavity coupling efficiency, corresponding to the percentage of photons equation (2): sent into the cavity which are reflected, is determined to be gk 5 0.54. The g 5 C B fibre-to-chip coupling efficiency is measured at CP 0.90. A homodyne out ~ z 4 meas 2 z SII (v) 1 2 Sxx sin (h) Refxmg sin (2h) ð3Þ detection scheme allows for high-efficiency detection of arbitrary quad- xzpf 2 ratures of the optical signal field. Characterization and optimization of the efficiency of the entire optical signal path and homodyne detection where Sxx(v) is the noise PSD of the mechanical position fluctuations { g 5 of the resonator and x (v)~(m (v2 {v2{ic v )) 1 is the mech- system yielded an overall set-up efficiency of set-up 0.48, correspond- m eff m i m g 5 g g 5 anical susceptibility characterizing the response of the mechanical ing to a total signal detection efficiency of tot set-up k 0.26. Figure 2c shows the noise spectrum of the thermal motion of the system to an applied force. The PSD S (v) contains noise stemming xx mechanical resonator obtained by setting the laser frequency near from coupling to the thermal bath, quantum back-action noise from the cavity resonance and tuning the relative local-oscillator phase the light field and any other technical laser noise driving the mechanics of the homodyne detector, h , to measure the quadrature of the (Supplementary Information). The three terms in Sout(v) in equa- lock II reflected signal in which mechanical motion is imprinted.
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