Quantum-noise reduction using a cavity with a movable mirror

Fabre, Claude; Pinard, M.; Bourzeix, S.; Heidmann, A.; Giacobino, E.; Reynaud, Serge

doi:10.1103/physreva.49.1337

Cited by 338 publications

(352 citation statements)

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“…crystalline resonators [35]. The properties of the system demonstrated here-a massive oscillator, prepared with very low average occupation, which is coupled to an ultra low loss fiber transport medium is pivotal for a variety of experiments and protocols involving photons and phonons, such as radiation pressure squeezing [36,37], entanglement [38] or QND measurements [32,39].…”

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confidence: 99%

Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit

et al. 2009

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The observation of quantum phenomena in macroscopic mechanical oscillators [1,2] has been a subject of interest since the inception of quantum mechanics. It may provide insights into the quantum-classical boundary, experimental investigation of the theory of quantum measurements [1,3,4], the origin of mechanical decoherence [5] and generation of non-classical states of motion.Prerequisite to this regime are both preparation of the mechanical oscillator at low phonon occupancy and a measurement sensitivity at the scale of the spread ∆x of the oscillator's ground state wavefunction. Over the past decade, it has been widely perceived that the most promising approach to address these two challenges are electro nanomechanical systems [2,6,7,8,9,10], which can be cooled with milli-Kelvin scale dilution refrigerators, and feature large ∆x ∼ 10 −14 m resolvable with electronic transducers such as a superconducting single-electron transistor [7,8,11], a microwave stripline cavity [9] or a quantum interference device [12]. In this manner, thermal occupation as low as 25 quanta [7,10] has been measured. Here we approach for the first time the quantum regime with a mechanical oscillator of mesoscopic dimensions-discernible to the bare eye-and 1000-times more massive than the heaviest nano-mechanical oscillators used to date. Imperative to these advances are two key principles of cavity optomechanics [13]: Optical interferometric measurement of mechanical displacement at the attometer level [14,15], and the ability to use measurement induced dynamic back-action [16,17,18,19] to achieve resolved sideband laser cooling [9,20] of the mechanical degree of freedom. Using only modest cryogenic pre-cooling to 1.65 K, preparation of a mechanical oscillator close to its quantum ground state (63 ± 20 phonons) is demonstrated.Simultaneously, a readout sensitivity that is within a factor of 5.5 ± 1.5 of the standard quantum limit [1,21] is achieved. Taking measurement backaction into account, this represents the closest approach to the Heisenberg uncertainty relation for continuous position measurements yet demonstrated. The reported experiments mark a paradigm shift in the approach to the quantum limit of mechanical oscillators using optical techniques and represent a first step into a new era of experimental investigation which probes the quantum nature of the most tangible harmonic oscillator: a mechanical vibration. * These authors contributed equally to this work. † tobias.kippenberg@epfl.ch 2 The experimental setting of the present work is a cavity optomechanical system, which parametrically couples optical and mechanical degrees of freedom via radiation pressure. In the present case, toroidal microresonators are employed which exhibit (cf. Fig. 1 Fig. 1b). The quality factors of the RBM can reach values up to 80,000 if clamping losses are mitigated by modal engineering [24]. To achieve a regime of low mechanical oscillator occupancy we apply laser cooling to a cryogenically pre-cooled micromechanical oscillator with high ...

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Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit

et al. 2009

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“…Furthermore, our knowledge of the other modes' dynamical behavior [17] appears as a major issue on the road to the quantum ground state as their out-of-resonance tails will no longer be negligible for extreme cooling ratios. Other possible novel effects in quantum optics include the experimental demonstration of the Standard Quantum Limit [21,22], radiation-pressure induced squeezing of light [23], Quantum Non Demolition measurements [24] or non-classical states of the resonator motion [25,26].…”

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Radiation-pressure cooling and optomechanical instability of a micromirror

Arcizet

Cohadon

Briant

et al. 2006

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PACS numbers:Recent experimental progress in table-top experiments [1,2] or gravitational-wave interferometers [3] has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers [4,5,6]. The appearance of such optomechanical instabilities [7,8] is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall [9], on the resonance frequency of a specially designed flexure oscillator [10], and through the optomechanical instability of a silica micro-toroidal resonator [11]. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator [12,13,14], either by passive [15] or active cooling techniques [16,17,18].The resonator is placed at the end of a linear cavity, along with a conventional coupling mirror (Fig. 1a). As we are only interested in the motion at frequencies Ω close to a resonance frequency Ω m of the resonator, the mirror dynamics can be approximated as the one of a single harmonic oscillator, with resonance frequency Ω m , mass M , damping Γ m and mechanical susceptibility:The resonator is submitted to a radiation pressure force F rad induced by the intracavity field. Depending on the detuning Ψ ≡ 4πL/λ [2π], where L is the cavity length and λ the laser wavelength, any small displacement x of the resonator induces a variation of the intracavity power P and of the radiation pressure (see Fig. 1b). As a consequence, the spring constant k = M Ω 2 m of the resonator is balanced by the radiation pressure force: for a positive detuning, the displacement creates a negative linear force and thereby an additional binding force, increasing the effective spring constant, whereas for a negative detuning, the force corresponds to a softening of the oscillator. Effects are null at resonance, maximum at half-width of the optical resonance, and proportional to the incident power. These effects hav...

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“…On the opposite, blue detuned side, damping is effectively reduced. If this effect overcomes intrinsic friction, an arbitrary thermal fluctuation will be amplified into an oscillation with increasing amplitude, driving the coupled system into a nonlinear regime (Aguirregabiria and Bel, 1987;Fabre et al, 1994;Braginsky et al, 2001;Marquardt et al, 2006). Finally, the system will settle into a stable, self-sustained oscillation, where radiation power input and dissipation are in balance.…”

Section: The Basic Optomechanical Setupmentioning

confidence: 99%