Erratum: Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes [Phys. Rev. A<b>77</b>, 033804 (2008)]

Genes, Claudiu; Vitali, David; Tombesi, Paolo; Gigan, Sylvain; Aspelmeyer, M.

doi:10.1103/physreva.79.039903

Cited by 196 publications

(397 citation statements)

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“…It is possible to model this deviation by taking an intracavity-power dependent heating of the mechanical mode into account. Heating of the mechanical mode can be caused by both quantum [1,33] or classical fluctuations [20] of the radiation pressure force. While the latter is ruled out in our experiment by the use of a low-noise laser source (quantum limited in amplitude and phase for the Fourier frequency of interest), the former effect cannot account for the heating due to its much smaller magnitude, as detailed below.…”

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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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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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“…It has also provided a good approach for fundamental studies of the transition between the quantum and the classical world [3]. This phenomenon can be realized in the optomechanical systems consisting of an optical cavity with a movable end mirror or with a membrane in the middle [4][5][6][7].…”

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Controllability of optical bistability, cooling and entanglement in hybrid cavity optomechanical systems by nonlinear atom–atom interaction

Dalafi

Naderi

Soltanolkotabi

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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We investigate the effects of atomic collisions as well as optomechanical mirror-field coupling on the optical bistability in a hybrid system consisting of a Bose-Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mirror-field and atom-field entanglements we find an interpretation for the cooling of the Bogoliubov mode. The advantage of this hybrid system in comparison to the bare optomecanical cavity with a two-mode moving mirror is the controllability of the frequency of the secondary mode through the s-wave scattering interaction.

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“…Following [27,28], we study the stability of this solution by applying the Routh-Hurwitz criterion [29], which at positive effective detuning ∆ = ∆ c + g > 0 is simplified to a constraint on pump strength,…”

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Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

Taylor

2014

Phys. Rev. A

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Optomechanics allows the transduction of weak forces to optical fields, with many efforts approaching the standard quantum limit. We consider force-sensing using a mirror-in-the-middle setup and use two coupled cavity modes originated from normal mode splitting for separating pump and probe fields. We find that this two-mode model can be reduced to an effective single-mode model, if we drive the pump mode strongly and detect the signal from the weak probe mode. The optimal force detection sensitivity at zero frequency (DC) is calculated and we show that one can beat the standard quantum limit by driving the cavity close to instability. The best sensitivity achievable is limited by mechanical thermal noise and by optical losses. We also find that the bandwidth where optimal sensitivity is maintained is proportional to the cavity damping in the resolved sideband regime. Finally, the squeezing spectrum of the output signal is calculated, and it shows almost perfect squeezing at DC is possible by using a high quality factor and low thermal phonon-number mechanical oscillator.Dramatic progress in coupling mechanics to light [1][2][3][4] suggests that such devices may be used in a wide variety of settings to explore quantum effects in macroscopic systems. Furthermore, such systems can be exquisitely sensitive to small perturbations, such as forces induced either by acceleration as in accelerometer [5] or by, e.g., coupling to surfaces or fields as in atomic force microscopy [6]. For such force measurements, a high quality factor (Q) mechanical oscillator acts as a test mass, transducing a force into a time-dependent displacement of the oscillator [7,8]. By using interferometric techniques to monitor the position of the oscillator, one can infer the force via optical signals. However, the radiation pressure coupling between the mechanical mode and optical mode has three consequences: photon shot noise, quantum backaction and dynamical backaction [1,9]. The dynamical backaction modifies the oscillator dynamics [10] and makes laser cooling [11,12] or amplification of phonons [13] in the mechanical system possible. Photon shot noise and quantum backaction, the former decreases with increasing input laser power while the latter increases with increasing input laser power, introduce two sources of noise on the displacement readout of the oscillator motion. An optimal compromise between these two noise sources leads to the standard quantum limit (SQL) in force sensing [7].The SQL, however, is itself not a fundamental limit. By using squeezed states of light [14], employing quantum nondemolition (QND) measurement [15], or by cavity detuning [16], the SQL can be surpassed. Here we show that in a coupled two-mode optomechanical system, if we drive it appropriately, the interaction between cavity photons and the mechanical oscillator will generate squeezed states of the output light. Measuring an appropriate quadrature of the output light field, we would get fewer fluctuations than that of the vacuum state, which makes it possib...

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Erratum: Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes [Phys. Rev. A77, 033804 (2008)]

Cited by 196 publications

References 1 publication

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

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

Controllability of optical bistability, cooling and entanglement in hybrid cavity optomechanical systems by nonlinear atom–atom interaction

Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit

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