Quantum dynamics of a mechanical resonator driven by a cavity

Armour, A. D.; Rodrigues, D. A.

doi:10.1016/j.crhy.2012.03.006

Cited by 18 publications

(51 citation statements)

References 42 publications

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“…For this weak driving regime, it was found that mechanical states with sub-Poissonian statistics can be created in the SPSC regime. This conclusion was corroborated by numerical simulations [8][9][10]. Other works reported similar quantum states [11-13] over some parameter regions in the SPSC regime, and signalled a connection to the self-sustained oscillations present in the nonlinear regime.…”

supporting

confidence: 75%

Quantum nonlinear dynamics of optomechanical systems in the strong-coupling regime

Machado

Blanter

2016

Phys. Rev. A

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With an increasing coupling between light and mechanics, nonlinearities begin to play an important role in optomechanics. We solve the quantum dynamics of an optomechanical system in the multi-photon strong coupling regime retaining nonlinear terms. This is achieved by performing a Schrieffer-Wolff transformation on the Hamiltonian including driving terms. The approach is valid away from the red-and blue-sideband drive. We show that the mechanical resonator displays self-sustained oscillations in regimes where the linearized model predicts instabilities, and that the amplitude of these oscillations is limited by the nonlinear terms. Related oscillations of the photon number are present due to frequency mixing of the shifted mechanical and cavity frequencies. This leads to additional peaks in the cavity's power spectral density. Furthermore, we show that it is possible to create phonon states with sub-Poissonian statistics when the system is red-detuned. This result is valid even with strong driving and with initial coherent states.By coupling light and mechanics, optomechanical systems enable control of light by mechanical motion and vice versa. This coupling of light to modes of a mechanical resonator is often achieved via radiation pressure. Its nature is intrinsically nonlinear but its strength is typically smaller than all other physical parameters [1], undermining the significance of nonlinear effects. The majority of the observed physical phenomena can be thus understood using a linear description.The achievement of cooling a mechanical mode to its ground state [2,3] paves the way to state preparation and it increased the interest in quantum effects in mechanical motion, specifically creation of non-classical mechanical states. Such states can only be created in a nonlinear system, shifting the focus of attention to the single-photon strong coupling (SPSC) regime, where quantum dynamics and properties have been analyzed theoretically. The exact solution for the isolated system was discovered [4,5]. Dissipation, noise and the coherent drive have also been investigated by including them in the equations of motion and treating them as perturbations to the exact solution [6,7]. For this weak driving regime, it was found that mechanical states with sub-Poissonian statistics can be created in the SPSC regime. This conclusion was corroborated by numerical simulations [8][9][10]. Other works reported similar quantum states [11-13] over some parameter regions in the SPSC regime, and signalled a connection to the self-sustained oscillations present in the nonlinear regime. Experimentally, the SPSC regime remains a challenge, though considerable progress has been made.Higher single-photon coupling strengths were already obtained in a variety of setups where the single-photon coupling surpasses the mechanical frequency Ω [14] (or is close to it [15]). However, in these setups, the cavity linewidth exceeds the single-photon coupling. Alternatively, the interaction can be enhanced by coherently driving the system. The d...

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confidence: 75%

Quantum nonlinear dynamics of optomechanical systems in the strong-coupling regime

Machado

Blanter

2016

Phys. Rev. A

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“…Theoretical work suggests that it is possible to prepare a state with quantum signatures in the phonon statistics such as phonon antibunching and even negative Wigner density [19][20][21][22][23][24]. However, the requirements to see phonon antibunching scale unfavorably with the system parameters, so that sub-Poissonian phonon statistics has eluded experimental observation.…”

Section: Introductionmentioning

confidence: 99%

Sub-Poissonian phonon lasing in three-mode optomechanics

Lörch¹,

Hammerer²

2015

Phys. Rev. A

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We propose to use the resonant enhancement of the parametric instability in an optomechanical system of two optical modes coupled to a mechanical oscillator to prepare mechanical limit cycles with sub-Poissonian phonon statistics. Strong single-photon coupling is not required. The requirements regarding sideband resolution, circulating cavity power, and environmental temperature are in reach with state of the art parameters of optomechanical crystals. Phonon antibunching can be verfied in a Hanburry Brown-Twiss measurement on the output field of the optomechanical cavity.

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“…The effective FPE derived here exactly reproduces the one of Rodrigues and Armour [25,26] when neglecting the different description of the Kerr nonlinearity of the cavity, which is treated in the standard master-equation picture there. In comparison to Refs.…”

Section: Introductionmentioning

confidence: 55%

“…The second approach concerns the case of weak driving fields for which the cavity essentially stays close to its ground (vacuum) state that corresponds to the regime considered in Refs. [25,26]. In this case, the master equation [Eq.…”

Section: B Fokker-planck Equation For the Mechanical Oscillatormentioning

confidence: 97%

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Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

et al. 2014

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Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Phys. Rev. Lett. 109, 253601 (2012)]. Here, we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime that correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation and is based on techniques borrowed from the laser theory due to Haake and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte Carlo simulations and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e., outside the single-photon strong-coupling regime, for strong cavity drive and rather large limit-cycle amplitudes. The approach taken here provides a natural starting point for further studies of quantum effects in optomechanics

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Quantum dynamics of a mechanical resonator driven by a cavity

Cited by 18 publications

References 42 publications

Quantum nonlinear dynamics of optomechanical systems in the strong-coupling regime

Quantum nonlinear dynamics of optomechanical systems in the strong-coupling regime

Sub-Poissonian phonon lasing in three-mode optomechanics

Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

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