Simultaneous cooling of coupled mechanical resonators in cavity optomechanics

Lai, Deng-Gao; Zou, Fen; Hou, Bo‐Yu; Xiao, Yun‐Feng; Liao, Jie‐Qiao

doi:10.1103/physreva.98.023860

Cited by 101 publications

(52 citation statements)

References 67 publications

(70 reference statements)

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“…In this section, we adopt the method of covariance matrix and use quantum Langevin equations in Equation to study the cooling dynamical behavior of the double MRs. Mathematically, the final MPN of the two MRs can be calculated by the relation

\begin{matrix} true \\ right n_{i} = \frac{1}{2} [false⟨ δ q_{i}^{2} false⟩ + false⟨ δ p_{i}^{2} false⟩ - 1] \end{matrix}

where

δ q_{i}^{2}

and

δ p_{i}^{2}

are the variances of position and momentum operators of two resonators (

i = 1, 2

). The dynamics of quantum fluctuations can be written in the form of matrices

\begin{matrix} true \\ right \overset{u}{true} (t) = A (t) u (t) + n (t) \end{matrix}

where

u^{T} false(t false) = false(δ q_{a}, δ p_{a}, δ q_{1}, δ p_{1}, δ q_{2}, δ p_{2} false)

is the vector of quadrature fluctuation operators, with the subscripts denoting the cavity mode and two mechanical modes,

n^{T} (t) = false(- \sqrt{κ} q_{a, in}, - \sqrt{κ} p_{a, in}, - \sqrt{γ_{1}} q_{1, in}, - \sqrt{γ_{1}} p_{1, in}

,…”

Section: Engineering Cooling Dynamics Using Fmsmentioning

confidence: 99%

“…It has been proved that ground‐state cooling of the double MRs can be realized under the resolved sideband regime

(κ < ω_{m})

. In order to realize the ground‐state cooling in USB regime, the Stokes heating processes must to be well suppressed.…”

Section: Engineering Cooling Dynamics Using Fmsmentioning

confidence: 99%

“…Recently, a scheme for cooling a single MR with periodical modulation has been proposed by Wang et al., in which the cooling efficiency is improved by using the FM. As a primary candidate for studying the macroscopic quantum coherence, cooling of double MRs possesses particular importance in quantum optics, and some distinctive dynamic properties will be emerged due to the competition between driving field and thermal dissipation. Therefore, in this paper, we propose a cooling scheme for the coupled MRs with periodical modulation and investigate the cooling dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The first MR is directly coupled to the optical cavity via radiation pressure, and simultaneously coupled with another MR through the so‐called position–position coupling, but the second MR does not interact directly with the cavity mode. We also adopt the idea of Stokes sideband suppression, but different from the previous investigations . Here, the cavity and double MRs are modulated periodically in our present work.…”

Section: Introductionmentioning

confidence: 99%

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Frequency‐Modulation‐Enhanced Ground‐State Cooling of Coupled Mechanical Resonators

et al. 2019

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The coupled mechanical resonators (MRs) are the prominent candidate for studying macroscopic quantum coherence. The prerequisite for observing macroscopic mechanical coherence is cooling the MRs to their ground state. Here, a theoretical scheme is proposed for improving the cooling of two coupled MRs by imposing frequency modulation (FM) upon the system to suppress the Stokes heating processes. By the methods of covariance analysis and numerical simulations, it is demonstrated that the cooling of double MRs can be realized in both stable and unstable regions with high efficiency compared to the cooling without FM, even if in unresolved sideband (USB) regime. By modulating the parameters appropriately, the cooling efficiencies of two MRs can be flexibly adjusted.

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\begin{matrix} true \\ right n_{i} = \frac{1}{2} [false⟨ δ q_{i}^{2} false⟩ + false⟨ δ p_{i}^{2} false⟩ - 1] \end{matrix}

where

δ q_{i}^{2}

and

δ p_{i}^{2}

are the variances of position and momentum operators of two resonators (

i = 1, 2

). The dynamics of quantum fluctuations can be written in the form of matrices

\begin{matrix} true \\ right \overset{u}{true} (t) = A (t) u (t) + n (t) \end{matrix}

where

u^{T} false(t false) = false(δ q_{a}, δ p_{a}, δ q_{1}, δ p_{1}, δ q_{2}, δ p_{2} false)

is the vector of quadrature fluctuation operators, with the subscripts denoting the cavity mode and two mechanical modes,

n^{T} (t) = false(- \sqrt{κ} q_{a, in}, - \sqrt{κ} p_{a, in}, - \sqrt{γ_{1}} q_{1, in}, - \sqrt{γ_{1}} p_{1, in}

,…”

Section: Engineering Cooling Dynamics Using Fmsmentioning

confidence: 99%

“…It has been proved that ground‐state cooling of the double MRs can be realized under the resolved sideband regime

(κ < ω_{m})

. In order to realize the ground‐state cooling in USB regime, the Stokes heating processes must to be well suppressed.…”

Section: Engineering Cooling Dynamics Using Fmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Frequency‐Modulation‐Enhanced Ground‐State Cooling of Coupled Mechanical Resonators

et al. 2019

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“…Generally, the physical phenomena involved many photons is easily observed because the coupling between the photons and phonons is effectively enhanced by a factor of the square root of the cavity photon number under the linearization frame. In the many-photon coupling case, many advances have been made in relating topics such as normal-mode splitting [5][6][7][8], quantum cooling of mechanical resonators [9][10][11][12][13][14][15][16], optomechanical entanglement [17][18][19][20][21], optomechanically induced transparency [22][23][24], and generation of squeezed light [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Enhancement of few-photon optomechanical effects with cross-Kerr nonlinearity

et al. 2019

Self Cite

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Few-photon optomechanical effects are not only important physical evidences for understanding the radiation-pressure interaction between photons and mechanical oscillation, but also have wide potential applications in modern quantum technology. Here we study the few-photon optomechanical effects including photon blockade and generation of the Schrödinger cat states under the assistance of a cross-Kerr interaction, which is an inherent interaction accompanied the optomechanical coupling in a generalized optomechanical system. By exactly diagonalizing the generalized optomechanical Hamiltonian and calculating its unitary evolution operator, we find the physical mechanism of the enhancement of photon blockade and single-photon mechanical displacement. The quantum properties in this generalized optomechanical system are studied by investigating the second-order correlation function of the cavity field and calculating the Wigner function and the probability distribution of the rotated quadrature operator for the mechanical mode. We also study the influence of the dissipations on the few-photon optomechanical effects.

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Simultaneous Cooling of Two Mechanical Resonators with Intracavity Squeezed Light

2021

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A scheme is proposed to cool two mechanical resonators simultaneously to the quantum ground state, whatever sideband resolution, in an optomechanical system with χ(2) nonlinear medium, where the cavity light is squeezed. By selecting the system parameters appropriately, the influence from cavity dissipation can be completely removed and the quantum backaction heating is suppressed at the same time. It is found that the cooling performance is determined by the coupling strength and frequency detuning between two mechanical resonators. The numerical results indicate that the final phonon occupancy of the two mechanical resonators is no longer strictly limited by the sideband resolution and the cooling scheme can work well no matter in weak or strong effective optomechanical coupling regime.

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Simultaneous cooling of coupled mechanical resonators in cavity optomechanics

Cited by 101 publications

References 67 publications

Frequency‐Modulation‐Enhanced Ground‐State Cooling of Coupled Mechanical Resonators

Frequency‐Modulation‐Enhanced Ground‐State Cooling of Coupled Mechanical Resonators

Enhancement of few-photon optomechanical effects with cross-Kerr nonlinearity

Simultaneous Cooling of Two Mechanical Resonators with Intracavity Squeezed Light

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