Effects of Casimir force on high-order sideband generation in an optomechanical system

Jie Yao; Yafei Yu; Zhiming Zhang

doi:10.3788/COL201816.111201

Journals >Chinese Optics Letters >Volume 16 >Issue 11 >Page 111201 > Article

Chinese Optics Letters
Vol. 16, Issue 11, 111201 (2018)

Effects of Casimir force on high-order sideband generation in an optomechanical system

Jie Yao, Yafei Yu^*, and Zhiming Zhang^**

Author Affiliations

Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices (School of Information and Optoelectronic Science and Engineering); Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China

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DOI: 10.3788/COL201816.111201 Cite this Article Set citation alerts

Jie Yao, Yafei Yu, Zhiming Zhang. Effects of Casimir force on high-order sideband generation in an optomechanical system[J]. Chinese Optics Letters, 2018, 16(11): 111201 Copy Citation Text

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Abstract

We introduce a Casimir force in a conventional optomechanical system to study the high-order sideband generation. In this system, a nanosphere is placed near the moveable mirror of the conventional optomechanical system. The moveable mirror is coupled to the cavity field and the nanosphere by the optomechanical interaction and the Casimir interaction, respectively. We find that the amplitude and cutoff order of the high-order sideband can be enhanced by decreasing the sphere–mirror separation (increasing the Casimir force) and increasing the optomechanical coupling strength. Our proposal provides an alternative method for generating the high-order sidebands and for measuring the Casimir force.

H = ℏ ω_{c} {\hat{a}}^{†} \hat{a} + (\frac{{\hat{p}}^{2}}{2 m} + \frac{1}{2} m ω_{m}^{2} {\hat{x}}^{2}) - ℏ g {\hat{a}}^{†} \hat{a} \hat{x} - \frac{π^{3} ℏ c R}{720 {(d - \hat{x})}^{2}} + i ℏ ε_{l} ({\hat{a}}^{†} e^{- i ω_{l} t} - H.c) + i ℏ (ε_{p} {\hat{a}}^{†} e^{- i ω_{p} t} - H.c),

(1)

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H_{rot} = ℏ Δ_{l} {\hat{a}}^{†} \hat{a} + (\frac{{\hat{p}}^{2}}{2 m} + \frac{1}{2} m ω_{m}^{2} {\hat{x}}^{2}) - ℏ g {\hat{a}}^{†} \hat{a} \hat{x} - \frac{π^{3} ℏ c R}{720 {(d - \hat{x})}^{2}} + i ℏ ε_{l} ({\hat{a}}^{†} - H.c) + i ℏ (ε_{p} {\hat{a}}^{†} e^{- i δ t} - H.c),

(2)

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\dot{\hat{p}} = - m ω_{m}^{2} \hat{x} + ℏ g {\hat{a}}^{†} \hat{a} + \frac{2 π^{3} ℏ c R}{720 {(d - \hat{x})}^{3}} - Γ_{m} \hat{p} + {\hat{F}}_{th}, \dot{\hat{x}} = \frac{\hat{p}}{m}, \dot{\hat{a}} = - (i Δ_{l} + κ - i g \hat{x}) \hat{a} + ε_{l} + ε_{p} e^{- i δ t} + \sqrt{2 κ} {\hat{a}}_{in},

(3)

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\dot{p} = - m ω_{m}^{2} x + ℏ g a^{*} a + \frac{2 π^{3} ℏ c R}{720 {(d - x)}^{3}} - Γ_{m} p, \dot{x} = \frac{p}{m}, \dot{a} = - (i Δ_{l} + κ - i g x) a + ε_{l} + ε_{p} e^{- i δ t} .

(4)

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a_{s} = \frac{ε_{l}}{(i Δ_{l} + κ) - i g x_{s}}, x_{s} = \frac{1}{m ω_{m}^{2}} [ℏ g {| a_{s} |}^{2} + \frac{2 π^{3} ℏ c R}{720 {(d - x_{s})}^{3}}] .

(5)

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S_{out} (ω) \propto | \int_{- \infty}^{+ \infty} S_{out} (t) e^{- i ω t} d t |,

(6)

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Jie Yao, Yafei Yu, Zhiming Zhang. Effects of Casimir force on high-order sideband generation in an optomechanical system[J]. Chinese Optics Letters, 2018, 16(11): 111201

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