Mechanical squeezing in a dissipative optomechanical system with two driving tones

Sumei Huang and Aixi Chen

Phys. Rev. A 103, 023501 – Published 3 February 2021

Abstract

The squeezed state of a macroscopic mechanical oscillator can be exploited to enhance the sensitivity of precision measurements. Here, we theoretically demonstrate that the displacement squeezing of a mechanical oscillator in a dissipative optomechanical system can be generated by the use of two driving tones tuned to the first upper and lower mechanical sidebands. We find that the displacement squeezing of the mechanical oscillator is determined by the powers of the two driving tones and the temperature of the environment. Even when the temperature of the environment is as high as 20 mK, the mechanical squeezing beyond 3 dB can be achieved. Moreover, we show that the mechanical squeezing can be detected by directly measuring the cavity output spectrum.

Received 7 November 2020
Accepted 19 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.023501

Physics Subject Headings (PhySH)

Optomechanics Quantum optics

Micromechanical & nanomechanical oscillators

Atomic, Molecular & Optical

Authors & Affiliations

Sumei Huang ^* and Aixi Chen^†

Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

^*Corresponding author: sumei@zstu.edu.cn
^†Corresponding author: aixichen@zstu.edu.cn

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Issue

Vol. 103, Iss. 2 — February 2021

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Images

Figure 1
The degree of the displacement squeezing (dB) of the mechanical oscillator as a function of the blue-detuned laser power $℘_{+} / ℘_{-}$ for different red-detuned laser powers $℘_{-} = 18 μ W$ (blue middle-dashed and pink short-dashed curves), $100 μ W$ (red solid and cyan long-dashed curves), $200 μ W$ (green solid curve with a disk marker and brown dotted curve), and $300 μ W$ (black solid curve with a square marker and orange dot-dashed curve) when $T = 0$ K. The blue middle-dashed curve, red solid curve, green solid curve with a disk marker, and black solid curve with a square marker correspond to the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The pink short-dashed, cyan long-dashed, brown dotted, and orange dot-dashed curves correspond to the combination of the dispersive and dissipative couplings ( $g_{ω} = 2 π \times 2 MHz / nm \times q_{zpf}, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The horizontal black dotted line represents that the degree of the mechanical displacement squeezing is 3 dB.
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Figure 2
The degree of the displacement squeezing (dB) and the effective thermal occupancy $n_{eff}$ of the mechanical oscillator as a function of the red-detuned laser power $℘_{-}$ ( $μ W$ ) for different temperatures of the environment $T = 0$ K (blue middle-dashed and pink short-dashed curves), 20 mK (red solid and cyan long-dashed curves), 40 mK (green solid curve with a disk marker and brown dotted curve), and 60 mK (black solid curve with a square marker and orange dot-dashed curve) when $℘_{+} / ℘_{-} = 0.63$ . The blue middle-dashed curve, red solid curve, green solid curve with a disk marker, and black solid curve with a square marker correspond to the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The pink short-dashed, cyan long-dashed, brown dotted, and orange dot-dashed curves correspond to the combination of the dispersive and dissipative couplings ( $g_{ω} = 2 π \times 2 MHz / nm \times q_{zpf}, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The horizontal black dotted line in the upper panel represents that the degree of the mechanical displacement squeezing is 3 dB.
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Figure 3
The degree of the displacement squeezing (dB) of the mechanical oscillator as a function of the temperature $T$ (mK) of the environment for different red-detuned laser powers $℘_{-} = 18 μ W$ (blue middle-dashed and pink short-dashed curves), $100 μ W$ (red solid and cyan long-dashed curves), $200 μ W$ (green solid curve with a disk marker and brown dotted curve), $300 μ W$ (black solid curve with a square marker and orange dotdashed curve) when $℘_{+} / ℘_{-} = 0.63$ . The blue middle-dashed curve, red solid curve, green solid curve with a disk marker, and black solid curve with a square marker correspond to the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The pink short-dashed, cyan long-dashed, brown dotted, and orange dot-dashed curves correspond to the combination of the dispersive and dissipative couplings ( $g_{ω} = 2 π \times 2 MHz / nm \times q_{zpf}, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ). The horizontal black dotted line represents that the degree of the mechanical displacement squeezing is 3 dB.
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Figure 4
The spectrum $S_{\tilde{z} out} (0.626 π, ω)$ (dB) of the output quadrature fluctuation versus the normalized frequency $ω / ω_{m}$ when $℘_{-} = 18 μ W$ and $T = 0$ K. The blue solid curve corresponds to the absence of the blue-detuned laser $(℘_{+} = 0)$ for the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ), the red dotted curve corresponds to the presence of the blue-detuned laser ( $℘_{+} / ℘_{-} = 0.63$ ) for the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ), the green dashed curve corresponds to the presence of the blue-detuned laser ( $℘_{+} / ℘_{-} = 0.63$ ) for the combination of the dispersive and dissipative couplings ( $g_{ω} = 2 π \times 2 MHz / nm \times q_{zpf}, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ).
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Figure 5
The contour plot of the spectrum $S_{\tilde{z} out} (ϕ, ω)$ (dB) of the output quadrature fluctuation versus the normalized frequency $ω / ω_{m}$ and the phase $ϕ / π$ of the local oscillator field for the purely dissipative coupling ( $g_{ω} = 0, g_{κ} = - 2 π \times 26.6 MHz / nm \times q_{zpf}$ ) when $℘_{-} = 18 μ W, ℘_{+} / ℘_{-} = 0.63$ , and $T = 0$ K.
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