Optomechanically induced absorption in parity-time-symmetric optomechanical systems

X. Y. Zhang, Y. Q. Guo, P. Pei, and X. X. Yi

Phys. Rev. A 95, 063825 – Published 16 June 2017

Abstract

We explore the optomechanically induced absorption (OMIA) in a parity-time- ( $PT$ -) symmetric optomechanical system (OMS). By numerically calculating the Lyapunov exponents, we find out the stability border of the $PT$ -symmetric OMS. The results show that in the $PT$ -symmetric phase the system can be either stable or unstable depending on the coupling constant and the decay rate. In the $PT$ -symmetric broken phase the system can have a stable state only for small gain rates. By calculating the transmission rate of the probe field, we find that there is an inverted optomechanically induced transparency (OMIT) at $δ = - ω_{M}$ and an OMIA at $δ = ω_{M}$ for the $PT$ -symmetric optomechanical system. At each side of $δ = - ω_{M}$ there is an absorption window due to the resonance absorption of the two generated supermodes. Comparing with the case of optomechanics coupled to a passive cavity, we find that the active cavity can enhance the resonance absorption. The absorption rate at $δ = ω_{M}$ increases as the coupling strength between the two cavities increases. Our work provides us with a promising platform for controlling light propagation and light manipulation in terms of $PT$ symmetry, which might have potential applications in quantum information processing and quantum optical devices.

Received 11 December 2016
Revised 24 April 2017

DOI:https://doi.org/10.1103/PhysRevA.95.063825

Physics Subject Headings (PhySH)

Light propagation, transmission & absorption Nonlinear optics Optomechanics

Micromechanical & nanomechanical oscillators Quantum cavities

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

X. Y. Zhang¹, Y. Q. Guo¹, P. Pei¹, and X. X. Yi^2,*

¹Department of Physics, Dalian Maritime University, Dalian 116026, China
²Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun, 130024, China

^*yixx@nenu.edu.cn

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Vol. 95, Iss. 6 — June 2017

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Images

Figure 1
(a) Schematic illustration of a $PT$ -symmetric OMS. It includes a passive OMS (with microtoroidal cavity mode ${\hat{a}}_{1}$ and a mechanical mode $\hat{b}$ ) coupled to an active microtoroidal cavity mode ${\hat{a}}_{2}$ with tunneling strength $g_{1}$ . Here ${\hat{a}}_{in, 1}$ and ${\hat{a}}_{out, 1}$ are the input and output field of the loss cavity. $κ_{1}$ ( $Γ_{M}$ ) and $κ_{2}$ are the optical (mechanical) loss rate and gain rate. (b) Level diagram describing the physics of the $PT$ -symmetric OMS: the blue detuned driving field at frequency $ω_{d}$ (red arrow) induces a transition from the state $| n_{1}, n_{2}, n_{M} + 1 〉$ ( $n_{1}, n_{2}, n_{M}$ represent the Fock state of the passive cavity, active cavity, and the mechanical oscillator, respectively) to the state $| n_{1} + 1, n_{2}, n_{M} + 2 〉$ . The cavity photons produced in the down-conversion process are degenerate with the near-resonant probe field at frequency $ω_{p} = ω_{d} + ω_{M}$ (green arrow), resulting in a constructive interference which is responsible for the OMIA.
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Figure 2
Three borders. The black solid line stands for the border between the $PT$ -symmetric phase and the $PT$ -symmetry-broken phase, while the blue dashed-dotted line denotes the border between the stable and unstable regimes for $g = 0$ and the red dashed line denotes the border between the stable and unstable regimes for $g = 2 π \times 36.3$ kHz ${nm}^{- 1}$ . The power of the driving field is $P_{d} = 1.51$ mW. Other parameters are $Δ_{1} = Δ_{2} = ω_{M}$ .
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Figure 3
Transmission rate $T$ of the probe field as a function of the probe detuning $δ$ near (a) $δ = - ω_{M}$ and (b) $δ = ω_{M}$ . The driving field power is $P_{d} = 1.51$ mW. Other parameters are ${\bar{Δ}}_{1} = ω_{M}$ .
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Figure 4
Transmission rate $T$ of the probe field as a function of the probe detuning $δ$ near (a) $δ = - ω_{M}$ and (b) $δ = ω_{M}$ . The coupling strength between the two cavities are $g_{1} = 0.3, g_{1} = 0.5 κ_{1}$ , and $g_{1} = 0.8 κ_{1}$ . The driving field power is $P_{d} = 1.51$ mW. Other parameters are ${\bar{Δ}}_{1} = Δ_{2} = ω_{M}$ and $κ_{2} = 0.2 κ_{1}$ .
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Figure 5
Transmission rate $T$ of the probe field as a function of the probe detuning $δ$ near $δ = - ω_{M}$ . The coupling strength between the first cavity and the mechanical oscillator is $g = 0$ and $g = 2 π \times 36.3$ kHz ${nm}^{- 1}$ . The coupling strength between the two cavities is (a) $g_{1} = 0.3 κ_{1}$ , (b) $g_{1} = 0.5 κ_{1}$ , and (c) $g_{1} = 0.8 κ_{1}$ . The gain rate of the second cavity is $κ_{2} = - 0.2 κ_{1}$ and the driving field power is $P_{d} = 1.51$ mW. Other parameters are the same as in Fig. 4.
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Figure 6
Transmission rate $T$ of the probe field as a function of the probe detuning $δ$ near $δ = ω_{M}$ . The radiation pressure interaction strength is $g = 0$ and $g = 2 π \times 36.3$ kHz ${nm}^{- 1}$ . The coupling strength between the two cavities is (a) $g_{1} = 0.5 κ_{1}$ , (b) $g_{1} = 1.0 κ_{1}$ , and (c) $g_{1} = 2.5 κ_{1}$ . Other parameters are the same as in Fig. 5.
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