Light storage and cavity supermodes in two coupled optomechanical cavities

Yong He

Phys. Rev. A 94, 063804 – Published 1 December 2016

Abstract

We theoretically investigate a hybrid optomechanical system including two coupled optomechanical cavities in the presence of two strong pump fields and a weak probe field. The photon-hopping coupling of the cavities gives rise to two cavity supermodes whose resonant frequencies can be obtained in the probe transmission spectrum. In a strong photon-hopping coupling regime, there is a large coupling rate between the probe field and one of the two cavity supermodes that is called a bright mode. The optomechanical couplings between the bright mode and two mechanical resonators can cause double optomechanically induced transparency (OMIT), which can be employed to both separately and simultaneously store two weak probe pulses with different central frequencies. We obtain the group delay (light storage time) of the probe field in the hybrid optomechanical system. The results suggest that compared with that of a single cavity optomechanical system, the maximum value of the storage time roughly quadrupled in a particular case. The physical origin of the results is discussed. The hybrid optomechanical system opens an avenue of light storage in cavity optomechanics.

Received 12 July 2016

DOI:https://doi.org/10.1103/PhysRevA.94.063804

Physics Subject Headings (PhySH)

Light-matter interaction Optomechanics Quantum optics

Atomic, Molecular & Optical

Authors & Affiliations

Yong He^*

School of Mathematics and Physics, Changzhou University, Changzhou 213164, China

^*hey@cczu.edu.cn

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Vol. 94, Iss. 6 — December 2016

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Images

Figure 1
Schematic diagram of two coupled optomechanical cavities via the photon-hopping interaction. Two strong pump fields $P_{1}, P_{2}$ with identical frequency $ω_{p u}$ are used to drive optical cavities 1 and 2, respectively. A weak probe field $ω_{p r}$ passes through the two cavities to reveal the optical response of the hybrid system, such as double OMIT, group delay, and so on. The inset shows that to achieve long-time light storage, $ω_{\pm} = ω_{p u} \pm ω_{m, i}$ , with $ω_{\pm}$ being cavity supermodes due to the photon-hopping interaction and $ω_{m, i}$ being the mechanical frequency of the mechanical mode $i$ .
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Figure 2
(a) The probe transmission ${| T |}^{2}$ versus $λ$ and $(ω_{p r} - ω_{c, 2})$ , showing two cavity supermodes. The red dashed line shows $ω_{p r} = ω_{c, 2} + λ - δ$ . (b) The probe transmission as a function of $(ω_{p r} - ω_{c, 2})$ with different photon-hopping coupling strengths $λ / 2 π = 0, 1, 3$ GHz. Three transmission peaks on the right (left) side originate from the resonant absorption of the bright mode $ω_{+}$ (dark mode $ω_{-}$ ) to the probe field. (c) The coupling rate $f_{+, in}$ ( $f_{-, in}$ ) between the bright mode (dark mode) and the probe field as a function of $λ$ . Other parameters are $Δ_{1} / 2 π = 1$ GHz, $Δ_{2} / 2 π = - 1$ GHz, and $C = 15$ .
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Figure 3
Two peaks of the probe transmission spectrum showing the absorption of the hybrid system to the probe field with frequency $ω_{p r} = ω_{p u} + ω_{m, i}$ ( $i = 1, 2$ ). The inset illustrates energy transfer from the probe field to the pump field. Other parameters are $Δ_{1} / 2 π = 1$ GHz, $Δ_{2} / 2 π = - 1$ GHz, $C = 200$ , and $λ / 2 π = 1$ GHz.
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Figure 4
(a) The probe transmission spectrum with different optomechanical cooperativity $C = 0, 200$ , illustrating double OMIT with two transparency windows. The inset interprets the physical origin of every transparency window (quantum interference between two optical pathways). (b) The width of the two transparency windows versus the optomechanical cooperativity ( $C = 10, 100, 200, 500$ ). Other parameters are $Δ_{1} / 2 π = - 0.5$ GHz, $Δ_{2} / 2 π = - 2.5$ GHz, and $λ / 2 π = 2$ GHz.
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Figure 5
(a) The group delays $τ_{1}, τ_{2}$ (corresponding to the two transparency windows) as a function of $C$ . (b) The group delay $τ_{2}$ versus $λ$ and $C$ . Other parameters are $Δ_{1} / 2 π = (\sqrt{5} - 2.8)$ GHz, $Δ_{2} / 2 π = (\sqrt{5} - 4.8)$ GHz, and $λ / 2 π = 2$ GHz.
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Figure 6
(a) The group delay $τ_{2}$ as a function of $C$ with $λ / 2 π = 0, 1, 2, 3.666, 5$ GHz. (b) The group delay $τ_{2}$ as a function of $λ$ with $C = 9$ . (c) The parameter $Γ_{opt, 2} / (C γ_{2} / 2)$ versus $λ$ , with $Γ_{opt, 2}$ being the optomechanical damping rate of mechanical resonator 2. Other parameters are $Δ_{1} / 2 π = (\sqrt{{(λ / 2 π)}^{2} + 1} - 2.8)$ GHz and $Δ_{2} / 2 π = (\sqrt{{(λ / 2 π)}^{2} + 1} - 4.8)$ GHz.
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