Double optomechanically induced transparency in coupled-resonator system

doi:10.1016/j.optcom.2014.07.083

Optics Communications

Volume 333, 15 December 2014, Pages 261-264

https://doi.org/10.1016/j.optcom.2014.07.083 Get rights and content

Abstract

We propose a scheme to generate double optomechanically induced transparency (OMIT) in an optomechanical system consisted of two tunneling-coupled resonators. One cavity is coherently driven by the pump and probe laser fields and the other cavity couples to a high-Q mechanical oscillator via radiation pressure. We follow the standard procedure in derivation of the response of probe field in the coupled-resonator optomechanical system and find that based on the coupled-resonator-induced transparency, when we couple the optomechanical interaction into the system the transparency window is split into two transparency windows for probe field.

Introduction

Quantum coherence in atoms has led to several interesting and unexpected phenomena. One typical aspect is electromagnetically induced transparency (EIT), where interference among electronic transitions has many applications such as slow light, reduced self-focusing and defocusing [1], and quantum memory [2]. Furthermore, double EIT is investigated, where two transparency windows appear. Double EIT also has potential applications such as that it could enable deterministic all-optical two-qubit gates for quantum computing [3] and generate NOON state as resources for quantum technology applications [4]. In addition, from the perspective of dispersion engineering or quantum-information storage, dielectric nanostructures appear to be an alternative promising system [5], [6], [7], and similar phenomena of EIT in atomic system due to the interference between the resonant pathways have been studied in the microcavity systems [8], [9], [10], [11], [12], [13], [14], [15]. Moreover, multiple transparency windows in the nanostructure allow transmissions of the probe light at multiple different frequencies simultaneously, and could be useful for multi-channel all-optical quantum network and multi-channel quantum information processing (QIP).

In general, EIT in microcavity system can be generated via either tunneling interaction between resonators [16] or cavity optomechanical interaction [17], both of which can be regarded as a strict analog of EIT in atomic system originating from interference effects [17]. In tunneling-coupled resonators, coupled-resonator-induced transparency and absorption that are remarkably similar to EIT and electromagnetically induced absorption (EIA) in atoms have been experimentally demonstrated [8], [9], in which the tunneling interaction is realized for typical whispering-gallery modes (WGMs) that propagate along the sphere׳s equator. When bringing two spheres nearly into contact, their WGMs can be evanescently coupled. Moreover, a new theoretical mechanism for stopping light has been proposed using a waveguide side coupled to optical resonators [18], [19]. Recently, with the advancement of micro- and nano-fabrication techniques, the mechanical oscillator possesses ultrahigh Q factor, for example the mechanical lifetimes can reach one second that have been demonstrated using stressed silicon nitride nanobeam [20] and nanomembrane [21] mechanical resonators operating in the MHz frequency regime. Further the mechanical response to thermal forces can be controlled by an optical field and ground-state laser cooling is experimentally achievable [22], [23]. Thus optomechanical system becomes an essential ingredient for quantum storage. In order to write and read out the optical information as a long-lived mechanical excitation, the phenomenon analogous to EIT is proposed by Agarwal and Huang [17], where when a high-quality cavity coupled a nanomechanical mirror under the optomechanical action, the pump–probe response shares all the features of the $Λ$ atomic system. In addition, optomechanically induced transparency (OMIT) does not rely on naturally occurring resonances and could therefore also be applied to previously inaccessible wavelength regions in EIT through the fabrication design such as the technologically important near-infrared. By now OMIT has been experimentally observed in several groups in both optical and microwave regimes [10], [11], [12], [13], [24]. In combination of coupled-resonator-induced transparency and OMIT, it is possible to realize double OMIT analogous to phenomenon of double EIT in atoms. When one extents the single transparency window to the double in the nanostructure system, some new physics and applications in all-optical communication will arise.

In this work, we present the generation of double OMIT in an optomechanical system consisted of two coupled resonators, in which two cavity modes are tunneling coupled and the coupling strength is tunable by adjusting the positions of the resonators. One cavity is coherently driven by the pump and probe laser fields and the other cavity couples to a high-Q mechanical oscillator via radiation pressure. We follow the standard procedure in derivation of the response of probe field in the coupled-resonator optomechanical system and find that there exist two transparency windows for probe field. Thus based on the coupled-resonator-induced transparency, when we add another degree of freedom via optomechanical interaction to couple to the transparency window, it breaks down the symmetry of EIT line and splits the single EIT into two transparency windows, leading the occurrence of double OMIT.

The paper is organized as follows. In Section 2, we introduce the coupled-resonator optomechanical system, and Section 3 we discuss the presence of double OMIT in the system. Finally we give the conclusion.

Section snippets

Model

For an optomechanical system consisted of two coupled optical resonators as shown in Fig. 1, two cavity fields are coupled via the photon tunneling interaction, the cavity on the left is driven by pump and probe laser fields, and the cavity on the right couples to the motion of oscillator through the radiation pressure [25]. The Hamiltonian of the system in the rotating frame of pump laser frequency is given by $\hat{H} = \sum_{i = 1, 2} Δ_{i} {\hat{a}}_{i}^{†} {\hat{a}}_{i} + ω_{m} {\hat{b}}^{†} \hat{b} + J ({\hat{a}}_{1}^{†} {\hat{a}}_{2} + {\hat{a}}_{2}^{†} {\hat{a}}_{1}) - g {\hat{a}}_{2}^{†} {\hat{a}}_{2} ({\hat{b}}^{†} + \hat{b}) + i ε_{c} ({\hat{a}}_{1}^{†} - {\hat{a}}_{1}) + i ε_{p} ({\hat{a}}_{1}^{†} e$

Discussion

Now we turn to discuss the feasibility of double OMIT in the coupled-resonator optomechanical system, and the relationship of the double OMIT to the tunneling strength of the two resonators and the optomechanical coupling strength. We take the parameters in the recent whispering-gallery microcavity (WGM) optomechanical system [10], where the mass m=20 ng, single photon coupling strength $g / 2 π = 2.16 kHz$ , damping rate of mechanical oscillator $γ_{m} / 2 π = 41.0 kHz$ , decay rate of cavity field $κ_{1} / 2 π = 15.0 MHz$ ,

Conclusion

To conclude, we present the generation of double OMIT in an optomechanical system in combination of coupled-resonator-induced transparency and optomechanically induced transparency schemes, which consists of two tunneling-coupled resonators. One cavity is coherently driven by pump and probe laser fields and the other cavity couples to a high-Q mechanical oscillator via radiation pressure. We follow the standard procedure in derivation of the response of probe field in the coupled-resonator

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Double optomechanically induced transparency in coupled-resonator system

Abstract

Introduction

Section snippets

Model

Discussion

Conclusion

Phys. Today

Nat. Photonics

Phys. Rev. A

Phys. Rev. Lett.

Nature (London)

Nature (London)

Phys. Rev. A

Phys. Rev. Lett.

Phys. Rev. A

Science

Nature (London)

Nature (London)

Phys. Rev. A

Phys. Rev. A

Phys. Rev. A

Phys. Rev. A