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Journal of Modern Optics

Electromagnetically induced transparency in a quadratically coupled optomechanical system with an atomic medium

Yan Han, Jiong Cheng, Ling Zhou

Published Aug 23, 2012• 10 citations
Publisher

Abstract

We investigate a quadratically coupled optomechanical cavity system filled with a two-level atomic medium. The output of the cavity field exhibits analogous electromagnetically induced transparency when the optomechanical system interacts with the coupling and probe fields, respectively. We show that the introduction of the atomic medium can enhance the fluctuation of the displacement of the membrane as well as its energy. With the increasing of the atomic number, the dip of the absorption becomes deep.

DOI
10.1080/09500340.2012.714000

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We investigate a quadratically coupled optomechanical cavity system filled with a two-level atomic medium. The output of the cavity field exhibits analogous electromagnetically induced transparency when the optomechanical system interacts with the coupling and probe fields, respectively. We show that the introduction of the atomic medium can enhance the fluctuation of the displacement of the membrane as well as its energy. With the increasing of the atomic number, the dip of the absorption becomes deep.
Abstract We study the reflected and transmitted output properties of a weak probe field incident upon an optomechanical cavity separated by a membrane oscillator and filled with two-level cold atoms. We find that electromagnetically induced transparency (EIT) and optomechanically induced transparency (OMIT) may simultaneously exist owing to separate cavity–atom coupling and cavity-oscillator coupling, respectively. It is more interesting that the hybrid EIT and OMIT phenomena can be manipulated on demand to exhibit various spectral features on dispersion, transmission, and reflection. In particular, we discover the new hybrid double transparency window (a narrow OMIT dip appearing inside the wide EIT window), analogous to double EIT for a four-level atomic system in inverted-Y configuration. Meanwhile, we can reduce the hybrid EIT–OMIT to a single EIT or OMIT shape by changing the magnitude of the driving field power or the atomic number as desired. Furthermore, by changing the system’s detuning it is possible to change the location and the profile of the EIT, therefore switching the shape of the hybrid EIT–OMIT from symmetric to asymmetric, as well as for the profile to change from a absorption dip-like EIT to dispersion-like EIT in both real and imaginary parts of the output probe field. Also, by modifying system’s detuning we have control over the distribution of the output energy, something difficult to achieve with only one of the sub-systems available.
We describe how electromagnetically induced transparency can arise in quadratically coupled optomechanical systems. Due to quadratic coupling, the underlying optical process involves a two-phonon process in an optomechanical system, and this two-phonon process makes the mean displacement, which plays the role of atomic coherence in traditional electromagnetically induced transparency (EIT), zero. We show how the fluctuation in displacement can play a role similar to atomic coherence and can lead to EIT-like effects in quadratically coupled optomechanical systems. We show how such effects can be studied using the existing optomechanical systems.
We study an ensemble of identical -type atoms confined inside a cavity optomechanical system. We show that when the atoms have no absorption and dispersion the output field of the optomechanical system present a transparency phenomenon. The oscillation of the mirror does not affect the transparency of the atomic medium while the existence of the atomic medium results in two transparency windows of the output cavity field. We also show that the frequency of the oscillation mirror affects the analogy transparency of the output cavity field.
We investigate a hybrid optomechanical system composed of a micromechanical oscillator as a movable membrane and an atomic three-level ensemble within an optical cavity. We show that a suitably tailored cavity field response via electromagnetically induced transparency (EIT) in the atomic medium allows for strong coupling of the membrane's mechanical oscillations to the collective atomic ground-state spin. This facilitates ground-state cooling of the membrane motion, quantum state mapping, and robust atom-membrane entanglement even for cavity widths larger than the mechanical resonance frequency.
We theoretically investigate a multimode quadratic coupling optomechanical system (OMS) assisted with N cold Λ-type three-level atoms. The coupling interaction between two mechanical membranes (MR1 and MR2) and the cavity is quadratic. The three-level atoms interact with an external controlling field and an internal cavity field. The optical cavity is driven by a strong coupling field and a weak probe field. In the resolved sideband regime, four transparency windows are obtained due to the atomic coherence and quadratic coupling in the absorption spectrum for the suitable choice of the controlling parameters. We analyze how to vary the number of the transparency window dips and to adjust their mutual spacing by changing the controlling parameters such as strength of the quadratic coupling between MR1 (MR2) and the cavity, the collective coupling strength between the atomic ensemble and the cavity field, the Rabi frequency associated with the coupling interaction between the controlling field and the three-level atom, power of the coupling field, different frequencies and decay rates of MR1 (MR2), decay rate of the cavity field, and the environmental temperature. Further, we also demonstrate the normal-mode splitting in the generated Stokes and anti-Stokes field in the OMS, where the changing collective coupling strength affects the splitting width of the output field at the Stokes (anti-Stokes) frequency.