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Physica Scripta

Normal-mode splitting in the atom-assisted optomechanical cavity

Yan Han, Jiong Cheng, Ling Zhou

Published Nov 7, 2013• 10 citations
Publisher

Abstract

We investigate the normal-mode splitting for a cavity optomechanical system filled with two-level atomic media. The cavity field is pumped by a strong coupling laser and probed by a weak laser. We report that the movable mirror is multistable in the range of parameters. Under the resolved sideband regime, the normal-mode splitting of the output field can be seen. Our results show that the splitting separation in the absorption spectrum depends linearly on the number of atoms.

DOI
10.1088/0031-8949/88/06/065401

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We investigate the normal-mode splitting for a cavity optomechanical system filled with two-level atomic media. The cavity field is pumped by a strong coupling laser and probed by a weak laser. We report that the movable mirror is multistable in the range of parameters. Under the resolved sideband regime, the normal-mode splitting of the output field can be seen. Our results show that the splitting separation in the absorption spectrum depends linearly on the number of atoms.
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.
In this paper, we study theoretically bipartite and tripartite continuous variable entanglement as well as normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-P\'erot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing wave of the cavity mode. We first derive the general form of the Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of the cavity mode structure. We then restrict our treatment to the first vibrational sideband of the mechanical resonator and derive a tripartite atom-field-mirror Hamiltonian. We show that when the optical cavity is intensely driven, one can generate bipartite entanglement between any pair in the tripartite system and that, due to entanglement sharing, atom-mirror entanglement is efficiently generated at the expense of optical-mechanical and optical-atom entanglement. We also find that in such a system, when the Lamb-Dicke parameter is large enough, one can simultaneously observe the normal mode splitting into three modes.
Abstract We study the pump-probe response in an optomechanical cavity accommodating an ensemble of two-level atoms interacting with a cavity mode, which is pumped by a strong driving field and probed by a weak signal field. The atomic excitation is examined without taking any approximations and may be in any regimes ranging from the low limit to the high limit for a given collective coupling constant between the atomic ensemble and the cavity mode. This then results in different absorption and dispersion spectra (such as optomechanically induced transparency, Fano-resonance, normal-mode splitting) when the excitation transfer from cavity mode to atomic ensemble is controlled to change from ineffective to effective. This indicates that a hybrid optomechanical response is indeed determined by the excitation of the atomic ensemble embedded in the optomechanical cavity. It is also of interest that the output signal component and the inside atomic polarization show either synchronous or asynchronous behaviors depending on how the atom-field detuning is chosen, i.e. equal to the mechanical resonator frequency or its negative. Such features may open up an effective avenue in coherently manipulating the internal atomic polarization via the external signal field, and vice versa.
We consider the dynamics of a movable mirror (cantilever) of a cavity coupled through radiation pressure to the light scattered from ultracold atoms in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the displacement spectrum of the cantilever. We show that for large pump intensities the steady-state displacement of the cantilever shows bistable behavior. Due to atomic back action, the displacement spectrum of the cantilever is modified and depends on the position of the condensate in the Brillouin zone. We further analyze the occurrence of splitting of the normal mode into three modes due to mixing of the mechanical motion with the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction.
Strong coupling in optomechanical systems is the basic condition for observing many quantum phenomena such as optomechanical squeezing and entanglement. Normal-mode splitting (NMS) is the most evident signature of strong coupling systems. Here we show the NMS in the spectra of the movable mirror and the output field in an optomechanical system can be flexibly engineered by a combination of optical parametric amplifier (OPA) and coherent feedback (CF). Moreover, the NMS could be enhanced by optimizing the parameters such as input optical power, OPA gain and phase, CF strength in terms of amplitude reflectivity of beam splitter.
ABSTRACT Hybrid optomechanical systems that combine a cavity field, mechanical motion, and intracavity atomic media offer a versatile platform for engineering normal‐mode structure and macroscopic quantum correlations. Most atom‐assisted systems rely on passive absorbing media, leaving the role of an inverted ensemble acting as a resonant intracavity gain element largely unexplored. Here, we investigate a driven optomechanical cavity containing a movable mirror and two resonant atomic ensembles, one prepared in its ground state and the other inverted, thereby realizing a combined absorptive–amplifying intracavity response. We find that the inverted ensemble acts as an active control resource: tuning the gain coupling reshapes the hybrid‐mode structure and produces resolved normal‐mode peaks in both the mechanical and optical spectra, while the absorbing ensemble independently sets the mode linewidths and relative peak amplitudes. The coupling parameters control and redistribute the bipartite and tripartite Gaussian entanglement shared among the optical, mechanical, and atomic modes, with the mechanical thermal occupation setting the robustness of the correlations. Formulated with experimentally feasible parameters of existing strong‐coupling optomechanics, the scheme provides a tunable route to controlling normal‐mode splitting and quantum correlations in hybrid quantum systems.