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Physical Review A

Duality and bistability in an optomechanical cavity coupled to a Rydberg superatom

Dong Yan, Zhihai Wang, Chun-Nian Ren, Hang Gao, Yong Li, Jin-Hui Wu

Published Feb 11, 2015• 39 citations
Publisher

Abstract

We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.

DOI
10.1103/physreva.91.023813

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•Mar 29, 2015•0 citations
We study the steady-state behaviors of a typical optomechanical cavity coupled to cold Rydberg atoms with dipole-dipole interactions. The interacting atoms are described as one superatom of three collective states in a ladder configuration in the limit of a strong dipole blockade and a weak cavity field. We find that this hybrid system exhibits phenomena of conditional duality and nonlinear bistability in terms of mirror displacement, number of cavity photons, and Rydberg population, depending on the detuning of the cavity field, the strength of the optical driving field, and the number of cold atoms. It is of particular interest that the two branches of relevant curves may intersect to yield a nontrivial duality and bistability. Such correlated optical, mechanical, and atomic responses arise from the efficient feedback between atom-light and optomechanical interactions and have realistic applications, e.g., in realizing accurate optomechanical detection or attaining deterministic single photons.
We investigate the steady-state properties of a hybrid system where many cold atoms are confined in an optical cavity with a movable end mirror. The confined cold atoms interact with an external pump field and an internal cavity field in the three-level $\ensuremath{\Lambda}$ configuration. The internal cavity field is excited by an external driving field and exerts a radiation pressure upon the movable end mirror. Then the coupled atom-light and optomechanical interactions offer an efficient nonlinear feedback mechanism permitting the observation of three steady-state solutions for relevant variables near one atomic resonance. We find, in particular, that the weak-cavity-field assumption may result in very large errors for the first and second solutions when the number of cavity photons is only about 106{10}^{6}106. The main reason is that a typically weak light field can result in a sufficiently strong atom-light interaction in a very small cavity. Going beyond the weak-cavity-field assumption also allows us to observe an otherwise absent bistable behavior for the first solution in terms of mirror displacement and cavity photons, which is easy to control by modulating the pump and driving fields.
We investigate steady-state entanglement in a hybrid optomechanical cavity coupled to a Rydberg atomic ensemble confined within a single blockade region. The ensemble behaves as one superatom due to the rigid dipole blockade effect. Through optomechanical coupling, three types of bipartite entanglement emerge among the cavity, the Rydberg superatom, and the movable mirror. As the principal quantum number of the Rydberg atoms increases (leading to reduced atomic decay rates), the direct cavity–mirror coupling entanglement is redistributed into direct cavity–superatom coupling entanglement and indirect superatom–mirror coupling entanglement. Counterintuitively, this redistribution culminates in the complete suppression of two direct coupling entanglements, leaving only the indirect coupling entanglement persistent under resonant Stokes sideband conditions. Systematic parameter tuning reveals entanglement transfer pathways and establishes the preference of the superatom–mirror entanglement for specific principal quantum numbers. Furthermore, we demonstrate the thermal robustness of the surviving entanglement up to experimentally accessible temperatures. These findings advance the understanding of quantum entanglement in hybrid quantum systems and suggest applications in quantum information processing.
We study the optical bistability and dynamics in a hybrid optomechanical system, where the cavity mode is coupled to the mechanical resonator via radiation pressure and to a two-level atom via the Jaynes–Cummings coupling. The nonlinearity due to optomechanical coupling and the addition of an atom leads to bistable behaviors of the steady-state intracavity photon number and atomic population inversion. We show that the optical bistability can be effectively controlled by the Rabi frequency of the atomic driving field, the cavity–atom coupling strength, and the amplitude and frequency of the cavity pump field. Moreover, the effects of different initial conditions of the cavity field and the amplitude of the cavity pump field on the dynamics of the system also have been discussed.
In this paper, the phenomenon of the optical bistability of a cavity field is theoretically investigated in an optomechanical system containing an N-type atomic ensemble. In this hybrid optomechanical system, the atoms are coupled with two controlling light fields besides coupling with the cavity field. Under the nonresonant condition, we analyze the influences of the coupling strength between cavity and atoms, Rabi frequencies of the controlling light field, the detuning between the controlling light field and atoms, and pump field power on the optical bistable behavior of mean intracavity photon number. The nonlinear distribution of the mean intracavity photon number has a potential application in field optical switches and optical bistable devices.
Rydberg atoms have attracted considerable attention due to their several singular properties, such as strong long-range interactions, extremely long lifetimes, and very large polarizability. These characteristics make Rydberg atoms a good candidates for cavity quantum electrodynamics, quantum information, and many-body physics. Recently, the study of optomechanics has become a rapidly developing field due to its important applications in cooling of mechanical resonators, implementing precision measurements, slowing light, and preparing quantum entanglement. Obviously, optomechanical systems pave the way for quantum information processing and quantum communication. Specially, there is significant interest in quantum optomechanics due to its high compatibility that can be combined, to build hybrid systems for certain purposes, with the ultracold atoms, a superconducting single electron transistor, a magnetostrictive actuation, a charged oscillator resonator, etc. In this work, we investigate the optomechanically induced transparency (OMIT) and the resulting effect of slow light in a hybrid system composed of a Rydberg atomic ensemble embedded inside a simple optomechanical cavity. As a typical effect of destructive quantum interference, OMIT is widely used in quantum optics and quantum information processing. Based on the Rydberg blockade effect, a Rydberg atomic ensemble in the same blockade region embedded inside an optomechanical cavity can be regarded as a superatom that contains only a single Rydberg excitation. Therefore, the problem of exponentially increasing system size with the number of atoms increasing can be circumvented easily. The hybrid system becomes a coupling between a Rydberg superatom and an optomechanical cavity and the coupling strength is enhanced by a factor of square root of the number of atoms in the ensemble. In this system, the perfect OMIT, namely, an ideal OMIT dip with a very narrow window, can be attained when an effect of non-rotating wave approximation (NRWA) is considered. Further, we demonstrate that the term of NRWA plays a key important role in achieving perfect OMIT by comparing the optomechanical spectra obtained with and without NRWA effects. Our results show that in the resolved sideband regime the higher the quality factor of cavity is, the stronger the slow light effect becomes in the window of the perfect OMIT. Particularly, in achieving the ultraslow light, the long lifetime of the Rydberg atom shows its superiority.
We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the single driving laser as well as by varying different system parameters provided by the hybrid interaction. Significantly, even though the atomic cavity is not driven by any laser pump and there is no coupling with the mechanical oscillator directly, the intracavity optical field in the atomic cavity also exhibits bistability due to the optical coupling with the optomechanical cavity. In essence, our work emphasizes the possibility of realization of a better controllable optical switch depending on the hybrid interaction.