We investigate the effects of atomic collisions as well as optomechanical mirror-field coupling on the optical bistability in a hybrid system consisting of a Bose-Einstein condensate inside a driven optical cavity with a moving end mirror. It is shown that the bistability of the system can be controlled by the s-wave scattering frequency which can provide the possibility of realizing a controllable optical switch. On the other hand, by studying the effect of the Bogoliubov mode, as a secondary mechanical mode relative to the mirror vibrations, on the cooling process as well as the bipartite mirror-field and atom-field entanglements we find an interpretation for the cooling of the Bogoliubov mode. The advantage of this hybrid system in comparison to the bare optomecanical cavity with a two-mode moving mirror is the controllability of the frequency of the secondary mode through the s-wave scattering interaction.
We consider an optomechanical cavity made by two moving mirrors which contains a Kerr-down conversion nonlinear crystal. We show that the coherent oscillations of the two mechanical oscillators can lead to splitting in the electromagnetically induced transparency (EIT) resonance, and appearance of an absorption peak within the transparency window. In this configuration the coherent induced splitting of EIT is similar to driving a hyperfine transition in an atomic Lambda-type three-level system by a radio-frequency or microwave field. Also, we show that the presence of nonlinearity provides an additional flexibility for adjusting the width of the transparency windows. The combination of an additional mechanical mode and the nonlinear crystal suggests new possibilities for adjusting the resonance frequency, the width and the spectral positions of the EIT windows as well as the enhancement of the absorption peak within the transparency window.
In this paper, we have investigated theoretically the influence of atomic collisions on the behaviour of a one-dimensional Bose-Einstein condensate inside a driven optical cavity. We develop the discrete-mode approximation for the condensate taking into account the interband transitions due to the s-wave scattering interaction. We show that in the Bogoliubov approximation the atom-atom interaction shifts the energies of the excited modes and also plays the role of an optical parametric amplifier for the Bogoliubov side mode which can affect its normal-mode splitting behaviour. On the other hand due to the atomic collisions the resonance frequency of the cavity is shifted which leads to the decrease of the number of cavity photons and the depletion of the Bogoliubov mode. Besides, it reduces the effective atom-photon coupling parameter which consequently leads to the decrease of the entanglement between the Bogoliubov mode and the optical field.
Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model. The model is based on the generalized deformed oscillator algebra, )as a function of number operator N determines not only the intensity dependence of atom-field coupling when the model Hamiltonian is expressed in terms of nondeformed field operators but also the structure of initial state of the radiation field. With the field initially being in three different types of q-deformed coherent states, each of them corresponding to a particular form of the function ) (N f , the quantum collapse and revival effects as well as atomic dipole squeezing are studied for both on-and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures, which are, absent in the nondeformed Jaynes-Cummings model and the dipole squeezing may be enhanced PACS numbers: 42.50. Lc , 32.90.+a
The interaction of a single-mode field with both a weak Kerr medium and a parametric nonlinearity in an intrinsically nonlinear optomechanical system is studied. The nonlinearities due to the optomechanical coupling and Kerr-down conversion lead to the bistability and tristability in the mean intracavity photon number. Also, our work demonstrates that the lower bound of the resolved sideband regime and the minimum attainable phonon number can be less than that of a bare cavity by controlling the parametric nonlinearity and the phase of the driving field. Moreover, we find that in the system under consideration the degree of entanglement between the mechanical and optical modes is dependent on the two stability parameters of the system. For both cooling and entanglement, while parametric nonlinearity increases the optomechanical coupling , the weak Kerr nonlinearity is very useful for extending the domain of the stability region to the desired range in which the minimum effective temperature and maximal entanglement are attainable. Also, as shown in this paper, the present scheme allows to have significant entanglement in the tristable regime for the lower and middle branches which makes the current scheme distinct from the bare optomechanical system.
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