Atomic quadrature squeezing and quantum state transfer in a hybrid atom-optomechanical cavity with two Duffing mechanical oscillators

In this paper, we investigate theoretically the quantum state transfer in a laser driven hybrid optomechanical cavity with two Duffing-like anharmonic movable end mirrors containing an ensemble of identical two-level trapped atoms. The quantum state transfer from the Bogoliubov modes of the two anharmonic oscillators to the atomic mode results in the atomic quadrature squeezing beyond the standard quantum limit of 3 dB which can be controlled by both the optomechanical and atom-field coupling strengths. Interestingly, the generated atomic squeezing can be made robust against the noise sources by means of the Duffing anharmonicity. Moreover, the results reveal that the presence of the Duffing anharmonicity provides the possibility of transferring strongly squeezed states between the two mechanical oscillators in a short operating time and with a high fidelity

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.Comment: 14 pages, 12 figure

Phase noise and squeezing spectra of the output field of an optical cavity containing an interacting Bose-Einstein condensate

We present a theoretical study of the phase noise, intensity and quadrature squeezing power spectra of the transmitted field of a driven optical cavity containing an interacting one-dimensional Bose-Einstein condensate. We show how the pattern of the output power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to a one-to-one correspondence between the splitting of the peaks in the phase noise power spectrum of the cavity output field and the \textit{s}-wave scattering frequency of the atom-atom interaction, one can measure the strength of interatomic interaction. Besides, we show how the atomic collisions affect the squeezing behavior of the output field

Generation of nonlinear coherent states in a coherently pumped micromaser under intensity-dependent Jaynes-Cummings model

In this paper the possibility of generating nonlinear coherent states of the radiation field in a micromaser is explored. It is shown that these states can be provided in a lossless micromaser cavity under the weak Jaynes-Cummings interaction with intensity-dependent coupling of large number of individually injected two-level atoms in a coherent superposition of the upper and lower states. In particular, we show that the so-called nonlinear squeezed vacuum and nonlinear squeezed first excited states, as well as the even and odd nonlinear coherent states can be generated in the presence of two-photon transitions.Comment: 15 page

Controlling steady-state bipartite entanglements and quadrature squeezing in a membrane-in-the-middle optomechanical system with two Bose-Einstein condensates

We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave scattering frequency of the other one. Since the \textit{s}-wave frequency of each BEC depends on the transverse trapping frequency of the atoms which is an experimentally controllable parameter, one can control the entanglement and squeezing of each BEC through the trapping frequency of the other one

Dynamical Behaviours of the Nonlinear Atom-Field Interaction in the Presence of Classical Gravity: f-Deformation Approach

In this paper, we investigate the effects of a classical gravitational field on the dynamical behaviour of nonlinear atom-field interaction within the framework of the f-deformed Jaynes-Cummings model. For this purpose, we first introduce a set of new atomic operators obeying an f-deformed su(2) algebraic structure to derive an effective Hamiltonian for the system under consideration. Then by solving the Schrodinger equation in the interaction picture and considering certain initial quantum states for the atomic and radiation subsystems, we analyze the influence of gravity on the temporal evolution of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics, and deformed quadrature squeezing of the radiation field

Control and manipulation of electromagentically induced transparency in a nonlinear optomechanical system with two movable mirrors

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 oscil- lators 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 coher- ent 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 non- linearity 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

Generation of motional nonlinear coherent states and their superpositions via intensity-dependent coupling of a cavity field to a micromechanical membrane

We propose a theoretical scheme to show the possibility of generating motional nonlinear coherent states and their superposition for an undamped vibrating micromechanical membrane inside an optical cavity. The scheme is based on an intensity-dependent coupling of the membrane to the radiation pressure field. We show that if the cavity field is initially prepared in a Fock state, the motional state of the membrane may evolve from vacuum state to a special type of nonlinear coherent states. By examining the nonclassical properties of the generated state of the membrane, including the quadrature squeezing and the sub-Poissonian statistics, we find that by varying the Lamb-Dicke parameter and the membrane's reflectivity one can effectively control those properties. In addition, the scheme offers the possibility of generating various types of the so-called nonlinear multicomponent Schrodinger cat sates of the membrane. We also examine the effect of the damping of the cavity field on the motional state of the membrane

The effect of atomic collisions on the quantum phase transition of a Bose-Einstein condensate inside an optical cavity

In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose-Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom-atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s-wave scattering frequency when the the strength of the transverse pumping has been fixed.Comment: 10 pages, 10 figure

Influence of atomic collisions on spectrum of light scattered from an f-deformed Bose-Einstein condensate

In this paper, we investigate the spectrum of light scattered from a Bose-Einstein condensate in the framework of f-deformed boson. We use an f-deformed quantum model in which the Gardiners phonon operators for BEC are deformed by an operator-valued function, f(n), of the particle-number operator n. We consider the collisions between the atoms as a special kind of f-deformation. The collision rate k is regarded as the deformation parameter and the spectrum of light scattered from the deformed BEC is analyzed. In particular, we find that with increasing the values of deformation parameters k and eta=1/N (N, total number of condensate atoms) the scattering spectrum shows deviation from the spectrum associated with nondeformed Bose-Einstein condensate.Comment: 17 pages, 4figure