A study on optomechanically induced transparency (OMIT) and the slow light in an optomechanical system (OMS) with a degenerate optical parametric amplifier (OPA) is conducted. The system consists of the degenerate OPA, two charged mechanical resonators, and a fixed mirror. The coupling interaction between the cavity and a charged mechanical resonator is expressed by the radiation pressure term. There is no interaction between the cavity and the other charged mechanical resonator, while there is Coulomb interaction between the two charged mechanical resonators. In such a nonlinear OMS, we consider OMIT and the slow light by changing the Coulomb coupling strength, the phase of the optical field driving the OPA, the nonlinear parameter of the OPA, and the power of the pump field. We find that the Coulomb coupling strength has a significant impact on the spacing between the two transparency dips due to the mechanical dressed modes. Moreover, one may achieve long-lived slow light (group delay of several milliseconds) and a switching from superluminal to subluminal propagation via adjustment of the controlling parameters of the system.

We investigate the behavior of a linearly polarized pulse interacting with a multilevel rotary chiral medium. Due to the strong chirality induced by electromagnetic fields together with the Fizeau effect, the two spatially refracted [left-circularly polarized (LCP) and right-circularly polarized (RCP)] beams of the incident pulse show typical dual rotation. First of all, we present a modified form of Snell’s law, which describes the unusual refraction of two beams in a chiral medium. Then we study the properties of the refraction beams and find that the angle between the two beams, the divergence angle, rotates in the spinning direction of the rotary medium. In addition, the chirality and rotation of the medium are controlled by external sources, so we can manipulate the exact position of the divergence angle. This property of the system can be used to measure the degree of birefringence of a chiral medium. The difference in refractive indices of the LCP and RCP beams has an equivalent effect on the orbital angular momenta of the beams; thus, the probe field can be modulated efficiently and may find applications in spintronics. Moreover, the scheme can be useful for metamaterial applications, accurate position control of the transmitted images, and pulse. A possible experimental realization of the model is also discussed.

We investigate the freezing and sudden transition in the dynamical behavior of quantum and classical correlations in a system composed of two identical non-interacting qubits locally subjected to their own non-equilibrium environments. In contrast to the equilibrium case, one can observe striking results when a bipartite quantum system couples with the non-equilibrium dephasing environment with non-stationary and non-Markovian features. Remarkably, the finite time interval in which the quantum correlation remains impervious to decoherence can be further prolonged as the environment deviates from equilibrium. This reveals that the non-equilibrium parameter provides an alternative tool to efficiently control the appearance of a sudden transition in the decay rates of correlations and their immunity towards the decoherence. Furthermore, for certain initial states, the appearance of another time-interval over which quantum correlation remains constant and the revival of classical correlation not only depends on the non-Markovianity but also on the non-equilibrium parameter.

We theoretically investigate a multimode quadratic coupling optomechanical system (OMS) assisted with $N$ cold $\mathrm{\Lambda }$-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.

Correlations in the open quantum systems manifest a rich phenomenology under the influence of various physical sources of noise. We theoretically study the dynamics of quantum correlations and their classical counterparts in a two-qubit system, measured by one-norm geometric quantifiers. We consider both qubits are initially prepared in the arbitrary $X$-type states and locally subjected to nonequilibrium dephasing environments with non-Markovian and nonstationary statistical features. We then explore the effects of nonequilibrium on the abrupt changes in the evolution of geometric correlations in the weak- and strong-coupling regimes. Particularly, in the weak-coupling regime, we show that the environmental nonequilibrium feature can efficiently control the appearance of double-sudden transitions and the decay rate in geometric quantum correlation dynamics. However, in the strong-coupling case, we show that the nonequilibrium nature can prolong the interval for the frozen quantum correlation and suppresses the number of multiple sudden changes in its decay rate. Moreover, the abrupt change from decay to a constant regime in classical correlation evolution reveals the emergence of the pointer-state basis. We show that the pointer-state basis appearance can be retarded in the weak-coupling case when the environment deviates from equilibrium. However, in a strong-coupling regime, we observe the metastable pointer-states basis characterized by multiple, successive sudden transitions in classical correlation dynamics. Remarkably, we unveil that the nonequilibrium feature may suppress the apparition of the metastable pointer-states basis.

We study the resonant tunneling of ultraslow atoms through a system of high quality microwave cavities. We find that the phase tunneling time across the two coupled cavities exhibits more frequent resonances as compared to the single cavity interaction. The increased resonances are instrumental in the display of an alternate sub and superclassical character of the tunneling time along the momentum axis with increasing energies of the incident slow atoms. Here, the intercavity separation appears as an additional controlling parameter of the system that provides an efficient control of the superclassical behavior of the phase tunneling time. Further, we find that the phase time characteristics through two cavity system has the combined features of the tunneling through a double barrier and a double well arrangements.