Narrow Results

We approach the case of two coupled oscillators where the first one may correspond to a photonic field, while the second one is damped and driven. We model the oscillator's damping via a bath and consider the relevant master equation. We use perturbation theory to handle it. We then path integrate over the effective Hamiltonian of the two oscillators and derive the path integrated density matrix. We suppose that initially both of the oscillators are in coherent states and study the quadrature squeezing effect of the second oscillator.

The squeezing and statistical features of the intracavity field produced by a three-level laser coupled to a vacuum reservoir with input coherent field are studied in this paper. Employing the propagator method, we determine the Q-function for the cavity field produced by a driven three-level laser. Using this Q-function, we have calculated the mean intensity, the quadrature variance, and the squeezing spectrum of the cavity field. It has been discovered that, despite the fact that the input coherent field improves the mean intensity of the cavity field, it has no effect on the quadrature squeezing of the cavity field. The degree of squeezing increases with the rate at which atoms are injected into a cavity and a substantial degree of squeezing is found close to the maximum initial injected atomic coherence.

We investigate nonclassical properties of the output of a Bose–Einstein condensate in Milburn's model of intrinsic decoherence. It is shown that the squeezing property of the atom laser is suppressed due to decoherence. Nevertheless, if some very special conditions were satisfied, the squeezing properties of atom laser could be robust against the decoherence.

The properties of the even and odd negative binomial states are investigated. Mainly we concentrate on the statistical properties for such states and we consider the squeezing phenomenon by examining the variation in the quadrature variances. Using the Pegg–Barnett formalism of phase operator, the phase probability distributions of the states are discussed, and also the phase and number squeezing with different parameters are studied. The numerical computation results show that the phase probability distributions for the even and odd NBSs can clearly exhibit the different features of quantum effects.

The set of maximally fermion–boson entangled Bell super-coherent states is introduced. A superposition of these states with separable bosonic coherent states, represented by points on the super-Bloch sphere, we call the Bell-based super-coherent states. Entanglement of bosonic and fermionic degrees of freedom in these states is studied by using displacement bosonic operator. It acts on the super-qubit reference state, representing superposition of the zero and the one super-number states, forming computational basis super-states. We show that the states are completely characterized by displaced Fock states, as a superposition with non-classical, the photon added coherent states, and the entanglement is independent of coherent state parameter $\alpha$ and of the time evolution. In contrast to never orthogonal Glauber coherent states, our entangled super-coherent states can be orthogonal. The uncertainty relation in the states is monotonically growing function of the concurrence and for entangled states we get non-classical quadrature squeezing and representation of uncertainty by ratio of two Fibonacci numbers. The sequence of concurrences, and corresponding uncertainties $\hslash F_n/F_{n+1}$, in the limit $n\to \infty$, convergent to the Golden ratio uncertainty $\hslash /\phi$, where $\phi =\frac{1+\sqrt{5}}{2}$ is found.