Analytical operator solution of master equations describing phase-sensitive processes

We present a method of solving master equations which may describe, in their most general form, phase sensitive processes such as decay and amplification. We make use of the superoperator technique.Comment: 10 pages, LaTex, 3 figures, accepted for publication in International Journal of Modern Physics

Optical realization of nonlinear quantum dynamics

In a cavity filled with a Kerr medium it is possible to generate the superposition of coherent states, i.e. Schroodinger cat states may be realized in this system. We show that such a medium may be mimicked by the propagation of a conveniently shaped Gaussian beam in a GRIN device. This is attained by introducing a second order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media, may split into two Gaussian beams

Entanglement between motional states of a single trapped ion and light

We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-$Q$ cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic relative phases.Comment: 4 pages, LaTe

Recovering coherence from decoherence: a method of quantum state reconstruction

We present a feasible scheme for reconstructing the quantum state of a field prepared inside a lossy cavity. Quantum coherences are normally destroyed by dissipation, but we show that at zero temperature we are able to retrieve enough information about the initial state, making possible to recover its Wigner function as well as other quasiprobabilities. We provide a numerical simulation of a Schroedinger cat state reconstruction.Comment: 8 pages, in RevTeX, 4 figures, accepted for publication in Phys. Rev. A (november 1999

Cauchy-Riemann beams

By using operator techniques, we solve the paraxial wave equation for a field given by the multiplication of a Gaussian function and an entire function. The latter possesses a unique property, being an eigenfunction of the {\it perpendicular} Laplacian with a zero eigenvalue, a consequence of the Cauchy-Riemann equations. We demonstrate, both theoretically and experimentally, the inherent rotation of this field during its propagation. The explanation for these rotations lies in the utilization of the quantum (Bohm) potential. The simplicity of this outcome reveals promising prospects: it enables the analytical deduction of the Fraunhofer or Fresnel diffraction pattern. In essence, this means that obtaining the Fresnel or Fourier transform of a function satisfying the Cauchy-Riemann equations becomes a straightforward task

States interpolating between number and coherent states and their interaction with atomic systems

Using the eigenvalue definition of binomial states we construct new intermediate number-coherent states which reduce to number and coherent states in two different limits. We reveal the connection of these intermediate states with photon-added coherent states and investigate their non-classical properties and quasi-probability distributions in detail. It is of interest to note that these new states, which interpolate between coherent states and number states, neither of which exhibit squeezing, are nevertheless squeezed states. A scheme to produce these states is proposed. We also study the interaction of these states with atomic systems in the framework of the two-photon Jaynes-Cummings model, and describe the response of the atomic system as it varies between the pure Rabi oscillation and the collapse-revival mode and investigate field observables such as photon number distribution, entropy and the Q-function.Comment: 26 pages, 29 EPS figures, Latex, Accepted for publication in J.Phys.

Symplectic evolution of Wigner functions in markovian open systems

The Wigner function is known to evolve classically under the exclusive action of a quadratic hamiltonian. If the system does interact with the environment through Lindblad operators that are linear functions of position and momentum, we show that the general evolution is the convolution of the classically evolving Wigner function with a phase space gaussian that broadens in time. We analyze the three generic cases of elliptic, hyperbolic and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which is shortest in the hyperbolic case. We also derive an exact formula for the evolving linear entropy as the average of a narrowing gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy.Comment: this new version treats the dissipative cas