Salvatore Solimeno

Quantum Harmonic Oscillator with Time‐Dependent Frequency

The temporal evolution of the state vector relative to a harmonic oscillator with time‐dependent frequency is examined. The Schrodinger equation is solved by choosing the instantaneous eigenstates of the Hamiltonian as the basis, thus getting an infinite set of coupled linear differential equations. This formulation is particularly suitable for studying the cases in which the Hamiltonian undergoes a very slow or a sudden variation from an initial constant value into a final one. A rigorous proof of adiabatic invariance to all orders in the slowness parameter is given for the transition probabilities. An application to the evolution of an initially coherent state is made.

Evolution of a coherent state of an harmonic oscillator with time-dependent frequency

Abstract The problem of a quantum harmonic oscillator with time-dependent frequency is considered for the case in which the initial state is a coherent one.

The effect of pump coherence on frequency conversion and parametric amplification

The consequences of the deviation from ideal coherence of the driving (pump) field in nonlinear processes are examined. A detailed treatment of the processes of parametric amplification and frequency upconversion is presented. The treatment utilizes two different approximation methods to suit the two different physical situations considered. For slow phase variations of the pump field an adiabatic approach is useful, whereas in the treatment of fast phase variations (the nonadiabatic case) an equation describing the time evolution of the P representation is found to be a good starting point. In this latter case, a closed hierarchy of equations for the moments of the photon number distribution in the signal (or idler) mode is found. In particular, we find that the efficiencies of both the amplification and the upconversion processes are reduced as a result of pump incoherence, the reduction becoming more severe in the highly incoherent case. For the frequency converter, the very nature of the process is modified as compared to the ideal case, and this modification is again of particular significance for the highly incoherent pump. Second-order moments are explicitly calculated and some of the statistical properties of the output signals are examined.

Quantum effects in second harmonic generation

A simple quantum-mechanical model shows a new qualitative feature of the process of second harmonic generation. This feature is the impossibility of complete depletion of the fundamental wave and is not present in the classical description.

Optical response of a misaligned and suspended Fabry-Perot cavity

The response to a probe laser beam of a suspended, misaligned, and detuned optical cavity is examined. A five degree of freedom dynamical model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product

A property of the coherent states of an electromagnetic field

\ensuremath{\varpi}\ensuremath{\tau}

Guiding, diffraction, and confinement of optical radiation

of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement, and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility. The presented model can describe radiation pressure effects recently appeared in the VIRGO antenna and give a framework for designing the next generation of gravitational wave antennas where such effects would be of critical relevance.

Influence of guiding structures on spontaneous and stimulated emission: Raman scattering in optical fibers

Abstract The non-existence of an infinite set of orthogonal fully coherent states is proved for a class of states whose mean number of photons has an upper bound.