Moorad Alexanian

Trapping and Fock state generation in a two-photon micromaser

Abstract We present a detailed theory of a two-photon micromaser and study the properties of the photon field in this system. The Hamiltonian of twophoton processes is obtained by an exact unitary transformation from that of a three-level atom interacting with a single-mode field. We discuss trapping states and the realization of a photon number state.

Integral representation for non-Maxwellian distributions and the approach to equilibrium

Abstract An integral representation is proved for the nonequilibrium distribution function of Maxwell molecules. The asymptotic approach to statistical equilibrium is studied for general initial conditions. A whole class of initial states is found which does not approach the final equilibrium state by first relaxing into the BKW mode.

Field‐Theoretic Formulation of Quantum Statistical Mechanics

The notions of strong convergence of state vectors, introduced by Haag in his formalism of axiomatic quantum field theory, are extended to the case of vectors with an infinite number of particles but finite densities. Some general properties of nonequilibrium distribution functions are derived without the use of power series expansions or any other simplifying assumption. An integral representation is obtained for the distribution functions which makes it possible to discuss their behavior for small and large energies and to obtain some information about the singularities of these functions when continued analytically.

Scattering of two coherent photons inside a one-dimensional coupled-resonator waveguide

We consider the coherent propagation of n photons in a one-dimensional coupled-resonator waveguide for n=2,3,4.... The scattering by a three-level atom, which resides in one of the resonators of the waveguide and gives rise to only two-photon transitions, results in a perfect quantum switch that allows either total reflection or total transmission. This is to be contrasted to the case of a single photon inside a one-dimensional resonant waveguide scattered by a two-level system with single-photon transitions where only total reflection can be accomplished; viz. the system behaves only as a perfect mirror but not as an ideal, transparent medium.

Temporal second-order coherence function for displaced-squeezed thermal states

We calculate the quantum mechanical, temporal second-order coherence function for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz. a displaced–squeezed thermal state. The calculation involves first dynamical generation at time t of the Gaussian state from an initial thermal state and subsequent measurements of two photons a time apart. The generation of the Gaussian state by the parametric amplifier insures that the temporal second-order coherence function depends only on , via , for the given Gaussian state parameters, Gaussian state preparation time t, and average number of thermal photons. It is interesting that the time evolution for displaced thermal states shows a power decay in rather than an exponential one as is the case for general, displaced–squeezed thermal states.

Thermodynamic aspect of the glass transition

A new characterization of the thermodynamic transition underlying the glass transformation is proposed. The definition incorporates both the continuous nature of the transition from supercooled liquid to amorphous solid as well as history dependent effects. Contrary to usual approaches of considering differences of thermodynamic quantities between the (metastable) equilibrium liquid and a glass, viz. δX> ≡ Xe − Xg, the present characterization of the glass transition is based on differences between a supercooled liquid-amorphous solid branch and the stable crystalline solid, that is, ΔX ≡ Xl −Xc. For the hard-sphere and the soft-sphere models, the present general definition of the glass transition reduces to δ(Cp) → O+ as T → T+g which implies a minimum in the excess entropy δS. However, for more general pair potentials, for instance, Lennard-Jones model, δ(Cp) 0 at tthe transition point, albeit small. This behavior suggests that the glass transition is indeed dictated by the repulsive part of the potential.

Nonclassicality criteria: Quasiprobability distributions and correlation functions

We use the exact calculation of the quantum mechanical, temporal characteristic function

Two-photon absorption in strong fields

\ensuremath{\chi}(\ensuremath{\eta})

The Glass Transition in the Hard‐sphere Fluid

and the degree of second-order coherence

Integral representation for non-maxwell models and the approach to equilibrium

{g}^{(2)}(\ensuremath{\tau})