Richard D'Souza

Absorption intensities of zero-phonon single and double transitions in the multipole-induced spectrum of solid hydrogen

Abstract The theory of absorption intensities of some zero-phonon single and double transitions in solid H 2 is discussed. General expressions are developed for the integrated absorption coefficients of (i) the single transitions ( v ′ = v , J ′ = l) ← ( v ″ = 0, J ″ = 0) in solid para -H 2 and ( v ′ = v , J ′ = l + 1) ← ( v ″ = 0, J ″ = 1) in ortho -H 2 interspersed in a matrix of solid para -H 2 , and (ii) the double transition [( v ′ = v 1 , J ′ = l) ← ( v ″ = 0, J ″ = 0)] + S v 2←0 (0) in solid para -H 2 .

Non-linear Resonant Transient and Steady-state Response in a Classical Model

The Doppler-broadened steady state and transient response of a thermal ensemble of anharmonic oscillators to incident laser radiation is investigated. Non-linear polarization of this classical system is obtained by analytically solving the dynamical equations up to third order in the electric field. Except for the sign of the third-order transient polarization, the results are in striking contrast to those obtained in semi-classical theory. In particular, the classical response at resonance is unsaturated up to this order. The Doppler-integrated third-order free induction decay (FID) signal vanishes in the usual approximation of the homogeneous width being smaller than the Doppler width. The physical conclusion of the paper is negative: resonant non-linear and coherent effects such as saturation and nutation typical of the quantum mechanical two-level atoms do not arise for classical anharmonic oscillators.

Generalised quasiprobability distribution for Hermite polynomial squeezed states

Abstract Generalized quasiprobability distributions (QPD) for Hermite polynomial states are presented. These states are solutions of an eigenvalue equation which is quadratic in creation and annihilation operators. Analytical expressions for the QPD are presented for some special cases of the eigenvalues. For large squeezing these analytical expressions for the QPD take the form of a finite series in even Hermite functions. These expressions very transparently exhibit the transition between, P, Q and W functions corresponding to the change of the s-parameter of the QPD. Further, they clearly show the two-photon nature of the processes involved in the generation of these states.

Generalized distribution of negative binomial states

We present analytical expression for the s-parametrized quasiprobability distribution W((alpha) , (epsilon) , s) for the negative binomial states. As special cases, for s equals -1, 0, and 1, W((alpha) , (epsilon) , s) reduces to the Q-distribution, the Wigner distribution, and the Glauber-Sudarshan P-function, respectively.

Area Theorem for a Model of Classical Anharmonic Oscillators

The propagation effects of linearly polarized near-resonant laser radiation through a thermal ensemble of Doppler-broadened anharmonic oscillators are considered. The dynamical equations of motion are analytically solved by a perturbation approach to obtain the nonlinear polarization. Subsequent self-consistent analysis of the Maxwell wave equation then leads to a classical area theorem, which is in qualitative agreement up to third order with the corresponding quantum mechanical result. There is, however, a discrepancy between the respective coefficients of the third-order terms.