Lowest-order optical second-harmonic process in a two-level system

Ákos Gombkötő

K. Lahti, Ilkka Juhani Tittonen

Yoshitaka Tanimura, Tetsuhiro Suzuki, Ryogo Kubo

A general formulation is given for the second order optical process of a three-level system in contact with a heat bath consisting of harmonic oscillators with a proper frequency spectrum producing a Markoffian random perturbation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression and the result affords a basis to clarify the relation between the stochastic and dynamical approaches to treat the partial destruction of the quantum coherence of the optical process. As an example, a three-level system with intermediate-state interaction is treated in some detail.

J.R. Chamberlain

Marc Collette, Serge Gauvin

This work presents a quantum theory of the nonlinear optical process of second-harmonic generation (SHG) in one-dimensional microresonators. More specifically, we show how the manipulation of vacuum field fluctuations in high-confinement systems, leading to a spectrally (and spatially) modulated commutation relation for the photon's generalized formulations of their creation and annihilation operators, deeply affects SHG behavior and gives rise to a threshold level. The two main effects the modulated commutator has on this optical process are an inhibition of the SHG process at low pumping level and a significant (cubic) amplification of the second-harmonic signal production rate once the threshold is overcome (finally reaching the usual quadratic dependence at sufficiently high pumping level). Our predictions, which represent a concrete picture of a fractional quantum system, could be used to probe vacuum field fluctuations present in high-confinement microresonators and emphasize the fundamental importance of vacuum field fluctuations.

Ranjana Prakash, Pramila Shukla

We report here results for collapses and revivals phenomenon for a collection of M two-level atoms contained in a volume having dimensions much smaller than the radiation wavelength and existing in the Dicke state |r,m〉. We use a perturbation approach and obtain in the lowest contributing order of perturbation second harmonic, besides the main Rabi frequency. The amplitude of the fundamental depends on m only, but the amplitude of the harmonic has dependence on r as well as m. If the atoms are in superradiant states, only the second harmonic is obtained. Revival time for the second harmonic is one half that for the fundamental. It is interesting to note that the number of atoms M does not matter in Rabi frequency, collapse times, revival times or in amplitudes, and only r and m matter. Values of r and m of atoms in a Dicke state can be determined, in principle, by observing Rabi oscillations and average atomic inversion.