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arXiv:quant-ph/0109119 · The European Physical Journal D

Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

Mahmoud Abdel‐Aty, A.‐S. F. Obada

Published Sep 1, 2001• 4 citations
arXivHTMLPDF
DOI
10.1007/s100530170155

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The coupling of an electric field to an atomic beam prepared in a phase-locked coherent superposition of energy eigenstates is examined for a ring-laser cavity. The active medium is assumed to be a collection of noninteracting homogeneously broadened two-level atoms whose transition is electric-dipole allowed. The atom-field interaction is treated semiclassically and the atomic coherence injected into the cavity is assumed to be phase matched to the unidirectional plane-wave cavity mode. The polarization is derived for the case in which the electric-field-mode envelope has at most linear phase variations in time and is applied to the problem of frequency locking in a cavity. The presence of the atomic coherence causes the active medium to possess an inherent polarization, i.e., a field-independent contribution. This enables an optical cavity to support laser oscillation over the entire range of relative excitations, in particular, even for strongly absorbing media. A simple linear stability analysis is performed on the electric-field envelope by describing the medium with a slowly varying polarization valid when the time scales of the atomic response are much smaller than those of the variations in the envelope. The stability of frequency-locked oscillation depends on the detuning of the cavity from line center and the strength of the injected coherence relative to that of the injected population difference.
Stabilizing atoms exposed to intense laser fields has been a central topic in atomic physics for decades, inspiring several theoretical frameworks that describe the phenomenon under different resonance conditions and coupling regimes. Here, we theoretically investigate an ionizing electronic transition driven by a resonant pump field, in contrast to Kramers–Henneberger atoms, which are stabilized by non-perturbative, non-resonant laser pulses. We show that, above a critical pump intensity, the drive creates a metastable electronic bound state emerging from the continuum, which decays via two-photon ionization. We calculate the resulting resonant fluorescence spectrum and find a qualitatively different structure from the familiar Mollow triplet associated with bound-to-bound transitions. This fluorescence provides a time-resolved probe of the population in the metastable state. In analogy to how the AC Stark shift is a semiclassical counterpart of the single-photon Rabi splitting observed in optical cavities, the phenomenon we describe is best understood as a semiclassical analog of recently observed excitons bound by a single cavity photon.
A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.