Wave Equation for Dark Coherence in Three-Level Media

Abstract

We report the derivation of a wave equation for coherence in "dark state" two-photon-resonance spectroscopy. One of its consequences is a dark state area theorem. The dark area theorem is a single ordinary differential equation which is globally equivalent, in a way we describe, to the full set of five coupled nonlinear partial differential equations that govern space-time evolution of two-pulse coherence in a lambda medium. The predictions of the dark area theorem are open to test via laser spectroscopy in dilute vapors and inhomogeneously broadened solids.

Analytic solution and pulse area theorem for three-level atoms

“…Considering the fields defined by Eq. (19) it can be seen that the nth term in the Magnus expansion is proportional to the n-th power of the integral over the CW square pulse in the RWA Thus the approximation of dropping higher order terms in the Magnus expansion of the evolution operator is essentially a perturbation theory in the evolution operator with the small parameter, Ω R /∆ ≪ 1. Here ∆ = ω − ν is the detuning between the central field frequency and the transition frequency (either ω ab or ω cb ).…”

Storage and retrieval of light pulses at moderate powers

“…(2)- (3) gives the complete evolution of the atom-field system at any instant of time. The analytical solution of the Maxwell-Bloch equations not known though under special conditions some solutions are known [15]. Therefore we study the pulsepropagation problem only numerically.…”

Sub- and Superluminal Propagation of Intense Pulses in Media with Saturated and Reverse Absorption

“…The slow light ideas have been successfully used in storage and retrieval of light pulses [7,8]. The understanding of storage and retrieval of light pulses has been provided by Dey and Agarwal [9], using the adiabaton theory of Grobe, Hioe and Eberly [10].Work on pulse propagation continues to produce interesting results [11][12][13][14]. Recently, Bigelow et al[15] showed the propagation of light pulses in Ruby at a group velocity of 57.5 m/sec.…”