Interference at quantum transitions: lasing without inversion and resonant four-wave mixing in strong fields at Doppler-broadened transitions

Abstract

An influence of nonlinear interference processes at quantum transitions under strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow one to analyze the optical characteristics (including gain without inversion and enhanced refractive index at vanishing absorption) for various V , Λ and H configurations of interfering transitions by a simple substitution of parameters. Similar expressions for resonant four-wave mixing in Raman configurations are derived too. Crucial role of Doppler broadening is shown. The theory is applied to numerical analysis of some recent and potential experiments.Keywords: quantum interference, lasing without inversion, resonant four-wave mixing, Doppler and strong field effects. PACS: 42.50.Gy, 42.55.-f, 42.65 I INTRODUCTIONMany concepts of quantum optics were originated proceeding from the assumed equality of probabilities of induced transitions accompanied by an absorption and emission of photons predicted by A. Einstein. Requirement of population inversion for lasing is direct consequence from this equality.At the presence of several resonant electromagnetic fields, probability amplitudes of a coupled quantum states contain several oscillating components at close frequencies. Therefore alongside with squared modules of appropriate components cross terms indicating an interference of quantum transitions appear while calculating transitions probabilities. The coherent nonlinear optical phenomena stipulated by the indicated evolution of quantum states, driven by several fields, were called as nonlinear interference effects (N IE) [1,2]. In quantum optics N IE may result in different coupling of a radiation with atoms in absorbing and emitting states controlled by the auxiliary fields [3,4]. Various appearances of these effects are feasible. Soon after discovery of lasers Rautian and Sobelman [5] showed feasibility of amplification without inversion (AW I) in two-level systems. The features of AW I in optical three-level systems were explored in [6,2]. Studies of N IE in absorption/gain spectra including experiments on generation of an optical radiation in three-level systems, so that generation was possible only at the expense of nonlinear interference effects, drew much attention in 60th and 70th [7]. (Review of relevant optical experiments and of earlier papers on AW I in microwave range see in [9,8].) Coherent population trapping (CP T ) is one of the appearances of N IE for the states with negligible relaxation rates and Doppler effects. In 80th -90th studies of coherent interference processes at quantum transitions have been attra...

Inversionless gain in an optically-dense resonant Doppler-broadened medium

“…In order to simplify the proposed experiment we do not assume here a source of incoherent excitation of the medium (the formulas accounting for such excitation are provided in ref. [14,15]). Therefore the energy acquired by the probe field here is taken entirely from the driving fields.…”

“…The relevant solutions for elements of the density matrix, and consequently for the material parameters in the ED equations ( 1) and ( 2), are cumbersome. They are provided in [14,15], where the solution is found exactly with respect to E 1,3 and in the first approximation for E 4,2 . The various relaxation processes, Boltzmann excitation of the level n, distribution over rotational sub-levels and dependence on the molecule velocity were taken into account.…”

“…). In order to simplify the proposed experiment we do not assume here a source of incoherent excitation of the medium (the formulas accounting for such excitation are provided in ref [14,15]…”