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Journal of the Optical Society of America B

Coherent effects in a three-level gas medium on exposure to a strong bichromatic pumping field and a weak probe wave

Michael Z. Smirnov

Published Dec 1, 1992• 8 citations
Publisher

Abstract

The approximate analytical solution of equations for the density matrix of three-level atoms moving in a strong bichromatic pumping field and in a weak probe-wave field (V system) is obtained. It is demonstrated that two series of resonances with different parameters appear in the gain spectrum of the probe wave. When certain conditions are met, some resonances are found to be free from Doppler broadening. The relations describing the resonance broadening and shifts are derived.

DOI
10.1364/josab.9.002171

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Physical Review A•Dec 1, 1992•4 citations
The approximate analytical solution of equations for the density matrix of three-level atoms moving in a strong bichromatic pumping field and in a weak probe-wave field (V system) is obtained. It is demonstrated that two series of resonances with different parameters appear in the gain spectrum of the probe wave. When certain conditions are met, some resonances are found to be free from Doppler broadening. The relations describing the resonance broadening and shifts are derived.
This paper investigates stimulated emission and absorption near resonance for a driven system of interacting two-level atoms. Microscopic kinetic equations for the density matrix elements of N-atom states including atomic motion are built, taking into account atom-field and atom-atom interactions. Analytical solutions are given for the resulting macroscopic equations in different limits, for a system composed of a strong coherent “pump” field and a weak counter-propagating “probe” field. It was shown that the existence of a dipole-dipole (long-range) interaction between atoms separated by distance less than the pump wave-length can cause the formation of periodic polarization and population structures (gratings in time and space) in the pumped medium without a probe field. The magnitude of pump induced population grating can have a strong dependence on the relation between the pump field detuning and the polarization decay rate. The “interaction” between pump and probe induced polarization/population gratings through a dipole-dipole interaction mechanism causes the absorption line shape asymmetry. Under certain conditions, this asymmetry is revealed in increasing probe gain for the “red”-shifted (relative to pump) probe and suppressing the gain for the “blue”-shifted probe field when pump is “red”-shifted relative to the ensemble averaged resonant frequency. The theoretical results are consistent with experimental data for the probe gain or absorption as the function of frequency and the dependance of the gain on atomic density for sodium vapor when the pump laser is tuned near the D 2 line. Here the dependance of gain on particle density was explained in the terms of the long-range interaction between the atoms.
The effects of a strong standing wave field on the absorption behaviour of a weak probe field are studied. An absorptive medium is assumed to consist of stationary two-level atoms with arbitrary decay and pumping scheme. The spectrum with a resonant saturator does not exhibit emissive behaviour as in the travelling wave cases. With a detuned saturator the spectrum closely resembles the corresponding three-level spectrum. These features are explained from the standing wave induced spatial selectivity and inhomogeneity. The connections to Doppler-broadened spectra are discussed.
We study inhomogeneously broadened three-level atoms ($\ensuremath{\Lambda}$ configuration). Two energy levels are strongly coupled by an intense standing wave. A weak laser field at an adjacent transition is used as a probe. The probe response is calculated by Green's functions involving continued fractions. The general solution is extendable to other three-level configurations as well to other types of multimode saturators. The connection of various approximate solutions to the exact one is discussed. We concentrate on the Doppler-free case where both transitions have nearly equal frequencies. For this we derive a reasonably accurate closed-form solution, the parameter dependencies of which are investigated in detail. In addition to its average changes the dynamics of the saturated transition plays an important role in the steady-state probe response. The spectra show sharp resonances which cannot be explained in terms of traveling wave superposition models. The width of the velocity distribution has a strong effect on the shape of the spectrum---some resonances are smeared away because of incomplete Doppler dephasing. The relaxation processes influence differently the resonances, which facilitates their interpretation.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
The spectrum of absorption (amplification) of a weak probe field by two-level atoms colliding with atoms of a buffer gas in the field of a strong electromagnetic wave is studied theoretically. A universal, free of any collision model, solution is obtained for systems with small (compared to collision rates) Doppler broadening with no restrictions on the strong-field intensity and with the possible absence of dephasing of the light-induced dipole moment in elastic collisions of the gas particles. The relation of the collisional parameters of the problem with the characteristics of an elementary scattering event and with the macroscopic characteristics connected with the transport phenomena is established. It is found that the nontrivial features of the probe-field spectrum discovered by us previously [Zh. Éksp. Teor. Fiz. 127 , 320 (2005)] in the framework of the strong-collision model are not connected with a particular model of collisions and have a universal nature.
Nonlinear effects of sublevel coherence on resonant backward-degenerate four-wave mixing are analyzed in the saturation regime of an inhomogeneously broadened and optically thin gas medium, composed of \ensuremath{\Lambda}-type three-level atoms. No limitations are set to the pump-field intensities, and an analytical approach is presented in the Doppler limit and efficient transverse-optical-pumping regime. It is shown that coherent population trapping due to strong pump-field coupling has a negligible incidence in phase conjugation, while interference of two imbalanced coherent-population-injection channels determines the mixing process. Level-crossing emission resonances are found to exhibit particular line-shape characteristics: (1) an insensitivity to power shifts, (2) strong power-broadening accompanied by incomplete line splitting, or (3) field-induced line-broadening inhibition. The conditions under which these effects should be observable are identified, and their dependence on pump imbalance is remarked.