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Ukrainian Journal of Physics

Near Resonant Optical Absorption by a System Coupled with Two Laser Beams

Андрій Сіжук, Guangjiong Dong

Published Apr 17, 2020• 0 citations
Publisher

Abstract

The structure of a solution of the generalized Maxwell–Bloch system of equations describing the strongly pumped interacting two-level atoms is discussed. This structure is represented by means of the corresponding differential equations for each contributing process. The interaction between the processes is introduced through the interaction integral and is illustrated by the specific system of graphs. The method allows one to describe the quantum-field-induced long-range interaction prevailing over short-range collisions and causing the broadening, narrowing, and shifts of an absorption line shape. The description is given in terms of the interaction integrals which couple the collective atomic polarization and population inversion. The contributions from different effects are analyzed with the use of the additivity of the corresponding absorption/reemission rates.

DOI
10.15407/ujpe65.4.277

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The structure of a solution of the generalized Maxwell–Bloch system of equations describing the strongly pumped interacting two-level atoms is discussed. This structure is represented by means of the corresponding differential equations for each contributing process. The interaction between the processes is introduced through the interaction integral and is illustrated by the specific system of graphs. The method allows one to describe the quantum-field-induced long-range interaction prevailing over short-range collisions and causing the broadening, narrowing, and shifts of an absorption line shape. The description is given in terms of the interaction integrals which couple the collective atomic polarization and population inversion. The contributions from different effects are analyzed with the use of the additivity of the corresponding absorption/reemission rates.
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.
A numerical method is introduced that solves the optical Bloch equations describing a two-level atom interacting with a strong polychromatic pump field with an equidistant spectrum and an arbitrarily intense monochromatic probe field. The method involves a transformation of the optical Bloch equations into a system of equations with time-independent coefficients at steady state via double harmonic expansion of the density-matrix elements, which is then solved by the method of matrix inversion. The solutions so obtained lead immediately to the determination of the polarization of the atomic medium and of the absorption and dispersion spectra. The method is applied to the case when the pump field is bichromatic and trichromatic, and the physical interpretation of the numerically computed spectra is given.
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We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.
An analysis of near-resonant collisions between dissimilar atoms in the presence of a radiation field reveals their effect on the far wings of the absorption profile. Extending a model due to Cavalieri, Arimondo, and Matera, we take into account the collisional shifts of atomic levels, as well as the collisional coupling between atoms and the coupling with the radiation field. A general formula for the absorption profile is derived and expressed in terms of the universal line-shape function of the unified Franck-Condon treatment of pressure broadening. We show that in some cases collision-induced coherence can give rise to a strongly depressed red wing that exhibits transparency for some values of the laser detuning. \textcopyright{} 1996 The American Physical Society.
Optical properties of ensembles of coupled three-level quantum emitters are investigated in linear and non-linear regimes. The model of the Maxwell–Liouville von Neumann equations is implemented to explore the reflection, transmission, and absorption of a thin layer of atom-like emitters at low and high densities. The stimulated Raman adiabatic passage is analysed in systems of coupled quantum emitters of various densities. It is shown that coupling via local electromagnetic fields shifts the energy levels and modifies propagating fields leading to a mixed final population distribution and appearance of new absorption resonances. Strong femtosecond pulses induce population inversion in emitters leading to optical gain.