Kinetics and Optical Properties of the Strongly Driven Gas Medium of Interacting Atoms

Abstract

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.

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

“…Based on the model Hamiltonian, the microscopic evolution equations can be built for the -particle density matrix elements. As was shown in [21], the corresponding macroscopic kinetic equations in terms of the one-particle probability density matrix and the effective collective field can have the form of the generalized Maxwell-Bloch equations. Let ( , r) and ( , r) be the macroscopic probability densities to find an atom during the infinitesimal time interval ( − , + ) at the The open (without mirrors) system is coupled near the optical resonant transition with the two counterpropagating strong and relatively weak laser beams location of the physically small volume (r + r) in the excited and ground states, accordingly; and let ( , r) = * ( , r) be the polarization of the gas medium defining the averaged "off-diagonal" density matrix element for an atom.…”

“…allow us to represent the solution of the macroscopic Maxwell-Bloch equations (see [21]) with the generalized Rabi frequency (1) through the following terms:…”

“…( , r) for ∈ { , } , and ∈ { , } is a perturbation to (0) in the case of non-zero interaction term ⃒ ⃒ Ω Int ⃒ ⃒ ̸ = 0 and without external probe field |Ω 2 | = 0. The correctioñ ( , r) is induced, when both the strong and weak fields are applied without interatomic interaction ⃒ ⃒ Ω Int ⃒ ⃒ = 0, and˘( , r) takes into account the corrections to the absorption/reemission rates induced by the perturbed population inversion and the polarization ( , r) (see [21] for details). Therefore, |Ω 2 | ̸ = 0 and ⃒ ⃒ Ω Int ⃒ ⃒ ̸ = 0, and (2) ( , r) represents a strongly non-linear perturbation of the interaction item Ω Int (˘+˜+ ) induced by the dipole-dipole coupling of the perturbed population and the polarization of the medium.…”

“…The model system under discussion takes the quantization of an electromagnetic field into account. In comparison with the semiclassical description (e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17]), the quantum optics can uncover quantitatively and qualitatively new effects (see examples in [18][19][20][21][22][23][24][25][26]).…”

“…The well-known Maxwell-Bloch equations describe, strictly speaking, the model of interaction of the radiation field with a dilute ensemble of atoms in the semiclassical dipole approximation. The generalized Maxwell-Bloch system of equations for an optically dense medium is derived by the authors in [21]. The construction of the system of equations is based on the model Hamiltonian in the short time scale limit (see details in [27]).…”