Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonlinear theory of a three-level laser with microwave coupling: numerical calculation

H. Fearn, Willis E. Lamb, Marlan O. Scully

Published Sep 1, 1991• 0 citations

Abstract

A nondegenerate three-level atomic system is considered, and the possibility of lasering without population inversion via numerical computations is investigated. The atomic system consists of one upper level and two closely spaced lower levels, which are coherently mixed by a microwave field interaction. A numerical calculation is performed, based on a variable step formulation of the classic Adams formulae for solving first-order differential equations. This method of solution has been outlined by C. W. Gear and by L. F. Shampine and M. K. Gordon. The authors adapt this algorithm for use with complex double precision arrays and apply the resulting program to the Maxwell-Schrodinger equations of this atomic system. This enables the authors to carry out a strong field analysis of the atom-field interaction, since they are not restricting their analysis to perturbation theory.

DOI: 10.1117/12.46784

Related papers

Time-dependent dressed-states analysis of lasing without population inversion in a three-level ladder scheme

Doron Braunstein, R. Shuker

A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.

Laser PhysicsMar 1, 20084 citations

Dressed states analysis of lasing without population inversion in a three-level ladder scheme: Approximate analytic time dependent solutions

Doron Braunstein, R. Shuker

A dressed-state study of lasing without population inversion from a three level atom interacting with a bi-chromatic laser field, in the ladder configuration, is formulated. We allow the atomic system to be dressed by both laser filed photons (double dressing). The evolution of the system under consideration is being explored both analytically and numerically, within the transient regime. Time dependent approximate analytic solutions for dressed-state populations and coherences are derived, within the so called “secular approximation,” under resonant conditions. We also present time dependent numerical solutions for population and coherences in the off-resonance regime. A spectral analysis is also performed revealing the structure of various dressed states transitions. These are shown to be composed of quintets centered about the frequencies of the coupling and probe laser fields and having sidebands located symmetrically at positions shifted from line center at the Rabi and double Rabi frequencies.

Laser PhysicsFeb 1, 20094 citations

Optical mixing of frequencies of a strong bichromatic field interacting with a three-level atom. II. Numerical results

Constantine Mavroyannis, K.J. Woloschuk, D. A. Hutchinson +1 more

We have numerically calculated the excitation spectra arising from the 3rd order mixing of the frequencies ωa and ωb of two laser fields interacting with a three-level atom, where each laser field resonantly couples the ground state with each excited state of the atom, respectively. In the limit of high photon densities, the excitation spectra near the reduced frequency X = (ω−ωa + 2ωb)/γ0 ≈ 0 are considered as a function of the reduced Rabi frequencies ηa and ηb of the two laser fields, respectively and γ0 is the spontaneous emission probability. For ηa < ηb the spectra consist of a doublet peaked at [Formula: see text] and its intensity is constant. When ηa = ηb, the spectra are composed of five pairs of bands peaked at [Formula: see text], and [Formula: see text]. When ηa < ηb the computed spectra consist of five pairs of bands, where the intensities of the peaks at [Formula: see text] and [Formula: see text] are positive indicating absorption, those at [Formula: see text] are negative implying amplification, and the two pairs of peaks at [Formula: see text] have positive and negative components describing the mixed process of absorption–amplification. The intensities of these bands are found to vary as (ηa/ηb)2 for (ηa/ηb) > 1 and, therefore, the intensities of the bands are immensely enhanced as the value of the ratio (ηa/ηb) increases. The computed spectra for a wide selection of Rabi frequencies are graphically presented and compared with those derived by analytical methods.

Canadian Journal of PhysicsFeb 1, 198214 citations

On the non-linear spectroscopy including saturated absorption and four-wave mixing in two and multi-level atoms: a computational study

M Patel, Gerhard De Jager, Z Nkosi +2 more

In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.

Journal of Physics Conference SeriesOct 1, 20170 citations

Propagation of laser pulses and coherent population transfer in dissipative three-level systems: An adiabatic dressed-state picture

Michael Fleischhauer, Aaron S. Manka

The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.

Physical Review AJul 1, 1996134 citations

Three-level atom laser model with results and applications

Andrew M. Smith II, Crispin W. Gardiner

We present here a fully quantum-mechanical treatment of the laser using a three-level atom model. The phase-space method employed is identical to that in a previous publication of ours [Phys. Rev. A 38, 4073 (1988)] and again results in a Fokker-Planck description of the laser without any approximations. The third level only provides extra deterministic terms and, if it is regarded as a further reservoir to the lasing levels, then the resultant stochastic equations have much improved stability. These equations are suitable for extensive theoretical analysis of both the laser and optical bistability, although in this paper we have concentrated on the adiabatically eliminated limit and calculated the leading noise terms in various regimes. However, we do use the technique of direct numerical simulation to solve exactly the full system of laser equations. The results display clearly many of the known laser characteristics.

Physical Review AMar 1, 199014 citations