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Annual Meeting Optical Society of America

Spectra of ladder systems

Erkki Kyrola, Markus Lindberg

Published Jan 1, 1988• 0 citations
Publisher

Abstract

A strong laser field interacting with an atom or a molecule can induce a coherent process which includes a large number of energy levels. If we can find a transformation which eliminates the explicit time dependence of the interaction Hamiltonian (for example, the rotating-wave approximation), we can reduce the dynamic problem to the consideration of eigenvalues and eigenvectors of the Hamiltonian. However, the complexity of an arbitrary multilevel Hamiltonian usually forces us to use numerical methods, and, therefore, not much general understanding about multilevel systems can be achieved. We consider the multilevel problems in a more general setting. Our approach is based on the observation that an arbitrary Hamiltonian matrix can be transformed into a tridiagonal form by unitary transformation.1 A tridiagonal form represents a ladder-type multilevel system. From all W-level systems the ladder configuration is the simplest in the sense that the number of level connections is the smallest possible. This means that the most effective analysis of a given multilevel system can be achieved using the transformation to ladder configuration. The spectral analysis of ladders is facilitated by the connections to orthogonal polynomials and continued fractions. The investigations about the spectral properties of ladders are reported.

DOI
10.1364/oam.1988.my5

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A strong laser field interacting with an atom or a molecule can induce a coherent process which includes a large number of energy levels. If we can find a transformation which eliminates the explicit time dependence of the interaction Hamiltonian (for example, the rotating-wave approximation), we can reduce the dynamic problem to the consideration of eigenvalues and eigenvectors of the Hamiltonian. However, the complexity of an arbitrary multilevel Hamiltonian usually forces us to use numerical methods, and, therefore, not much general understanding about multilevel systems can be achieved. We consider the multilevel problems in a more general setting. Our approach is based on the observation that an arbitrary Hamiltonian matrix can be transformed into a tridiagonal form by unitary transformation.1 A tridiagonal form represents a ladder-type multilevel system. From all W-level systems the ladder configuration is the simplest in the sense that the number of level connections is the smallest possible. This means that the most effective analysis of a given multilevel system can be achieved using the transformation to ladder configuration. The spectral analysis of ladders is facilitated by the connections to orthogonal polynomials and continued fractions. The investigations about the spectral properties of ladders are reported.
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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.
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