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Journal of Experimental and Theoretical Physics Letters

Nonlinear interference effect in the Zeeman ion laser

Sergei A Babin, Sergey I. Kablukov, M. A. Kondratenko, David A. Shapiro

Published Aug 1, 1996• 1 citation
Publisher

Abstract

A narrow interference resonance in the power of a single-mode ion laser as a function of the magnetic field is recorded and investigated. The nonlinear interference effect in the Zeeman laser is calculated taking account of Coulomb diffusion in velocity space. The two-photon resonance is found to differ substantially from the diffusion-free case.

DOI
10.1134/1.567196

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A narrow interference resonance in the power of a single-mode ion laser as a function of the magnetic field is recorded and investigated. The nonlinear interference effect in the Zeeman laser is calculated taking account of Coulomb diffusion in velocity space. The two-photon resonance is found to differ substantially from the diffusion-free case.
The Coulomb broadening of a magneto-optical resonance of degenerate two-level ions in the field of a standing wave is calculated. Under the conditions of linear polarisation of this wave, of the normal Zeeman effect, and of weak saturation, the broadening is described by familiar expressions for multistage and two-photon resonances in separate three-level subsystems and the coefficients in these expressions depend on the angular momenta. The profile of a nonlinear resonance in the dependence of the output power of a single-frequency Zeeman ionic laser on the applied magnetic field consists of a narrow central interference peak, a wide diffusion part, and Lorentzian wings. It is shown that, in the case of a broad lower active level, the J → J+1 transitions are more favourable for the observation of a two-photon resonance and the relative amplitude of the resonance is not less than 2/7.
We consider the interference spectra arising from the competition between a spontaneous process and two processes induced by two laser fields, which are coupled with a three-level atom in the "Λ" configuration. In the low-intensity limit of both laser fields and on two-photon resonance, the frequency profiles of the two peaks, which arise from the spontaneous and induced processes, cancel each other out completely at the center of the line for zero detuning and at the finite values of the detuning as well. At high intensities of the laser fields and on two-photon resonance, the dynamic Stark effect dominates the spectra of the excited state of the atom. Expressions for the interference spectra and correlation functions are derived, which describe the physical process of the absorption of a laser photon at two different times by the ground state of the atom. Interference spectra and correlation functions are calculated for the two-photon off-resonance and for the proces of the absorption of a photon by the ground state of the atom. In this case, the intensities of the frequency dips take negative values indicating that stimulated emission prevails for certain values of the detunings. Using values for the parameters involved close to those for Ba+, the computed two-photon resonance and off-resonance spectra are graphically presented and discussed.
The simultaneous action of a RF perturbation between the Zeeman sublevels of an atomic transition, which is also sustaining laser oscillations, is given further consideration. General equations are derived that describe the phenomena in a rotating effective magnetic field basis. These are valid for any level of the RF perturbation, being then solved by iteration to third order in the laser electric field and integrated exactly over the atomic velocity distribution. Results are given for single-π-mode laser operation on aJ = 1 \rightarrow 0transition and for single-mode operation on each of the well-resolved σ components of the Zeeman splitting. The extension to more complex transitions, such as aJ = 1 \rightarrow 2, is then given. A dominant resonance peak in the laser intensity occurs when the RF equals the Zeeman splitting of either the upper or lower states of the transition. Population differences amongst the upper sublevels are more effective than those between the lower sublevels and give the smallest resonance widths. For operation on the σ modes, the main effect is a reduction in the saturation coefficient β, together with smaller changes in the coupling coefficients θ between the oscillations. Such changes will affect the general behavior near the singular points of the nonlinear equations, and will change the shape of the curves of mode intensities as functions of cavity detuning and magnetic field.
Coherent preparation of quantum states of atoms and ions by laser light can lead to electromagnetically induced transparency and related effects. In particular, the standing wave at the adjacent transition induces a new type of nonlinear resonance in the probe-field spectrum of a three-level system. The resonance is due to the effect of high-order harmonics of atomic coherence. However, the resonance is broadened and the reason of the broadening was unclear. The paper describes how the velocity changing collisions broaden the resonance. The analytic theory taking into account up to 4-th order of the perturbation theory is presented. The numerical calculations are described. The analytical formulas are shown to describe the experiment qualitatively while the numerical computation demonstrates quantitative agreement. The Coulomb dephasing is discussed as the physical mechanism of the broadening.
We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/b. We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.