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Quantum Optics Journal of the European Optical Society Part B

Hole burning and optical pumping by single-mode laser light

M. Elbel, M Simon, H Welp

Published Oct 1, 1990• 6 citations
Publisher

Abstract

A differential equation for the evolution of Bennet holes in a Maxwell distribution is derived on the basis of the Boltzmann equation. Characteristic forms of these holes are obtained with a sharp peak at the laser frequency and exponential wings attached to it. An experiment to verify the presence of these holes during optical pumping of metastable argon ions is reported here. Electro-optic modulation of the laser light represents a valuable method of overcoming the limit set by hole burning with regard to laser pumping.

DOI
10.1088/0954-8998/2/5/002

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AIP conference proceedings•Jan 1, 2001•0 citations
A differential equation for the evolution of Bennet holes in a Maxwell distribution is derived on the basis of the Boltzmann equation. Characteristic forms of these holes are obtained with a sharp peak at the laser frequency and exponential wings attached to it. An experiment to verify the presence of these holes during optical pumping of metastable argon ions is reported here. Electro-optic modulation of the laser light represents a valuable method of overcoming the limit set by hole burning with regard to laser pumping.
Based on the momentum method the Fokker-Planck equation is derived for a velocity distribution perturbed by monomode laser excitation (hole burning). If the used collision kernel applies to marked forward scattering and if the collision partner is assumed to be infinitely heavy, the FPE degenerates into the Legendre equation. While a proportional term accounts for the decay of atoms, an inhomogeneity accounts for their creation. The considered species is metastable argon ions. These ions are probably created by electronic ionization, while both electronic deexcitation and metastability exchange interfere in their destruction. The laser keeps the solution of the FPE at zero level for any velocity whose component along the laser beam upsilon z,0 follows from the laser frequency by the Doppler condition. We treat this constraint as a boundary condition for the solution. The latter is put up as a superposition of the Legendre function which solves the homogeneous part, with a special solution of the inhomogeneous equation. Free parameters are adjusted to the boundary condition. The thus obtained solution is finally integrated over all the velocity groups of atoms which under our assumptions are not coupled collisionally, to yield the expected shape of the signal. The velocity groups were assumed to be distributed according to Maxwell. We devised two types of experiments to measure the shape of the hole. Both are suited to measure holes on the wings as well as on the centre of the line. Remarkable similarity of the measured and the calculated signals is found.
Applying the momentum method, the Fokker-Planck equation is derived from the Boltzmann equation for the r -4 potential between atoms and ions. Two earlier attempts are revealed to be limiting cases of our more general equation, namely for very large and very small mass ratio of the collision partners. The Fokker-Planck equation, after being completed with a decay term and a source term, is solved by the Green's function method. The solution turns out to be composed of modes in the velocity space which decay independently towards a stationary spectrum. The amplitudes of the latter depend on the source term which we assume to be shaped like a delta -function if laser pumping is accounted for. Only for very long relaxation times does the lowest mode prevail in the spectrum which then merges into the Maxwell distribution. Several new lines for ion-atom pairs as well as atom-atom pairs have been measured. They are presented along with the fits using the aforementioned formula. As expected, the agreement is satisfactory only in the first case. In the second case the Fokker-Planck approximation no longer applies.
4^44He (2 3^33S1_11​) metastable atoms are optically pumped with intensity modulated light. The use of a single mode diode-pumped LNA laser as the pumping source, allows the study of resonance signals predicted by the optical pumping theory but not yet observed. Resonances are detected on the transmitted pumping beam at the modulation frequency and its harmonics. Application of this method to high sensitivity magnetometers is suggested.
There have recently been several studies of the performance of laser frequency stabilization using spectral holes in solids, instead of an external cavity, as a frequency reference. Here an analytical theory for Pound-Drever-Hall laser frequency stabilization using spectral hole-burning is developed. The interaction between the atomic medium and the phase modulated light is described using a linearized model of the Maxwell-Bloch equations. The interplay between the carrier and modulation sidebands reveals significant differences from the case of locking to a cavity. These include a different optimum modulation index, an optimum sample absorption, and the possibility to lock the laser in an inherent linear frequency drift mode. Spectral holes in solids can be permanent or transient. For the materials normally used, the dynamics and time scales of transient holes often depend on population relaxation processes between ground state hyperfine levels. These relaxation rates can be very different for different solid state materials. We demonstrate, using radio-frequency pumping, that the hyperfine population dynamics may be controlled and tailored to give optimum frequency stabilization performance. In this way also materials with initially non-optimum performance can be used for stabilization. The theoretical predictions regarding the inherent linear frequency drift is compared to experimental data from a dye laser stabilized to a spectral hole in a Pr(3+)3+:Y(2)SiO(5) crystal.
Investigations in the field of quantum optics very often requires a molecular simulation of transport phenomena. This paper presents a discrete kinetic model to deal with the quantum optical problem of hole burning. Based on a full discretization of the velocity space, Boltzmann-like equations are established to govern the temporal evolution of heavily disturbed Maxwell distributions of optically excited particles diffusing in a buffer gas. These model equations involve elastic collisions and the interaction of photons with three-level atoms by taking into account the Doppler effect. Important features of the developed model are the realistic simulation of the relaxation process and the existence of a stable and unique equilibrium solution.