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Journal of Experimental and Theoretical Physics Letters

Influence of atomic motion on the shape of two-photon resonance in gas

А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Aug 1, 2000• 40 citations
Publisher

Abstract

A gas of three-level atoms with Λ configuration of energy levels was taken as an example to demonstrate that the influence of particle motion on the two-photon resonances extends further than the residual Doppler shift ( k 1 − k 2 ) v . In particular, a narrow dip in the absorption spectrum (“dark” resonance) undergoes substantial narrowing, as compared to the atoms at rest. The width of this resonance is studied nonperturbatively as a function of the intensities of probe and strong fields.

DOI
10.1134/1.1316812

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A gas of three-level atoms with Λ configuration of energy levels was taken as an example to demonstrate that the influence of particle motion on the two-photon resonances extends further than the residual Doppler shift ( k 1 − k 2 ) v . In particular, a narrow dip in the absorption spectrum (“dark” resonance) undergoes substantial narrowing, as compared to the atoms at rest. The width of this resonance is studied nonperturbatively as a function of the intensities of probe and strong fields.
Dark resonances with widths below 30 Hz have been observed in a rubidium cell filled with neon as buffer gas at room temperature. We compare an approximate analytic solution of a \ensuremath{\Lambda} system to our data and show that under our experimental conditions the presence of the buffer gas reduces the power broadening of the dark resonances by two orders of magnitude. We also present numerical calculations that take into account the thermal motion and velocity-changing collisions with the buffer-gas atoms. The resulting dark-resonance features exhibit strong Dicke-type narrowing effects and thereby explain the elimination of Doppler shifts and Doppler broadening, leading to observation of a single ultranarrow dark line.
For pt.II see ibid., vol.9, p.1221 (1976). Discusses the steady-state response of a three-level atom in two-photon absorption. The applied laser fields can have arbitrary intensities (within the rotating-wave approximation (RWA)). A general expression is derived for the population excited on the uppermost energy level. Two special cases which allow a trivial Doppler averaging are treated in detail. For an off-resonant intermediate state the two-photon spectrum is a simple Lorentzian showing a power shift and modest cross power broadening. The same features are retained when several off-resonance intermediate levels are assumed. For very strong laser fields the Doppler shifts can be neglected in the first approximation. The corresponding spectra are analysed.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
The features of resonance fluorescence and absorption of resonance laser radiation in atomic vapors in a superthin cell with thickness L of the order of a wavelength lambda are investigated theoretically. Taking into account the Fabry-Perot interference effect, it is found that the dependence of the fluorescence and absorption spectra on the ratio L/lambda is substantially different. Coherent spectral narrowing - the Dicke effect - when L=(2n+1)lambda/2 and broadening of the spectral line when L = n lambda (n is a whole number) are observed in the absorption spectra. This effect is absent in the spector of resonance fluorescence in extended media. It is also shown that the processes of saturation and optical pumping significantly alter the spectral line shape as the laser intensity increases; in particular, additional sub-Doppler dips appear at the frequency of the atomic transitions. Calculated curves are given for the D2 lines of ^85Rb atoms. © 2004 Optical Society of America
As a rule the thermal motion removes the dark resonance from the spectrum of a three-level system driven by two strong fields. An example has been found where, conversely, the dark resonance manifests itself even after averaging over the velocities. The four-level system is studied with a closed cycle of four resonant fields, when two relatively strong fields interact with opposite transitions. If Rabi frequencies exceed relaxation constants, then the frequency dependence of the nonlinear susceptibility consists of several narrow peaks. Each peak corresponds to a ‘turning point’, the resonant frequency with zero derivative with respect to the velocity. It is shown that two peaks disappear when non-absorbing states coincide with the turning points. The coincidence occurs for equal Rabi frequencies of relatively weak fields.
Excitation of an atomic system subjected to a slowly varying external electromagnetic field is studied using a two-level model. Time evolution of the system is found using an approach which is nonperturbative in the field strength. There is no constraint to small values of the applied field, that is, the field (in appropriate energy units) need not be small compared to the difference in energies of the two levels. Rather, we use the fact that the situation of interest to us is where the frequency of the exciting field is small compared to the frequency associated with the level difference. Transition probabilities and resonance conditions are found which circumscribe both the large- and small-field limits. In the weak-field limit the previous results of high-order perturbation theory are readily recovered. For a monochromatic field the characteristic features of resonance excitation at high harmonic number of the applied field are (a) extremely narrow resonance widths and (b) shifts in resonance positions which are strong functions of field intensity. Because of this sensitivity, we are able to demonstrate that when slow temporal evolution of the field amplitude is taken into account (e.g., due to finite pulse duration) the appropriate mean excitation rate is that due to the uncorrelated contribution of many resonances. The results of this analysis are used to estimate excitation rates in a specific atomic system, Cd12+{\mathrm{Cd}}^{12+}Cd12+, which are then compared to multiphoton-ionization rates. Our calculations suggest that the ionization rate exceeds the excitation rate by several orders of magnitude.