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Journal of Physics B Atomic and Molecular Physics

Path integration method applied to (N-1)-resonant N-photon ionisation

Maciej Lewenstein, P. Zoller, Jan Mostowski

Published Feb 28, 1983• 7 citations
Publisher

Abstract

The authors investigate the problem (N-1) resonant N-photon ionisation of an atom driven by a stochastic field. The authors compare ionisation rates in the presence of a phase-diffusing laser field and light undergoing Gaussian amplitude fluctuations (chaotic field). In the case of the chaotic field the authors obtain exact results with the help of the functional integration method. They also present numerical results for the case of three-resonant four-photon ionisation.

DOI
10.1088/0022-3700/16/4/010

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Physical Review A•Apr 1, 1985•2 citations
The authors investigate the problem (N-1) resonant N-photon ionisation of an atom driven by a stochastic field. The authors compare ionisation rates in the presence of a phase-diffusing laser field and light undergoing Gaussian amplitude fluctuations (chaotic field). In the case of the chaotic field the authors obtain exact results with the help of the functional integration method. They also present numerical results for the case of three-resonant four-photon ionisation.
Presents a theoretical analysis of the effect of laser light statistics on two-photon resonant three-photon ionisation of sodium. The ionisation probability and the population of the atom in the resonant state are compared in the presence of an intensity stabilised laser with a diffusing phase (phase diffusion model) and light undergoing Gaussian amplitude fluctuations (chaotic field). In the limit of large bandwidth fields the resonant two-photon excitation is statistically decoupled from the following ionisation step. A decrease of the bandwidth results in a partial correlation between these two steps manifesting itself in an enhancement of the ionisation probability in the chaotic field. With increasing intensity and the onset of saturation of the bound-bound transition, the ionisation probability and resonant excited-state population in the chaotic field may become smaller than the one in the phase diffusing light. In the large-bandwidth limit the Stark shift in the chaotic field is enhanced, which has a pronounced effect on the effective power-law dependence of the ionisation probability.
The authors present exact solutions for N=1 and 2 N-photon off-resonance ionisation in the presence of a fluctuating radiation field with pre-Gaussian statistics. These pre-Gaussian fluctuations are composed of n independent two-state jump processes (telegraphs). Such telegraph-type fluctuations have a second-order intensity coherence function g that is normalised and bounded such that 1<or=g<or=2. In the limit n to infinity the pre-Gaussian noise converges to chaotic light with the well known g=2!. The authors show that an exact discussion of the N-photon ionisation rate can be given for such pre-Gaussian fluctuations.
The author presents a theory of resonant multiphoton ionisation by multimode laser light. He investigates N photon resonant N+1 photon ionisation for a high order bound-bound transition with the resonance dominated by the Stark shift. Two aspects of the problem are considered. He studies the bandwidth dependence for the resonant ionisation probability, approximating the multimode laser light by a chaotic field. Secondly, he investigates the effects of finite mode numbers of the multimode laser. Finally, the theory is compared with the recent experimental results of Lompre et al (1981).
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.
The effects of amplitude and phase fluctuations of the pump laser on the resonance fluorescence under two-photon resonant excitation are studied. The averaging of the stochastic Bloch equations is carried out within the approximation scheme that has recently been applied to the case of one-photon resonant excitation. In the case of two-photon resonant excitation the stochastic pump field gives rise to multiplicative nonlinear Gaussian fluctuation effects. The phase fluctuations are treated in the phase-diffusion model, and the averaging over the amplitude fluctuations is performed by means of generating-function methods. Both the intensity and the intensity correlation of the fluorescent light are studied. When the amplitude fluctuations are weak, the cases of one- and two-photon resonant excitations are similar. The difference between both cases consists of a modification of the Rabi frequency and a faster damping of the Rabi oscillations in the two-photon case. For sufficiently fast correlation decay of the amplitude fluctuations their effect can simply be described by a rate. In the general case of n-photon resonant excitation this rate is larger by a factor of n2{n}^{2}n2 than that in the case of one-photon resonant excitation. When the amplitude fluctuations are sufficiently strong, the Rabi oscillations are ``washed out.'' In the case of one-photon resonant excitation both the intensity and the intensity correlation function of the scattered light develop into step functions over time. In the two-photon case the dynamics of both quantities is determined by a new time constant which acts as both the oscillation time and the damping time. Consequently an overshoot peak occurs in both the intensity and the intensity correlation instead of the tendency to become step functions.