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Journal of Physics B Atomic and Molecular Physics

Intensity correlation of the resonance fluorescence from a single molecule

K.‐E. Süsse, W. Vogel, D.‐G. Welsch

Published Oct 28, 1981• 8 citations
Publisher

Abstract

The influence of both the finite band width of the laser pump and the effect of the frequency shift of the molecular vibration in the electronic transition on the intensity correlation function gamma 2,2 ( tau ) of the resonance fluorescence light from a single two-atom molecule are studied. In the case of small vibrational damping a double-exponential asymptotic behaviour of gamma 2,2 ( tau ) is found, which is independent of the bandwidth of the exciting laser light.

DOI
10.1088/0022-3700/14/20/005

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Physical Review A•Apr 1, 1985•2 citations
The influence of both the finite band width of the laser pump and the effect of the frequency shift of the molecular vibration in the electronic transition on the intensity correlation function gamma 2,2 ( tau ) of the resonance fluorescence light from a single two-atom molecule are studied. In the case of small vibrational damping a double-exponential asymptotic behaviour of gamma 2,2 ( tau ) is found, which is independent of the bandwidth of the exciting laser light.
The problem of resonance fluorescence from a two-level atom that is driven near resonance by a laser beam of finite bandwidth is tackled via the Heisenberg equations of motion, by a simple generalization of our previous treatment. It is found that the two-time intensity correlation function is again factorizable into a product of the mean light intensities at the two times, each of which is slightly modified under broad-band excitation from its value under monochromatic excitation. The spectrum of the fluorescence is affected rather more drastically, and, in general, becomes asymmetric under broad-band excitation.
The problem of resonant interaction between an electromagnetic radiation field and a vibronic system, such as a molecule or a localized electronphonon system, is considered. The vibronic coupling is assumed to result from displaced and distorted potential energy surfaces for the vibrational motion in the electronic quantum states involved in the resonant interaction with the radiation field. Furthermore, the vibrational energy relaxation is taken into account without assumptions about Markovian-type relaxation. In order to study correlation properties of higher than second order in the electric field strength of the light emitted a method of calculation of the expectation value of an arbitrary product combination of effective time evolution operators of the vibronic system is developed. The calculations are performed by utilizing Feynman's disentangling and operator ordering techniques and yield closed solutions in the low-temperature limit. The theory is used for studying the intensity and the normally ordered intensity correlation function of the resonance fluorescence light from a two-atom molecule excited by a relatively weak laser field, which undergoes phase fluctuations. It is shown that the vibronic coupling can give rise to an anticorrelation effect which is substantially stronger than in the case of resonance fluorescence from an atom. For the case of small vibrational damping a general formula which directly connects the asymptotic long-time behaviour of the normalized intensity correlation function with the vibrational relaxation in the molecule is deduced. It should be convenient for the determination of very small vibrational decay rates.
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.