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Journal of Physics B Atomic Molecular and Optical Physics

Optical Stark effect and photon statistics in the density matrix approach

T. Altevogt, H. Puff, R. Zimmermann

Published Jul 28, 1997• 1 citation
Publisher

Abstract

We analyse a pump - probe set-up for detecting the optical Stark effect on two-level atoms with a quantized pump field in terms of a density matrix approach (DMA). The approximation used reveals a method to calculate the probe absorption spectra without high computational effort. It is even applicable for large numbers of atoms where the exact calculation is not practicable. The probe spectra in the DMA reflect the photon statistics of the pump field and deviate only slightly from exact results for relevant experimental parameters.

DOI
10.1088/0953-4075/30/14/020

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We analyse a pump - probe set-up for detecting the optical Stark effect on two-level atoms with a quantized pump field in terms of a density matrix approach (DMA). The approximation used reveals a method to calculate the probe absorption spectra without high computational effort. It is even applicable for large numbers of atoms where the exact calculation is not practicable. The probe spectra in the DMA reflect the photon statistics of the pump field and deviate only slightly from exact results for relevant experimental parameters.
We theoretically analyze a pump–probe experiment to detect the optical Stark effect on impurity-bound excitons taking the quantization of the pump field into account. A density matrix approach allows the calculation of the probe absorption spectra with high accuracy. For bound excitons with low inhomogeneous broadening of several tens of μeV, the photon statistics of the pump field has a considerable influence on the lineshape of the Stark-shifted resonance. The effect should be clearly observable for broad photon number distributions and low pump detuning.
The optical Stark effect in a pump-probe setup is expected to show interesting additional features if the quantization of the pump field becomes important. A major effect is that the lineshape of a Stark-shifted resonance is strongly modified when squeezing the pump field. Furthermore, a probe gain is predicted here which does not appear in a semiclassical treatment. It appears for pump detunings considerably lower than the mean Rabi frequency. The nonclassical gain in the optical Stark effect is investigated on an ensemble of two-level systems (TLSs). A density matrix approach is presented which allows the accurate calculation of the probe absorption. The precise treatment of correlations between pairs of TLSs is crucial to explain details of the lineshape.
A numerical method is introduced that solves the optical Bloch equations describing a two-level atom interacting with a strong polychromatic pump field with an equidistant spectrum and an arbitrarily intense monochromatic probe field. The method involves a transformation of the optical Bloch equations into a system of equations with time-independent coefficients at steady state via double harmonic expansion of the density-matrix elements, which is then solved by the method of matrix inversion. The solutions so obtained lead immediately to the determination of the polarization of the atomic medium and of the absorption and dispersion spectra. The method is applied to the case when the pump field is bichromatic and trichromatic, and the physical interpretation of the numerically computed spectra is given.
The optical Stark effect of a two-level system coupled to a Brownian oscillator (i.e. a harmonic mode which in turn is coupled to a heat bath) is studied using equations of motion for a reduced density matrix. These equations, derived using path integral techniques, can be used to study the combined effects of strong fields and dephasing processes at finite temperature, and interpolate continuously from the coherent to the overdamped limits where they reduce to the stochastic Gaussian-Markovian equation. Numerical calculations of probe absorption spectra for various pump intensities are presented, and show dynamical Stark splitting. In contrast to the Bloch equations which contain an infinite-temperature dephasing, we find that at finite temperature, the Stark peaks may have different heights even when the pump pulse is on resonance.
Using pump-probe spectroscopy, a four level system (FLS) with a double V-type configuration is investigated under Doppler-free conditions. The semiclassical description of the atom-field interaction is used to derive the optical Bloch equations (OBE). Under steady-state and rotating wave approximation, the coupled OBE reduces to a system of simultaneous equations. The analytical expressions for the signal absorption are parametrically computed using theoretical data. The signal lineshapes exhibit two perfectly symmetric Lorentzians corresponding to two signal resonance frequencies when the pump position is exactly in the middle of the two signal resonance frequencies. These two Lorentzians repel each other and, hence, the shifts of the signal peak frequencies. For on-resonant pump, the ac (dynamic) Stark splittings are obtained. The off-resonant pump produces the two-photon resonances. The nonlinear polarization and hence the hyperpolarizability involving the lower pair of levels exhibit interesting results. The hyperpolarizability is synonymous with those of the quadratic Stark effects.