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physica status solidi (b)

Optical Stark Shift of Bound Excitons with Quantized Radiation Field

T. Altevogt, H. Puff, R. Zimmermann

Published Mar 1, 1998• 1 citation
Publisher

Abstract

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.

DOI
10.1002/(sici)1521-3951(199803)206:1<87::aid-pssb87>3.0.co;2-m

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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.
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.
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.
As an application of the nonlocal theory of radiation matter interaction, pump-probe spectra for ultrathin (<500 Å) platelets of CuCl have been calculated for the pumping condition between exciton and biexciton levels. Typical aspects such as (1) pump induced absorption to biexciton states, and (2) optical Stark shift and resonant broadening of size quantized exciton levels can be seen in the calculated response spectra. The spatial variation of the light field inside the samples depends sensitively on the frequency and slab thickness, which is clearly reflected in the response spectra as quasi k -selection rule. For thicker samples the k -selection rule becomes more strictly valid, as expected.
Band-edge absorption spectra for a probe beam under the action of a nonresonant pump beam are calculated and analyzed within the Hartree-Fock theory. As a result of many-body interactions, one obtains an exciton optical Stark shift with a constant (2D) or slightly increasing (3D) exciton oscillator strength in agreement with several recent experiments and in striking contrast to corresponding atomic observations. Apparently, the deviating results of earlier semiconductor experiments were partly caused by dynamical effects and partly by the presence of real excitations.