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Physical Review A

Photon statistics and the optical Stark effect

T. Altevogt, H. Puff, R. Zimmermann

Published Aug 1, 1997• 10 citations
Publisher

Abstract

We theoretically describe a pump-probe scheme for detecting the optical Stark effect on two-level atoms with a fully quantized pump field. The probe absorption reflects the photon statistics of the pump field for both the single-atom and multiatom case. Nonclassical features, without counterpart in the single-atom case appear in the multiatom absorption and result in strong variations of the absorption amplitude and nonclassical gain or absorption.

DOI
10.1103/physreva.56.1592

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We theoretically describe a pump-probe scheme for detecting the optical Stark effect on two-level atoms with a fully quantized pump field. The probe absorption reflects the photon statistics of the pump field for both the single-atom and multiatom case. Nonclassical features, without counterpart in the single-atom case appear in the multiatom absorption and result in strong variations of the absorption amplitude and nonclassical gain or absorption.
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.
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.
A theory of pump-probe spectroscopy is developed in which optical fields drive two-photon Raman transitions between ground states of an ensemble of three-level atoms. Effects related to the recoil the atoms undergo as a result of their interactions with the fields are fully accounted for in this theory. The linear absorption coefficient of a weak probe field in the presence of two pump fields of arbitrary strength is calculated. For subrecoil cooled atoms, the spectrum consists of eight absorption lines and eight emission lines. In the limit that ${\ensuremath{\chi}}_{1}\ensuremath{\ll}{\ensuremath{\chi}}_{2},$ where ${\ensuremath{\chi}}_{1}$ and ${\ensuremath{\chi}}_{2}$ are the Rabi frequencies of the two pump fields, one recovers the absorption spectrum for a probe field interacting with an effective two-level atom in the presence of a single pump field. However, when ${\ensuremath{\chi}}_{1}\ensuremath{\gtrsim}{\ensuremath{\chi}}_{2},$ new interference effects arise that allow one to selectively turn on and off some of these recoil-induced resonances.
Abstract In this paper, we examine the three-level optical Stark effect of excitons in InGaAs/InAlAs quantum dots using renormalized wavefunction formulation. The system was assumed to be irradiated by two lasers in which a strong laser dynamically couples electron-quantized levels, while a weaker laser probes interband absorption. Our results show that, in the presence of the resonant strong laser, two new absorption peaks of excitons appear in the absorption spectrum as a clear indication of the effect. In addition, we propose that the formation of the effect in low-dimensional structures could have connection to the splitting of electron levels. Furthermore, we seek to explain the essential dependence of the amplitude and position of two peaks on pump field detuning.
We have investigated resonant two-photon absorption and second harmonic generation in a microcavity geometry. In a single beam arrangement, the transmission depends on the intensity according to a simple two-level picture with an intensity-dependent coupling; at resonance, in particular, the system exhibits a two-photon Rabi splitting. In a pump and probe arrangement, the presence of the strong incident pump beam substantially modifies the absorption spectrum of the weak probe beam: for moderate pump intensities the behaviour can be interpreted as a two-photon version of the well-known optical Stark effect. At higher intensities, more complicated hyper-Raman processes take place, which give also rise to gain in well-determined spectral regions. Finally, we have shown how the non-linear coupling coefficient appearing in the model Hamiltonian is related to the material constants and geometrical parameters of a specific microcavity configuration.