Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Nonclassical gain in the optical Stark effect: density matrix approach

T. Altevogt, Ralf Zimmermann

Published Sep 27, 1999• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/19/311

Related papers

Optical Stark Shift of Bound Excitons with Quantized Radiation Field

T. Altevogt, H. Puff, R. Zimmermann

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.

physica status solidi (b)•Mar 1, 1998•1 citation

Photon statistics and the optical Stark effect

T. Altevogt, H. Puff, R. Zimmermann

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.

Physical Review A•Aug 1, 1997•10 citations

Analytical studies on pump-induced optical resonances in anM-typesix-level system

Saswata Ghosh, Swapan Mandal

In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 1, 2010•8 citations

Optical Stark effect and photon statistics in the density matrix approach

T. Altevogt, H. Puff, R. Zimmermann

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.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 28, 1997•1 citation

A theoretical study of the optical Stark effect in InGaAs/InAlAs quantum dots

Đinh Như Thảo, Lê Thị Ngọc Bảo, Dương Đình Phước +1 more

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.

Semiconductor Science and Technology•Jan 19, 2017•14 citations

Optical Stark Spectroscopy of a Brownian Oscillator in Intense Fields

Yoshitaka Tanimura, Shaul Mukamel

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.

Journal of the Physical Society of Japan•Jan 15, 1994•91 citations
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 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.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
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.
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.
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.