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Physical Review A

Inhibition of inhomogeneous dephasing by a strong stochastic optical field

P. Tchénio, Anne Débarre, J. Keller, J.-L. Le Gouët

Published Nov 1, 1988• 16 citations
Publisher

Abstract

We examine the buildup of atomic dipoles by a single broadband light pulse and their subsequent rephasing to produce a coherent transient signal. Within the assumption of short-time correlation for the light field, the theoretical model predicts the inhibition of inhomogeneous dephasing by the strong stochastic field. A geometrical picture of the effect is presented that uses a diffusion model of the Bloch vector headings on the Bloch sphere. The model is applied to the specific case of a stimulated photon echo in an angled-beam configuration. The corresponding experiment is performed in calcium vapor, and the expected inhibition effect is observed. The decay of the echo intensity as a function of the delay between the two first weak pulses is found to agree with the theoretical model.

DOI
10.1103/physreva.38.5235

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arXiv:1706.05327•Physical review. B./Physical review. B•Aug 18, 2017•22 citations
We examine the buildup of atomic dipoles by a single broadband light pulse and their subsequent rephasing to produce a coherent transient signal. Within the assumption of short-time correlation for the light field, the theoretical model predicts the inhibition of inhomogeneous dephasing by the strong stochastic field. A geometrical picture of the effect is presented that uses a diffusion model of the Bloch vector headings on the Bloch sphere. The model is applied to the specific case of a stimulated photon echo in an angled-beam configuration. The corresponding experiment is performed in calcium vapor, and the expected inhibition effect is observed. The decay of the echo intensity as a function of the delay between the two first weak pulses is found to agree with the theoretical model.
A theoretical analysis of the optical coherent transients that arise when a sample of two-level atoms is irradiated by a sequence of three broad-bandwidth pulses is presented. The first two pulses have a relative delay time of order of the correlation time of the pulse fluctuations and are sent into an atomic vapor from different directions. These pulses, whose temporal width is much greater than the delay time, can be correlated with one another and can be strong enough to saturate the two-level atomic transition. The third pulse is weak, noncorrelated with the first two, and is delayed in time so that it does not overlap them. We present a detailed examination of the transient signal that is produced when the third pulse is scattered by the spatial gratings in the population difference of atoms created by the first two pulses. Taking into account the effects of inhomogeneous and homogeneous broadening, we calculate the intensity of the transient signal, emitted in different directions, as a function of delay time. The signal is found to depend dramatically on the intensities of the excitation pulses. It is shown that, for strong excitation pulses, there is a direct dependence of the signal on the cross-correlation time of pulses ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$. This peak can have a very narrow dip near its maximum whose width is much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}$, if the pulses are fully correlated. We develop a representation of the time evolution of the Bloch vector of a two-level atom, driven by time-delayed pulses, that enables us to explain our results. In this representation, the two time-delayed pulses are replaced by two fully overlapping pulses having some effective amplitudes and atomic field detunings.
The power effects in the formation of stimulated photon echoes by broadband light pulses are examined both theoretically and experimentally. An angled-beam configuration is considered. Specific broadband features are expected to affect the signal intensity when the delay t12{t}_{12}t12​ between the two first excitation pulses is varied across zero. The power dependence of these features is examined. In order to determine the expression of the signal intensity one has to solve the Bloch equation with random coefficients. Standard methods for solving stochastic differential equations are proved to fail when excitation is produced by delayed correlated pulses. A qualitative picture is proposed, which predicts the saturation decay of the signal as a function of t12{t}_{12}t12​. Experimental recordings are in accordance with this conjecture.
A diagrammatic technique is developed to account for the saturation effects which occur when optical coherent transients are generated by broad-bandwidth light pulses. The paper is focused on the calculation of the two-atom, single-time dipole correlation function which originates the signal. In addition to the single-excitation-field situation, we examine the coherent transient generation by overlapping time-delayed correlated pulses. Our approach requires that one of the two correlated pulses be weak. The calculation of the delay dependence of the signal intensity is thoroughly worked out in the case of two-pulse and three-pulse transients in an angled-beam configuration.
Photon echo and free induction decay, i.e., representative coherent optical transients, are described for two level system whose transition frequency is modulated by the Gaussian-Markoffian process. Photon echo signal is shown to decay biexponentially and to be effective in fixing the magnitude and the correlation time of the frequency modulation. Then we present the transition of the free induction decay rate against laser intensity from the Bloch type at the weak laser field into the Redfield one at the strong laser field.
We study Rabi oscillations detected in the coherent optical response from various exciton complexes in a 20-nm-thick CdTe/(Cd,Mg)Te quantum well using time-resolved photon echoes. In order to evaluate the role of exciton localization and inhomogeneous broadening we use selective excitation with spectrally narrow ps pulses. We demonstrate that the transient profile of the photon echo from the localized trion (${\mathrm{X}}^{\ensuremath{-}}$) and the donor-bound exciton (D0X{\mathrm{D}}^{0}\mathrm{X}D0X) transitions strongly depends on the strength of the first pulse. It acquires a non-Gaussian shape and experiences significant advancement for pulse areas larger than $\ensuremath{\pi}$ due to non-negligible inhomogeneity-induced dephasing of the oscillators during the optical excitation. Next, we observe that an increase of the area of either the first (excitation) or the second (rephasing) pulse leads to a significant damping of the photon echo signal, which is strongest for the neutral excitons and less pronounced for the donor-bound exciton complex (D0X{\mathrm{D}}^{0}\mathrm{X}D0X). The measurements are analyzed using a theoretical model based on the optical Bloch equations which accounts for the inhomogeneity of optical transitions in order to reproduce the complex shape of the photon echo transients. In addition, the spreading of Rabi frequencies within the ensemble due to the spatial variation of the intensity of the focused Gaussian beams and excitation-induced dephasing are incorporated in our model, which is able to explain the fading and damping of Rabi oscillations. By analyzing the results of the simulation for ${\mathrm{X}}^{\ensuremath{-}}$ and D0X{\mathrm{D}}^{0}\mathrm{X}D0X complexes we are able to establish a correlation between the degree of localization and the transition dipole moments determined as $\ensuremath{\mu}({\mathrm{X}}^{\ensuremath{-}}$)=73 D and $\ensuremath{\mu}({\mathrm{D}}^{0}\mathrm{X}$)=58 D.