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Physical Review A

Power effects in broadband optical coherent transients

M. Defour, J. Keller, J.-L. Le Gouët

Published Dec 1, 1987• 15 citations
Publisher

Abstract

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 ${t}_{12}$ 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 ${t}_{12}$. Experimental recordings are in accordance with this conjecture.

DOI
10.1103/physreva.36.5226

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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.
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.
Formation of coherent transients by incoherent light pulses has stimulated renewed interest in time-resolved coherent spectroscopy. Standard theories conveniently account for the weak-field regime experiments, but they fail to interpret the power effects that occur during resonant excitation of a sample by time-delayed, correlated, broadband laser pulses. We report on a new approach to this problem. We have been able to determine the expectation value of the population grating induced by two time-delayed, correlated, broadband light pulses under the limitation that one of the fields is weak. We have developed a diagrammatic technique that seems promising for the calculation of actual coherent-transient signals in the strong-field regime.
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 theory is developed to describe the optical transient signals that arise when a sample of two-level atoms is irradiated by a sequence of two or 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. These pulses whose temporal width is much greater than the delay time are fully correlated with one another and can be strong enough to saturate the two-level atomic transition. In the case of three-pulse transients the third pulse is weak non-correlated with the first two and is delayed in time so that it does not overlap them. Taking into account the effects ofinhomogeneous and homogeneous broadening we calculate the intensity of the transient signals as a function of delay time. The signals are found to depend dramatically on the intensities of the excitation pulses. It is shown that for strong excitation pulses a direct dependence of the signal on the cross-correlation time of the pulses r occurs that does not exist when the pulses are weak. In particular for saturating pulses the signals exhibit a peak of width of order r . In the case of the two-pulse transient the peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large. This peak can have a very narrow dip near its maximum whose width is much