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Physical Review A

Optical coherent transients induced by time-delayed fluctuating pulses: Three-pulse transients

Vladimir Finkelstein, P. R. Berman

Published Jun 1, 1990• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.41.6193

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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 \ensuremathτc12{\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}\ensuremathτc12​ that does not exist when the pulses are weak. In particular, the strongest signals exhibit a peak of width of order \ensuremathτc12{\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}\ensuremathτc12​. This peak can have a very narrow dip near its maximum whose width is much smaller than \ensuremathτc12{\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{12}\ensuremathτc12​, 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.
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
The coherent transient signal emitted when a sample of two-level atoms is irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}1}$. They are correlated with one another, and have a relative delay time t12{\mathit{t}}_{12}t12​. It is shown that for strong excitation pulses the transient signal, as a function of t12{\mathit{t}}_{12}t12​, can exhibit a peak of width of order ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$. This peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large, in qualitative agreement with existing experimental data.
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.
Excitation of a three-level atom irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}1}$, relative delay time t12{\mathit{t}}_{12}t12​, and can be correlated with one another. It is shown that, for strong excitation pulses, the level populations and atomic coherence as functions of t12{\mathit{t}}_{12}t12​ can vary on a time scale much smaller than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$. This effect may lead to a means for obtaining high temporal and spatial resolution.
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.