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Physical Review A

Atomic response to optical fluctuating fields: Temporal resolution on a scale less than pulse correlation time

Vladimir Finkelstein

Published May 1, 1991• 8 citations
Publisher

Abstract

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 ${\mathit{t}}_{12}$, and can be correlated with one another. It is shown that, for strong excitation pulses, the level populations and atomic coherence as functions of ${\mathit{t}}_{12}$ 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.

DOI
10.1103/physreva.43.4901

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•Feb 3, 2009•1 citation
Excitation of a three-level atom irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth \ensuremathτc\ensuremath−1{\mathrm{\ensuremath{\tau}}}_{\mathit{c}}^{\mathrm{\ensuremath{-}}1}\ensuremathτc\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 \ensuremathτc{\mathrm{\ensuremath{\tau}}}_{\mathit{c}}\ensuremathτc​. This effect may lead to a means for obtaining high temporal and spatial resolution.
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.
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 transient, time-delayed, four-wave mixing experiment is performed in strontium vapor under stochastic excitation conditions. The first two broad-bandwidth laser pulses are correlated and their delay is adjustable. Thus they combine into a non-Markovian excitation process with adjustable memory time. One of the correlated pulses is allowed to be strong. In contrast with previous investigations, it is shown both theoretically and experimentally that under strong-field conditions the atoms are not able to keep the excitation memory over time intervals longer than the inverse laser bandwidth.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).