Optical coherent transients in cold atoms: From free-induction decay to optical precursors

Abstract

We report theoretical and experimental studies of the propagation of a square-modulated laser pulse through a laser-cooled atomic ensemble of two-level absorbers, as well as through a three-level system with electromagnetically induced transparency. We find that the transmission characteristics over a wide range of optical depth can be fully accounted for as optical coherent transients excited by the wide spectral content of the square-modulated optical pulse. We show that both time-domain atom-field coupled equations and frequency-domain linear dispersion theory give precisely the same description of the optical transients at a weak power limit. At low optical depth with moderate absorption, resonant excitation dominates and free-induction decay (FID) contributes mostly to the transient field. At high optical depth when absorption and propagation effects become significant, lossless optical precursors start to dominate the transient response. By varying the optical depth from 0 to 45, we observe that optical transients evolve gradually from FID to optical precursors. We thus show that FID and optical precursors, which have been considered as two different optical transients for many decades, can be unified within a single theoretical frame and they are the manifestations of the same physical process in two different regimes.

Optical precursors in the singular and weak dispersion limits

“…They found that the precursors have a large amplitude that is comparable to the amplitude of the incident signal and persist for many nanoseconds for the case when the signal frequency is very close to the resonance frequency of the Lorentz model dielectric ͉͑ c − 0 ͉ Շ ␦͒, making them easier to detect directly using standard fast detectors and oscilloscopes. This research prompted other studies [20], including the generation of optical precursors in a material displaying electromagnetically induced transparency [21,22]; the interplay between optical precursors, selfinduced transparency [23], and free-induction decay [24]; and the so-called precursor stacking [25].…”

“…5 and 6 will then remain valid, subject to the equivalence relations given in Eqs. (24) and (25), as the medium density is further decreased.…”

“…In these recent studies [20][21][22][23][24], the theoretical analysis proceeds by evaluating the integral in Eq. (1) using an approximate simplified expression for the complex index of refraction.…”

Marking slow light signals with fast optical precursors in the regime of electromagnetically induced transparency

“…It is difficult to extract the optical precursors while the main pulse remains. Recently, with the aid of electromagnetically induced transparency (EIT) [15,16], direct observation of precursors, which are separated from the delayed main fields due to the slow-light effect, has been achieved in cold atoms [11,[17][18][19]. Motivated by the observation of precursory spikes at the leading edge of biphoton correlation [20,21], the direct observation of heralded singlephoton precursors with step-and square-modulated wave packets passing through cold atomic EIT medium has been reported [22].…”

Optical precursors with tunneling-induced transparency in asymmetric quantum wells

“…It is difficult to extract the optical precursors while the main pulse remains. With the aid of electromagnetically induced transparency (EIT) [17], optical precursors can be separated from a main pulse through an opaque medium in time [18][19][20]. In this case the precursor signals are significantly ahead of the delayed main pulse due to the slow-light effect.…”