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Bulletin of the Russian Academy of Sciences Physics

Coherent forward scattering of a single photon wave packet in a resonant medium

R. N. Shakhmuratov, Farit G. Vagizov, J. Odeurs, Olga A. Kocharovskaya

Published Jul 1, 2010• 0 citations
Publisher

Abstract

The propagation of a single photon wave packet in a thick resonant medium was studied theoretically and experimentally. The well-known acceleration of wave packet decay was observed upon wave packet exiting from a medium with single resonant absorption line. It was found that in a medium with two closely spaced absorption lines, the restoration of the photon wave packet is observed after the acceleration of decay.

DOI
10.3103/s1062873810070142

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The propagation of a single photon wave packet in a thick resonant medium was studied theoretically and experimentally. The well-known acceleration of wave packet decay was observed upon wave packet exiting from a medium with single resonant absorption line. It was found that in a medium with two closely spaced absorption lines, the restoration of the photon wave packet is observed after the acceleration of decay.
The interaction of a single-photon wave packet with an initially excited two-level atom in free space is studied in semiclassical and quantum approaches. It is shown that the final state of the field does not contain doubly occupied modes. The process of the atom's transition to the ground state may be accelerated, decelerated, or even reversed by the incoming photon, depending on parameters. The spectrum of emitted radiation is close to the sum of the spectrum of the incoming single-photon wave packet and the natural line shape, with small and complicated deviations.
Propagation of a short quasi-monochromatic electromagnetic (light or radio) signal (wave packet) is considered. The carrier frequency of the signal is close to the frequency of the absorption spectral line (or group of lines) of a medium, and the spectrum width is large relative to the width of this spectral line (or group of lines). Analytic formulas for the temporal dependence of the signal are derived and numerically confirmed for paths of various lengths. It is shown that the signal is substantially distorted long before it noticeably decays owing to absorption. The signal’s temporal dependence turns out to be rather universal with respect to the form factor of the spectral line, the optical thickness of the substance layer, and the initial temporal dependence of the signal.
We consider the time-delayed coincidence counting of two photons emitted in a cascade by a single particle (atom, molecule, nucleus, etc.). The time-dependence of the probability amplitude of the second photon in the cascade has a sharply rising leading edge due to the detection of the first photon, as results from causality. If a macroscopic ensemble of resonant two-level absorbers is placed in the path of the second photon between the radiation source and the detector, the photon absorption does not follow Beer's law due to the time-asymmetric shape of the photon. For very short delay times almost no absorption takes place, even in an optically dense medium. We analyze the propagation of such a second photon in a thick resonant three-level absorber if a narrow electromagnetically induced transparency (EIT) window is present at the center of the absorption line. It is shown that the EIT medium can change the asymmetric time dependence of the photon probability amplitude to a bell shape (EIT filtering). This bell-shaped photon interacts much more efficiently with another ensemble of two-level absorbers chosen, for example, to store this photon and the information it carries. Ideally a photon wave packet with a Gaussian time-envelope is most effectively stored.
The radiation burst from a single $\ensuremath{\gamma}$-photon field interacting with a dense resonant absorber is studied theoretically and experimentally. This effect was discovered for the fist time by P. Helisto et al. [Phys. Rev. Lett. 66, 2037 (1991)] and it was named the ``gamma echo.'' The echo is generated by a 180${}^{\ensuremath{\circ}}$ phase shift of the incident radiation field, attained by an abrupt change of the position of the absorber with respect to the radiation source during the coherence time of the photon wave packet. Three distinguishing cases of the gamma echo are considered; i.e., the photon is in exact resonance with the absorber, close to resonance (on the slope of the absorption line), and far from resonance (on the far wings of the resonance line). In resonance the amplitude of the radiation burst is two times larger than the amplitude of the input radiation field just before its phase shift. This burst was explained by Helisto et al. as a result of constructive interference of the coherently scattered field with the phase-shifted input field, both having almost the same amplitude. We found that out of resonance the scattered radiation field acquires an additional component with almost the same amplitude as the amplitude of the incident radiation field. The phase of the additional field depends on the optical thickness of the absorber and resonant detuning. Far from resonance this field interferes destructively with the phase-shifted incident radiation field and radiation quenching is observed. Close to resonance the three fields interfere constructively and the amplitude of the radiation burst is three times larger than the amplitude of the input radiation field.