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Physical Review A

Slow γ photon with a doublet structure: Time delay via a transition from destructive to constructive interference of collectively scattered radiation with the incoming photon

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

Published Dec 2, 2009• 25 citations
Publisher

Abstract

Single $\ensuremath{\gamma}$ photon propagation in a dense absorptive medium with two widely spaced resonances is experimentally studied. After an initial fast decay, a revival of the photon amplitude in the form of a bump, exceeding the probability amplitude of the incident photon, is observed. The irradiation time of this bump delays approximately by the lifetime of the excited nuclei in the absorber. This effect is explained by the interference of the incoming radiation with the collectively scattered radiation, the phase of which is modulated with the frequency of the doublet splitting. Initially, the destructive interference changes to a constructive one, distinguishing the storage and retrieval stages of the photon propagation in a dense medium, i.e., the collective absorption and collective re-emission processes.

DOI
10.1103/physreva.80.063805

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Single \ensuremathγ\ensuremath{\gamma}\ensuremathγ photon propagation in a dense absorptive medium with two widely spaced resonances is experimentally studied. After an initial fast decay, a revival of the photon amplitude in the form of a bump, exceeding the probability amplitude of the incident photon, is observed. The irradiation time of this bump delays approximately by the lifetime of the excited nuclei in the absorber. This effect is explained by the interference of the incoming radiation with the collectively scattered radiation, the phase of which is modulated with the frequency of the doublet splitting. Initially, the destructive interference changes to a constructive one, distinguishing the storage and retrieval stages of the photon propagation in a dense medium, i.e., the collective absorption and collective re-emission processes.
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.
Slow light, produced in a medium with two widely spaced absorption resonances, is analytically studied. We show that a pulse with frequency tuned in the middle of such a doublet structure slows down due to its energy storage in the excited atomic states. If the lifetime of the atomic excitation is much longer than the pulse duration, the pulse shape is nicely reproduced at the output of a thick sample for pulses with smooth envelopes. Pulses with sharp edges are fairly reproduced at the output. Each abrupt change of the pulse amplitude is followed by transients, which are delayed together with the pulse. A possibility to slow down a single photon is also considered.
A single photon, emitted in a transition between two states, has a frequency distribution of intensity that is given by a Lorentzian if the transition is only naturally broadened and the period of observation TTT is long compared to the lifetime T1{T}_{1}T1​ of the excited state. However, when the observation time TTT is short or comparable to T1{T}_{1}T1​, the frequency spectrum is appreciably broadened. If only the delayed part of the emitted radiation field is detected, then the radiation spectrum does not change. However, if the radiation field is transmitted through a resonant absorber and then detected, the transmission spectrum of the delayed radiation field is narrowed. We show that this narrowing is due to the interference of the spectral components of the incident and coherently scattered fields. Experimental spectra of absorption of M\"ossbauer radiation, obtained by the coincidence technique, confirm this conclusion.
It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.
The pulsed radiation field propagating in a thick resonant absorber induces the polarization (quantified by the induced atomic dipoles in optical domain or the induced nuclear transition moments in gamma domain), which is distributed oscillatorily along the absorber forming a sandwich of polarization layers with opposite phases. As a result, the reemitted, scattered fields in different layers interfere with the incident input field destructively or constructively, giving rise to the well-known dynamical beats of the output radiation. We propose a method how to force these layers in the sandwich to reemit in phase with the incident field, which results in a strong radiation burst of short duration at the output of the absorber. We demonstrate this method experimentally for the 14.4 keV nuclear transition in 57{}^{57}57Fe.
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.