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arXiv:1712.09214 · Physical Review A

Time-delayed coincidence technique for subnatural-width spectroscopy as an interference phenomenon

R. N. Shakhmuratov, Farit G. Vagizov

Published Mar 18, 2019• 2 citations
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Abstract

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 $T$ is long compared to the lifetime ${T}_{1}$ of the excited state. However, when the observation time $T$ is short or comparable to ${T}_{1}$, 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.

DOI
10.1103/physreva.99.033831

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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.
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.
The time-delayed scattering in 14.4 keV Mossbauer resonance at 57 Fe has been intensively studied using pulsed synchrotron radiation source and delayed coincidence technique. Here, results of x-ray interferometric experiments are shown, which were obtained at KEK with this nuclear resonance. There, the interference arises from the beams re-emitted by different nuclei with some time interval after the absorption of a single incident photon. High visibility interference oscillations verified the coherent superposition as well as the complete coincidence in the time domain of the beams after the nuclear resonance. The collective nuclear excitations from a single photon are discussed with regard to the no-reduction of the detection probability. In addition, the phase information transfer in successive absorption and re-emission with time-delay, and the dispersion effect at the nuclear resonance are shown.
Spectra that are narrower than the natural width of decaying states can be achieved by beginning the observation of signals at a fixed delay time after excitation rather than immediately afterward. These signals are weaker (and noisier) than the full, time-unresolved signals. Applications of this line-narrowing technique to precision spectroscopy are discussed, and the properties of the resulting signals are studied. Numerical simulations demonstrate that time-resolved line narrowing is highly desirable in a large number of cases.
The so-called gamma-echo effect has been observed experimentally and analyzed using the semiclassical optical theory. Here the effect is reinterpreted using a new 1D quantum mechanical model. This leads to a different interpretation of the effect as a π phase-shift induced transparency. In the basic time-differential Mössbauer spectroscopic technique the forward-scattered recoil-free radiation is observed, in delayed coincidence, after passing through a nuclear-resonant absorber. The effect in question is produced most efficiently when the source of recoil-free radiation is moved abruptly causing a π phase shift of the source radiation during its radiative lifetime. Using the 1D model the effect is seen to arise from the constructive interference between the source radiation at a later time, and the radiation coming from the absorber excited at an earlier time. The exact form of the source modulation and the nuclear-resonant thickness of the resonant absorber determines the shape of the time-differential resonant gamma ray transmission spectrum. Numerical results are given using the familiar 57Fe recoil-free resonant transition. The π phase-shift-induced transparency allows the resonant gamma radiation, incident on the resonant absorber, to be transmitted through the absorber without appreciable attenuation.
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.
A complete solution of the time-dependent Schrodinger equation for the overall absorption-emission process is presented for a particular model system possessing an excited state manifold of (nearly) uniformly spaced molecular eigenstates with a lorentzian distribution of transition moment. Results for both narrow and broad band excitation are derived, and it is shown that the fluorescence quantum yield is essentially the same for both broad band and narrow band excitations. It is argued that the lifetime of the incident photon state is important in determining the presence or absence of structure in the absorption spectrum and, consequently, that the absorption spectrum observed depends upon both the optical density of the sample and the intensity of the incident light.