Ultimate capabilities for compression of the waveform of a recoilless γ-ray photon into a pulse sequence in an optically deep vibrating resonant absorber

Abstract

Recently, an exponentially decaying waveform (the time-dependence of detection probability) of a Mössbauer γ-ray photon was transformed into a regular sequence of short pulses in a sinusoidally vibrating recoilless resonant absorber [Nature, 508, 80-83 (2014)]. In the present paper, we show that the peak amplitude of the pulses can be considerably increased via joint adjustment of optical depth of the absorber and the initial phase of its vibration. This is due to reduction of the photoelectric absorption and maximizing the constructive temporal interference of spectral content of the single-photon wave packet in optically deep absorber. The ultimate capabilities for transforming a waveform of 14.4 keV photon from 57 Co radioactive source into a regular train of pulses in a harmonically vibrating 57 Fe recoilless resonant absorber are discussed. We show that the shortest pulse duration, produced by this technique, is limited by the highest available vibration frequency of a piezo-transducer and at present can be as short as 7.7 ps. The maximum achievable detection probability of the transformed photon at the experimentally feasible conditions is more than two times higher than peak detection probability of the photon emitted by the source and nearly 5.5 times higher than obtained in the above reference.

Acoustically induced transparency for synchrotron hard x-ray photons

“…As can be seen from Eqs. ( 10 ) and ( 11 ), the intensity, , of the outgoing single-photon field in the vibrating reference frame is also the intensity of the single-photon wave packet in the laboratory reference frame 6 , 19 , 30 , 31 , …”

Phase-sensitive nuclear target spectroscopy

“…Afterwards, the scattered light is transformed back to the laboratory frame. For a near-instantaneous δ(t )-like incident x-ray pulse as it is provided by a synchrotron radiation source, one finds for the response of the moving analyzer [44,45,50],…”

Observation of Acoustically Induced Transparency for γ -Ray Photons

“…However, the common tools for controlling quantum optical interfaces, such as intense spectrally narrow coherent sources and highfinesse cavities are still unavailable in hard x-ray/-ray range, preventing from a direct realization of the basic optical transparency techniques such as EIT and ATS-transparency, for high-energy photons. Several different techniques to control resonant interaction between hard x-ray/-ray photons and nuclear ensembles were developed, based on variation of hyperfine or external magnetic field [10,17,18], mechanical displacement (periodic or non-periodic) of an absorber or source with respect to each other including acoustic vibration [12,16,[19][20][21][22][23][24][25][26][27], and placing nuclei into a spatial sandwich-like nano-structure [11]. The 25% reduction in absorption of 14.4-keV photons was observed via anti-crossing of the upper energy sublevels of 57 Fe nuclei in a crystal of FeCO 3 taking place at 30 K [10].…”

“…The physical origin of AIT can be easily understood both in the laboratory reference frame and in the reference frame of the vibrating absorber ( In the vibrating reference frame, the spectrum of the incident single-photon wave packet is "seen" by nuclei as a comb of equidistant spectral components separated by the vibration frequency due to the Doppler effect ( Fig.2 red line, also see Supplemental Material) [12,22,26,27]. Amplitudes of the spectral components are proportional to Bessel functions of the first kind [12,22,26,27], (Fig.2). In the ideal case of monochromatic weak field and infinitely narrow spectral line of the absorber, the spectral sidebands are out of resonance and propagate through the medium without interaction with nuclei.…”