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Coherent control of the waveforms of recoilless γ-ray photons

Abstract

The concepts and ideas of coherent, nonlinear and quantum optics have been extended to photon energies in the range of 10–100 kiloelectronvolts, corresponding to soft γ-ray radiation (the term used when the radiation is produced in nuclear transitions) or, equivalently, hard X-ray radiation (the term used when the radiation is produced by electron motion). The recent experimental achievements in this energy range include the demonstration of parametric down-conversion in the Langevin regime1, electromagnetically induced transparency in a cavity2, the collective Lamb shift3, vacuum-assisted generation of atomic coherences4 and single-photon revival in nuclear absorbing multilayer structures5. Also, realization of single-photon coherent storage6 and stimulated Raman adiabatic passage7 were recently proposed in this regime. More related work is discussed in a recent review8. However, the number of tools for the coherent manipulation of interactions between γ-ray photons and nuclear ensembles remains limited. Here we suggest and implement an efficient method to control the waveforms of γ-ray photons coherently. In particular, we demonstrate the conversion of individual recoilless γ-ray photons into a coherent, ultrashort pulse train and into a double pulse. Our method is based on the resonant interaction of γ-ray photons with an ensemble of nuclei with a resonant transition frequency that is periodically modulated in time. The frequency modulation, which is achieved by a uniform vibration of the resonant absorber, owing to the Doppler effect, renders resonant absorption and dispersion both time dependent, allowing us to shape the waveforms of the incident γ-ray photons. We expect that this technique will lead to advances in the emerging fields of coherent and quantum γ-ray photon optics, providing a basis for the realization of γ-ray-photon/nuclear-ensemble interfaces and quantum interference effects at nuclear γ-ray transitions.

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Figure 1: Energy scheme of emission and resonant absorption of a 14.4-keV photon.
Figure 2: Experimental set-up for γ-photon waveform control.
Figure 3: Shaping of γ-photon.
Figure 4: Pulses of Mössbauer radiation.

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Acknowledgements

We acknowledge the support from the US NSF (grant no. PHY-1307346), the RFBR (grants nos 13-02-00831 and 12-02-00263) and The Ministry of Education and Science of the Russian Federation (contract no. 11.G34.31.0011). V.A. acknowledges support from the Dynasty Foundation.

Author information

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Authors

Contributions

F.V. developed the experimental methods, designed the experiment and derived all the experimental results. V.A., Y.V.R. and R.N.S. developed the theoretical description. V.A. and F.V. determined the optimal parameters for the experiments and provided the theoretical fit to experimental data. Y.V.R. and F.V. suggested the technique for observing the single-photon waveforms. R.N.S. obtained analytical solutions for some limiting cases. O.K. suggested the idea, coordinated the efforts and wrote the paper. All authors discussed the results and edited the manuscript.

Corresponding author

Correspondence to Olga Kocharovskaya.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Time dependences of a γ-photon detection probability for different values of modulation index.

The values of modulation index are p = 0.8 (blue dashed line), p = 1.8 (red solid line) and p = 2.8 (green dashed line). All the other parameters are the same as in our experiment (Fig. 3).

Extended Data Figure 2 Time dependences of a γ-photon detection probability for different detunings of the central frequency of the source, ωr, from the resonance frequency of the absorber, ωa.

The values of detuning are ωr − ωa = 0.5Ω (blue dashed line), ωr − ωa = Ω (red solid line) and ωr − ωa = 2Ω (green dashed line). All the other parameters are the same as in our experiment (Fig. 3).

Extended Data Figure 3 Variation of the waveform of a 14.4-keV γ-photon with a change in the vibration phase, , at the moment of detection of the preceding 122-keV γ-photon.

The parameter values are the same as in Fig. 3c, corresponding to double-pulse formation, except for the initial phases of vibration, which are as follows: , the same as in Fig. 3c (red solid line), (blue dashed line), (the same as in the inset of Fig. 3c (green dashed line)) and (cyan dashed line).

Extended Data Figure 4 Waveforms of 14.4-keV γ-photons produced at different frequencies of vibration, Ω.

The parameter values are the same as in Fig. 3c, corresponding to double-pulse (time-bin qubit) formation, except for the vibration frequencies, which are as follows: Ω/2π = 1.3 MHz (green dashed line), Ω/2π = 2.6 MHz (the same as in Fig. 3c (red solid line)) and Ω/2π = 5.2 MHz (blue dashed line).

Extended Data Figure 5 Count rate of 14.4-keV photons versus time for the case of Fig. 4.

The blue dots centred at the confidence intervals correspond to the experimental data, and the red and green solid curves are plotted according to equations (13) and (14) and, respectively, equation (15).

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Vagizov, F., Antonov, V., Radeonychev, Y. et al. Coherent control of the waveforms of recoilless γ-ray photons. Nature 508, 80–83 (2014). https://doi.org/10.1038/nature13018

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