# Rabi oscillations of X-ray radiation between two nuclear ensembles

## Abstract

The realization of the strong coupling regime between a single cavity mode and an electromagnetic resonance is a centrepiece of quantum optics. In this regime, the reversible exchange of a photon between the two components of the system leads to so-called Rabi oscillations. Strong coupling is used in the optical and infrared regimes, for instance, to produce non-classical states of light, enhance optical nonlinearities and control quantum states. Here, we report the first observation of Rabi oscillations of an X-ray photon between two resonant 57Fe layers embedded in two coupled cavities. The system is described by an effective Hamiltonian, in which the two layers couple strongly. We observe sinusoidal beating as the signature of the Rabi oscillations in the system’s temporal evolution, as well as the splitting of nuclear resonances in the reflected light spectrum. Our results significantly advance the development of the new field of X-ray quantum optics.

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## References

1. 1.

Vagizov, F., Antonov, V., Radeonychev, Y. V., Shakhmuratov, R. N. & Kocharovskaya, O. Coherent control of the waveforms of recoilless γ-ray photons. Nature 508, 80–83 (2014).

2. 2.

Liao, W.-T., Pálffy, A. & Keitel, C. H. Coherent storage and phase modulation of single hard-X-ray photons using nuclear excitons. Phys. Rev. Lett. 109, 197403 (2012).

3. 3.

Kong, X. & Pálffy, A. Stopping narrow-band X-ray pulses in nuclear media. Phys. Rev. Lett. 116, 197402 (2016).

4. 4.

Gunst, J., Keitel, C. H. & Pálffy, A. Logical operations with single X-ray photons via dynamically-controlled nuclear resonances. Sci. Rep. 6, 25136 (2016).

5. 5.

Liao, W.-T. & Pálffy, A. Optomechanically induced transparency of X-rays via optical control. Sci. Rep. 7, 321 (2017).

6. 6.

Röhlsberger, R., Schlage, K., Sahoo, B., Couet, S. & Rüffer, R. Collective Lamb shift in single photon superradiance. Science 328, 1248–1251 (2010).

7. 7.

Röhlsberger, R., Wille, H., Schlage, K. & Sahoo, B. Electromagnetically induced transparency with resonant nuclei in a cavity. Nature 482, 199–203 (2011).

8. 8.

Heeg, K. P. et al. Vacuum-assisted generation and control of atomic coherences at X-ray energies. Phys. Rev. Lett. 111, 073601 (2013).

9. 9.

Heeg, K. P. et al. Interferometric phase detection at X-ray energies via Fano resonance control. Phys. Rev. Lett. 114, 207401 (2015).

10. 10.

Heeg, K. P. et al. Tunable subluminal propagation of narrow-band X-ray pulses. Phys. Rev. Lett. 114, 203601 (2015).

11. 11.

Heeg, K. P. et al. Spectral narrowing of X-ray pulses for precision spectroscopy with nuclear resonances. Science 357, 375–378 (2017).

12. 12.

Raimond, J. M., Brune, M. & Haroche, S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001).

13. 13.

Weisbuch, C., Nishioka, M., Ishikawa, A. & Arakawa, Y. Observation of the coupled exciton–photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 69, 3314–3317 (1992).

14. 14.

Brune, M. et al. Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800–1803 (1996).

15. 15.

Raizen, M. G., Thompson, R. J., Brecha, R. J., Kimble, H. J. & Carmichael, H. J. Normal-mode splitting and linewidth averaging for two-state atoms in an optical cavity. Phys. Rev. Lett. 63, 240–243 (1989).

16. 16.

Saba, M. et al. High-temperature ultrafast polariton parametric amplification in semiconductor microcavities. Nature 414, 731–735 (2001).

17. 17.

Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

18. 18.

Haber, J. et al. Collective strong coupling of X-rays and nuclei in a nuclear optical lattice. Nat. Photon. 10, 445–449 (2016).

19. 19.

Baumann, K., Guerlin, C., Brennecke, F. & Esslinger, T. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

20. 20.

Majer, J. et al. Coupling superconduction circuits via a cavity bus. Nature 449, 443–447 (2007).

21. 21.

Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).

22. 22.

Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

23. 23.

Bloch, I., Dalibard, J. & Nascimbene, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

24. 24.

Sahoo, B. et al. Preparation and characterization of ultrathin stainless steel films. AIP Conf. Proc. 1347, 57–60 (2011).

25. 25.

Heeg, K. P. & Evers, J. X-ray quantum optics with Mössbauer nuclei embedded in thin-film cavities. Phys. Rev. A 88, 043828 (2013).

26. 26.

Heeg, K. P. & Evers, J. Collective effects between multiple nuclear ensembles in an X-ray cavity–QED setup. Phys. Rev. A 91, 063803 (2015).

27. 27.

Dudin, Y., Li, L., Bariani, F. & Kuzmich, A. Observation of coherent many-body Rabi oscillations. Nat. Phys. 8, 790–794 (2012).

28. 28.

Yoshie, T. et al. Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity. Nature 432, 200–203 (2004).

29. 29.

Khitrova, G., Gibbs, H., Kira, M., Koch, S. W. & Scherer, A. Vacuum Rabi splitting in semiconductors. Nat. Phys. 2, 81–90 (2006).

30. 30.

Kanter, E. P. et al. Unveiling and driving hidden resonances with high-fluence, high-intensity X-ray pulses. Phys. Rev. Lett. 107, 233001 (2011).

31. 31.

Doumy, G. et al. Nonlinear atomic response to intense ultrashort X rays. Phys. Rev. Lett. 106, 083002 (2011).

32. 32.

Glover, T. et al. X-ray and optical wave mixing. Nature 488, 603–608 (2012).

33. 33.

Rohringer, N. et al. Atomic inner-shell X-ray laser at 1.46 nanometres pumped by an X-ray free-electron laser. Nature 481, 488–491 (2012).

34. 34.

Fuchs, M. et al. Anomalous nonlinear X-ray Compton scattering. Nat. Phys. 11, 964–970 (2015).

35. 35.

Prince, K. et al. Coherent control with a short-wavelength free-electron laser. Nat. Photon. 10, 176–179 (2016).

36. 36.

van Bürck, U. Coherent pulse propagation through resonant media. Hyperfine. Interact. 123, 483–509 (1999).

37. 37.

Kagan, Y., Afanas’ev, A. M. & Kohn, V. G. On excitation of isomeric nuclear states in a crystal by synchrotron radiation. J. Phys. C 12, 615 (1979).

## Acknowledgements

J.H., C.S., L.B. and R.Rö. acknowledge the support of the Helmholtz Association through project-oriented funds. X.K. acknowledges financial support from the China Scholarship Council. X.K. and A.P. are part of and were supported by the DFG Collaborative Research Centre SFB 1225 (ISOQUANT). S.W. acknowledges funding by the Joachim Herz Foundation. The authors thank K. Heeg and J. Evers for helpful discussions.

## Author information

Authors

### Contributions

X.K. and A.P. proposed the experiment. J.H. and R.Rö. devised the experimental concept and designed the set-up. J.H. and S.W. fabricated the sample. C.S., J.G., L.B., J.H., R.Rü. and R.Rö. performed the experiment. J.H. performed the data analysis. J.H., X.K., A.P. and R.Rö. wrote the paper. All authors participated in discussing the results.

### Corresponding authors

Correspondence to Adriana Pálffy or Ralf Röhlsberger.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

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Reprints and Permissions

Haber, J., Kong, X., Strohm, C. et al. Rabi oscillations of X-ray radiation between two nuclear ensembles. Nature Photon 11, 720–725 (2017). https://doi.org/10.1038/s41566-017-0013-3

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