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Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system


The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems1,2,3, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting4,5,6,7,8 and superconducting9,10,11 systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter–light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators12. It has been suggested that an observation of the scaling of the resonant atom–photon coupling strength in the Jaynes–Cummings energy ladder13 with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature14. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom–field interaction in cavity QED. We explore atom–photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up15, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication16.

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Figure 1: Level diagram of a resonant ( νr = νge) cavity QED system.
Figure 2: Sample and experimental set-up.
Figure 3: Vacuum Rabi mode splitting with a single photon.
Figure 4: Vacuum Rabi mode splitting with two photons.
Figure 5: Experimental dressed state energy levels.


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

    Article  ADS  MathSciNet  Google Scholar 

  2. Mabuchi, H. & Doherty, A. C. Cavity quantum electrodynamics: Coherence in context. Science 298, 1372–1377 (2002)

    Article  ADS  CAS  Google Scholar 

  3. Walther, H., Varcoe, B. T. H., Englert, B.-G. & Becker, T. Cavity quantum electrodynamics. Rep. Prog. Phys. 69, 1325–1382 (2006)

    Article  ADS  Google Scholar 

  4. Reithmaier, J. P. et al. Strong coupling in a single quantum dot-semiconductor microcavity system. Nature 432, 197–200 (2004)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Peter, E. et al. Exciton-photon strong-coupling regime for a single quantum dot embedded in a microcavity. Phys. Rev. Lett. 95, 067401 (2005)

    Article  ADS  CAS  Google Scholar 

  7. Hennessy, K. et al. Quantum nature of a strongly coupled single quantum dot-cavity system. Nature 445, 896–899 (2007)

    Article  ADS  CAS  Google Scholar 

  8. Englund, D. et al. Controlling cavity reflectivity with a single quantum dot. Nature 450, 857–861 (2007)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  10. Chiorescu, I. et al. Coherent dynamics of a flux qubit coupled to a harmonic oscillator. Nature 431, 159–162 (2004)

    Article  ADS  CAS  Google Scholar 

  11. Johansson, J. et al. Vacuum Rabi oscillations in a macroscopic superconducting qubit LC oscillator system. Phys. Rev. Lett. 96, 127006 (2006)

    Article  ADS  CAS  Google Scholar 

  12. Zhu, Y. et al. Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations. Phys. Rev. Lett. 64, 2499–2502 (1990)

    Article  ADS  CAS  Google Scholar 

  13. Walls, D. & Milburn, G. Quantum Optics (Springer, Berlin, 1994)

    Book  Google Scholar 

  14. Carmichael, H. J., Kochan, P. & Sanders, B. C. Photon correlation spectroscopy. Phys. Rev. Lett. 77, 631–634 (1996)

    Article  ADS  CAS  Google Scholar 

  15. Blais, A., Huang, R. S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  16. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2000)

    MATH  Google Scholar 

  17. Thompson, R. J., Rempe, G. & Kimble, H. J. Observation of normal-mode splitting for an atom in an optical cavity. Phys. Rev. Lett. 68, 1132–1135 (1992)

    Article  ADS  CAS  Google Scholar 

  18. Boca, A. et al. Observation of the vacuum Rabi spectrum for one trapped atom. Phys. Rev. Lett. 93, 233603 (2004)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  20. Varcoe, B. T. H., Brattke, S., Weidinger, M. & Walther, H. Preparing pure photon number states of the radiation field. Nature 403, 743–746 (2000)

    Article  ADS  CAS  Google Scholar 

  21. Bertet, P. et al. Generating and probing a two-photon Fock state with a single atom in a cavity. Phys. Rev. Lett. 88, 143601 (2002)

    Article  ADS  CAS  Google Scholar 

  22. Thompson, R. J., Turchette, Q. A., Carnal, O. & Kimble, H. J. Nonlinear spectroscopy in the strong-coupling regime of cavity QED. Phys. Rev. A 57, 3084–3104 (1998)

    Article  ADS  CAS  Google Scholar 

  23. Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007)

    Article  ADS  CAS  Google Scholar 

  24. Guerlin, C. et al. Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889–893 (2007)

    Article  ADS  CAS  Google Scholar 

  25. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)

    Article  ADS  Google Scholar 

  26. Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502(R) (2008)

    Article  ADS  Google Scholar 

  27. Bouchiat, V., Vion, D., Joyez, P., Esteve, D. & Devoret, M. H. Quantum coherence with a single Cooper pair. Phys. Scripta T76, 165–170 (1998)

    Article  ADS  CAS  Google Scholar 

  28. Schuster, D. I. et al. AC Stark shift and dephasing of a superconducting qubit strongly coupled to a cavity field. Phys. Rev. Lett. 94, 123602 (2005)

    Article  ADS  CAS  Google Scholar 

  29. Schoelkopf, R. J. & Girvin, S. M. Wiring up quantum systems. Nature 451, 664–669 (2008)

    Article  ADS  CAS  Google Scholar 

  30. Schuster, I. et al. Nonlinear spectroscopy of photons bound to one atom. Nature Phys. 4, 382–385 (2008)

    Article  ADS  CAS  Google Scholar 

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We thank L. S. Bishop, J. M. Chow, T. Esslinger, L. Frunzio, A. Imamoğlu, B. R. Johnson, J. Koch, R. J. Schoelkopf and D. I. Schuster for discussions. This work was supported by SNF and ETHZ. P.J.L. was supported by the EU with an MC-EIF. A.B. was supported by NSERC, CIFAR and FQRNT.

Author Contributions J.M.F. performed the experiments and analysed the data using theory developed by A.B.; M.G. designed and fabricated the sample; M.B. contributed to sample characterization; R.B. contributed to the realization of the experimental set-up; and J.M.F. and A.W. co-wrote the paper. All authors discussed the results and commented on the manuscript. P.J.L. and A.W. supervised this work.

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Correspondence to J. M. Fink or A. Wallraff.

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Fink, J., Göppl, M., Baur, M. et al. Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system. Nature 454, 315–318 (2008).

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