Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED

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Abstract

Superconducting qubits1,2 behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multiphoton excitations3,4,5,6,7 occupies an important role. Moreover, coupling superconducting qubits to onchip microwave resonators has given rise to the field of circuit quantum electrodynamics8,9,10,11,12,13,14,15 (QED). In contrast to quantum-optical cavity QED (refs 16, 17, 18, 19), circuit QED offers the tunability inherent to solid-state circuits. Here, we report on the observation of key signatures of a two-photon-driven Jaynes–Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit20 coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one- and two-photon-driven level anticrossings of the qubit–resonator system. This results from the controlled symmetry breaking of the system hamiltonian, causing parity to become a not-well-defined property21. Our study provides fundamental insight into the interplay of multiphoton processes and symmetries in a qubit–resonator system.

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Figure 1: Experimental architecture and theoretical model.
Figure 2: Qubit microwave spectroscopy: data and simulations.
Figure 3: Qubit microwave spectroscopy close to the qubit–resonator anticrossing under two-photon driving: data and simulations.
Figure 4: Two-photon spectroscopy simulations close to the optimal point using the time-trace-averaging method.

References

  1. 1

    Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

  2. 2

    Wendin, G. & Shumeiko, V. S. in Handbook of Theoretical and Computational Nanotechnology Vol. 3 (eds Rieth, M. & Schommers, W.) 223–309 (American Scientific Publishers, Los Angeles, 2006).

  3. 3

    Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Rabi oscillations in a Josephson-junction charge two-level system. Phys. Rev. Lett. 87, 246601 (2001).

  4. 4

    Oliver, W. D. et al. Mach–Zehnder interferometry in a strongly driven superconducting qubit. Science 310, 1653–1657 (2005).

  5. 5

    Saito, S. et al. Parametric control of a superconducting flux qubit. Phys. Rev. Lett. 96, 107001 (2006).

  6. 6

    Sillanpää, M., Lehtinen, T., Paila, A., Makhlin, Y. & Hakonen, P. J. Continuous-time monitoring of Landau–Zener interference in a Cooper-pair box. Phys. Rev. Lett. 96, 187002 (2006).

  7. 7

    Wilson, C. M. et al. Coherence times of dressed states of a superconducting qubit under extreme driving. Phys. Rev. Lett. 98, 257003 (2007).

  8. 8

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

  9. 9

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

  10. 10

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

  11. 11

    Houck, A. A. et al. Generating single microwave photons in a circuit. Nature 449, 328–331 (2007).

  12. 12

    Astafiev, O. et al. Single artificial-atom lasing. Nature 449, 588–590 (2007).

  13. 13

    Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007).

  14. 14

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

  15. 15

    Wallraff, A. et al. Sideband transitions and two-tone spectroscopy of a superconducting qubit strongly coupled to an on-chip cavity. Phys. Rev. Lett. 99, 050501 (2007).

  16. 16

    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).

  17. 17

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

  18. 18

    Haroche, S. & Raimond, J.-M. Exploring the Quantum (Oxford Univ. Press, New York, 2006).

  19. 19

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

  20. 20

    Orlando, T. P. et al. Superconducting persistent-current qubit. Phys. Rev. B 60, 15398–15413 (1999).

  21. 21

    Liu, Y-X, You, J. Q., Wei, L. F., Sun, C. P. & Nori, F. Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit. Phys. Rev. Lett. 95, 087001 (2005).

  22. 22

    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).

  23. 23

    Simmonds, R. W. et al. Decoherence in Josephson phase qubits from junction resonators. Phys. Rev. Lett. 93, 077003 (2004).

  24. 24

    Deppe, F. et al. Phase coherent dynamics of a superconducting flux qubit with capacitive bias readout. Phys. Rev. B 76, 214503 (2007).

  25. 25

    Kakuyanagi, K. et al. Dephasing of a superconducting flux qubit. Phys. Rev. Lett. 98, 047004 (2007).

  26. 26

    Mariantoni, M. et al. On-chip microwave Fock states and quantum homodyne measurements. Preprint at <http://arxiv.org/abs/cond-mat/0509737> (2005).

  27. 27

    Liu, Y-X, Wei, L. F. & Nori, F. Generation of non-classical photon states using a superconducting qubit in a microcavity. Europhys. Lett. 67, 941–947 (2004).

  28. 28

    Moon, K. & Girvin, S. M. Theory of microwave parametric down-conversion and squeezing using circuit QED. Phys. Rev. Lett. 95, 140504 (2005).

  29. 29

    Cohen-Tannoudji, C., Diu, B. & Laloë, F. Quantum Mechanics (Wiley–Interscience, New York, 1977).

  30. 30

    Buckel, W. & Kleiner, R. Superconductivity (Wiley–VCH, Berlin, 2004).

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Acknowledgements

We thank H. Christ for fruitful discussions. This work is supported by the Deutsche Forschungsgesellschaft through the Sonderforschungsbereich 631. Financial support by the Excellence Cluster ‘Nanosystems Initiative Munich (NIM)’, the EuroSQIP EU project, the Ikerbasque Foundation and UPV-EHU Grant GIU07/40 is gratefully acknowledged. This work is partially supported by CREST-JST, JSPS-KAKENHI(18201018) and MEXT-KAKENHI(18001002).

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Correspondence to Frank Deppe.

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Deppe, F., Mariantoni, M., Menzel, E. et al. Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED. Nature Phys 4, 686–691 (2008) doi:10.1038/nphys1016

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