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Resolving photon number states in a superconducting circuit


Electromagnetic signals are always composed of photons, although in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting quantum bit (qubit) to signals on a microwave transmission line, it is possible to construct an integrated circuit in which the presence or absence of even a single photon can have a dramatic effect. Such a system1 can be described by circuit quantum electrodynamics (QED)—the circuit equivalent of cavity QED, where photons interact with atoms or quantum dots. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit could absorb and re-emit a single photon many times2. Here we report a circuit QED experiment in the strong dispersive limit, a new regime where a single photon has a large effect on the qubit without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition energy can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability of finding the corresponding photon number in the cavity. This effect is used to distinguish between coherent and thermal fields, and could be used to create a photon statistics analyser. As no photons are absorbed by this process, it should be possible to generate non-classical states of light by measurement and perform qubit–photon conditional logic, the basis of a logic bus for a quantum computer.

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Figure 1: A parameter space diagram for cavity QED.
Figure 2: A Cooper pair box inside a cavity, and spectral features of the circuit QED system.
Figure 3: Direct spectroscopic observation of quantized cavity photon number.
Figure 4: Qubit spectrum distinguishes between coherent and thermal distributions.

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  1. Blais, A., Huang, R., Wallraff, A., Girvin, S. & 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 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  4. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, Berlin, 2006)

    MATH  Google Scholar 

  5. Purcell, E. M. Spontaneous emission probabilities at radio frequencies. Phys. Rev. 69, 681 (1946)

    Article  Google Scholar 

  6. 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  CAS  Google Scholar 

  7. 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 

  8. Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996)

    Article  ADS  CAS  Google Scholar 

  9. Leibfried, D. et al. Experimental preparation and measurement of quantum states of motion of a trapped atom. J. Mod. Opt. 44, 2485–2505 (1997)

    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. 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 

  13. 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 

  14. Grangier, P., Levenson, J. A. & Poizat, J. P. Quantum non-demolition measurements in optics. Nature 396, 537–542 (1998)

    Article  ADS  CAS  Google Scholar 

  15. Caves, C. M., Thorne, K. S., Drever, R. W. P., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. Rev. Mod. Phys. 52, 341–392 (1980)

    Article  ADS  Google Scholar 

  16. Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)

    Article  ADS  CAS  Google Scholar 

  17. Brune, M. et al. From Lamb shift to light shifts: vacuum and subphoton cavity fields measured by atomic phase-sensitive detection. Phys. Rev. Lett. 72, 3339–3342 (1994)

    Article  ADS  CAS  Google Scholar 

  18. 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 

  19. Brune, M., Haroche, S., Lefevre, V., Raimond, J. M. & Zagury, N. Quantum nondemolition measurement of small photon numbers by Rydberg-atom phase-sensitive detection. Phys. Rev. Lett. 65, 976–979 (1990)

    Article  ADS  CAS  Google Scholar 

  20. 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 

  21. Nogues, G. et al. Seeing a single photon without destroying it. Nature 400, 239–242 (1999)

    Article  ADS  CAS  Google Scholar 

  22. Bertet, P. et al. Direct measurement of the Winger function of a one-photon Fock state in a cavity. Phys. Rev. Lett. 89, 200402 (2002)

    Article  ADS  CAS  Google Scholar 

  23. 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 

  24. Gambetta, J. et al. Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006)

    Article  ADS  Google Scholar 

  25. Irish, E. K. & Schwab, K. Quantum measurement of a coupled nanomechanical resonator-Cooper pair box system. Phys. Rev. B 68, 155311 (2003)

    Article  ADS  Google Scholar 

  26. Dykman, M. I. & Krivoglaz, M. A. Profiles of no-phonon lines of impurity centers interacting with local quasilocal vibrations. Sov. Phys. Solid State 29, 210–214 (1987)

    Google Scholar 

  27. Siddiqi, I. et al. Dispersive measurements of superconducting qubit coherence with a fast latching readout. Phys. Rev. B 73, 054510 (2006)

    Article  ADS  Google Scholar 

  28. Peil, S. & Gabrielse, G. Observing the quantum limit of an electron cyclotron: QND measurements of quantum jumps between Fock states. Phys. Rev. Lett. 83, 1287–1290 (1999)

    Article  ADS  CAS  Google Scholar 

  29. Ottl, A., Ritter, S., Kohl, M. & Esslinger, T. Correlations and counting statistics of an atom laser. Phys. Rev. Lett. 95, 090404 (2005)

    Article  ADS  Google Scholar 

  30. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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This work was supported in part by the National Security Agency under the Army Research Office, the NSF, the W. M. Keck Foundation and Yale University. A.A.H. acknowledges support from Yale University via a Quantum Information and Mesoscopic Physics Fellowship. A.B. was supported by NSERC, CIAR and FQRNT. Numerical simulations were performed on a RQCHP cluster.

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Correspondence to R. J. Schoelkopf.

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Schuster, D., Houck, A., Schreier, J. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

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