Abstract
The violation of Bell inequalities with two entangled and spatially separated quantum two-level systems (TLSs) is often considered as the most prominent demonstration that nature does not obey local realism. Under different but related assumptions of macrorealism—which macroscopic systems plausibly fulfil—Leggett and Garg derived a similar inequality for a single degree of freedom undergoing coherent oscillations and being measured at successive times. Here, we test such a ‘Bell’s inequality in time’, which should be violated by a quantum TLS. Our TLS is a superconducting quantum circuit in which Rabi oscillations are continuously driven while it is continuously and weakly measured. The time correlations present at the detector output agree with quantum-mechanical predictions and violate the Leggett–Garg inequality by five standard deviations.
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References
Bell, J. S. On the Einstein Podolvski Rosen paradox. Physics (N.Y.) 1, 195–200 (1965).
Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).
Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein–Podolsky–Rosen–Bohm gedanken experiment: A new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982).
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
Leggett, A. J. & Garg, A. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54, 857–860 (1985).
Ruskov, R., Korotkov, A. N. & Mizel, A. Signatures of quantum behavior in single-qubit weak measurements. Phys. Rev. Lett. 96, 200404 (2006).
Goggin, M. E. et al. Violation of the Leggett–Garg inequality with weak measurement of photons. Preprint at http://arxiv.org/abs/0907.1679 (2009).
Xu, J. S., Li, C. F., Zou, X. B. & Guo, G. C. Experimentally identifying the transition from quantum to classical with Leggett–Garg inequalities. Preprint at http://arxiv.org/abs/0907.0176 (2009).
Korotkov, A. N. & Averin, D. V. Continuous weak measurement of quantum coherent oscillations. Phys. Rev. B 64, 165310 (2001).
Ruskov, R. & Korotkov, A. N. Quantum feedback control of a solid-state qubit. Phys. Rev. B 66, 041401 (2002).
Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009).
Chow, J. M. et al. Entanglement metrology using a joint readout of superconducting qubits. Preprint at http://arxiv.org/abs/0908.1955 (2009).
Blais, A., Huang, R., 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).
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).
Leggett, A. J. Testing the limits of quantum mechanics: Motivation, state of play, prospects. J. Phys. Condens. Matter 14, R415–R451 (2002).
Leggett, A. J. Realism and the physical world. Rep. Prog. Phys. 71, 022001-6 (2008).
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502 (2008).
Gambetta, J. et al. Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect. Phys. Rev. A 77, 012112 (2008).
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 (2004).
Misra, B. & Sudarshan, E. C. G. The Zeno’s paradox in quantum theory. J. Math. Phys. Sci. 18, 756–763 (1977).
Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).
Bernu, J. et al. Freezing coherent field growth in a cavity by the quantum Zeno effect. Phys. Rev. Lett. 101, 180402 (2008).
Goan, H. S. & Milburn, G. J. Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement. Phys. Rev. B 64, 235307 (2001).
Shnirman, A., Mozyrsky, D. & Martin, I. Output spectrum of a measuring device at arbitrary voltage and temperature. Europhys. Lett. 67, 840–846 (2004).
Torrey, H. C. Transient nutations in nuclear magnetic resonance. Phys. Rev. 76, 1059–1068 (1947).
Il’ichev, E. et al. Continuous monitoring of Rabi oscillations in a Josephson flux qubit. Phys. Rev. Lett. 91, 097906 (2003).
Deblock, R., Onac, E., Gurevich, L. & Kouwenhoven, L. P. Detection of quantum noise from an electrically driven two-level system. Science 301, 203–206 (2003).
Manassen, Y., Hamers, R. J., Demuth, J. E. & Castellano, A. J. Jr Direct observation of the precession of individual paramagnetic spins on oxidized silicon surfaces. Phys. Rev. Lett. 62, 2531–2534 (1989).
Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008).
Bergeal, N. et al. Analog information processing at the quantum limit with a Josephson ring modulator. Nature Phys. 6, 296–302 (2010).
Acknowledgements
We acknowledge financial support from European projects EuroSQIP and SCOPE, and from ANR project Quantjo and C’Nano Ile-de-France for the nanofabrication facility at SPEC. We thank P. Sénat, P. Orfila, J-C. Tack and D. Bouville for technical support, and acknowledge useful discussions within the Quantronics group and with A. Lupascu, A. Wallraff, M. Devoret and R. Ruskov.
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A.N.K., P.B. and A.P-L. did the theoretical work, A.P-L., F.M., P.B., D.V. and D.E. designed the experiment, A.P-L. fabricated the sample, A.P-L., F.M., P.B. and F.N. carried out the measurements, A.P-L., F.M., D.V. and P.B. analysed the data, and all of the authors contributed to the writing of the manuscript.
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Palacios-Laloy, A., Mallet, F., Nguyen, F. et al. Experimental violation of a Bell’s inequality in time with weak measurement. Nature Phys 6, 442–447 (2010). https://doi.org/10.1038/nphys1641
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DOI: https://doi.org/10.1038/nphys1641
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