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

Abstract

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.

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Acknowledgements

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). https://doi.org/10.1038/nature07112

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