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Observation of quantum state collapse and revival due to the single-photon Kerr effect


To create and manipulate non-classical states of light for quantum information protocols, a strong, nonlinear interaction at the single-photon level is required. One approach to the generation of suitable interactions is to couple photons to atoms, as in the strong coupling regime of cavity quantum electrodynamic systems1,2. In these systems, however, the quantum state of the light is only indirectly controlled by manipulating the atoms3. A direct photon–photon interaction occurs in so-called Kerr media, which typically induce only weak nonlinearity at the cost of significant loss. So far, it has not been possible to reach the single-photon Kerr regime, in which the interaction strength between individual photons exceeds the loss rate. Here, using a three-dimensional circuit quantum electrodynamic architecture4, we engineer an artificial Kerr medium that enters this regime and allows the observation of new quantum effects. We realize a gedanken experiment5 in which the collapse and revival of a coherent state can be observed. This time evolution is a consequence of the quantization of the light field in the cavity and the nonlinear interaction between individual photons. During the evolution, non-classical superpositions of coherent states (that is, multi-component ‘Schrödinger cat’ states) are formed. We visualize this evolution by measuring the Husimi Q function and confirm the non-classical properties of these transient states by cavity state tomography. The ability to create and manipulate superpositions of coherent states in such a high-quality-factor photon mode opens perspectives for combining the physics of continuous variables6 with superconducting circuits. The single-photon Kerr effect could be used in quantum non-demolition measurement of photons7, single-photon generation8, autonomous quantum feedback schemes9 and quantum logic operations10.

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Figure 1: Device layout and energy level diagram of the two-cavity, one-qubit device.
Figure 2: Technique for measuring the generalized Husimi Q functions.
Figure 3: Time evolution of Q 0 for a coherent state in the nonlinear cavity.
Figure 4: Wigner function of the multi-component cat states emerging during the Kerr interaction.


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We thank M. H. Devoret, M. D. Reed, M. Hatridge and A. Sears for discussions. This research was supported by the National Science Foundation (NSF) (PHY-0969725), the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) through the Army Research Office (W911NF-09-1-0369), and the US Army Research Office (W911NF-09-1-0514). Use of facilities was supported by the Yale Institute for Nanoscience and Quantum Engineering (YINQE) and the NSF (MRSECDMR 1119826). S.M.G. acknowledges support from the NSF (DMR-1004406). M.M. and Z.L. acknowledge support from French Agence Nationale de la Recherche under the project EPOQ2 (ANR-09-JCJC-0070). S.E.N. acknowledges support from the Swiss NSF. E.G. acknowledges support from EPSRC (EP/I026231/1).

Author information




G.K. and B.V. performed the experiments. G.K., B.V., Z.L. and M.M. analysed the data. G.K., B.V. and L.F. fabricated the qubits. G.K., B.V., H.P. and S.E.N. designed the device and calculated the device parameters. G.K., E.G., S.M.G. and R.J.S. conceived the experiment and all authors co-wrote the paper.

Corresponding author

Correspondence to R. J. Schoelkopf.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-5 and Supplementary References. (PDF 1186 kb)

Evolution of the Q function of a coherent state in a Kerr medium

This video shows the evolution of the Q function of a coherent state in a Kerr medium. The left frame shows the measured data while the right frame shows a simulation, which was obtained by numerically solving a master equation for the same interaction times. The total evolution was measured over 6.05µs, showing two coherent state revivals. (MOV 17414 kb)

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Kirchmair, G., Vlastakis, B., Leghtas, Z. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013).

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