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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)
Haroche, S. & Raimond, J. M. Exploring the Quantum: Atoms, Cavities, And Photons (Oxford Univ. Press, 2006)
Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009)
Paik, H. et al. Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011)
Yurke, B. & Stoler, D. The dynamic generation of Schrodinger cats and their detection. Physica B+C 151, 298–301 (1988)
Braunstein, S. L. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005)
Grangier, P., Levenson, J. & Poizat, J. Quantum non-demolition measurements in optics. Nature 396, 537–542 (1998)
Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012)
Kerckhoff, J., Nurdin, H., Pavlichin, D. S. & Mabuchi, H. Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys. Rev. Lett. 105, 040502 (2010)
Milburn, G. Quantum optical Fredkin gate. Phys. Rev. Lett. 62, 2124–2127 (1989)
Saleh, B. E. A. & Teich, M. C. Fundamentals of Photonics (Wiley Series in Pure and Applied Optics, 1991)
Slusher, R. E., Hollberg, L., Yurke, B., Mertz, J. & Valley, J. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett. 55, 2409–2412 (1985)
Franken, P., Hill, A., Peters, C. & Weinreich, G. Generation of optical harmonics. Phys. Rev. Lett. 7, 118–119 (1961)
Fisher, R. A., Kelley, P. L. & Gustafson, T. K. Subpicosecond pulse generation using the optical Kerr effect. Appl. Phys. Lett. 14, 140–143 (1969)
Nigg, S. E. et al. Black-box superconducting circuit quantization. Phys. Rev. Lett. 108, 240502 (2012)
Bourassa, J., Beaudoin, F., Gambetta, J. M. & Blais, A. Josephson-junction-embedded transmissionline resonators: from Kerr medium to in-line transmon. Phys. Rev. A 86, 013814 (2012)
Bergeal, N. et al. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature 465, 64–68 (2010)
Yurke, B. et al. Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier. Phys. Rev. Lett. 60, 764–767 (1988)
Yin, Y. et al. Dynamic quantum Kerr effect in circuit quantum electrodynamics. Phys. Rev. A 85, 023826 (2012)
Hoffman, A. et al. Dispersive photon blockade in a superconducting circuit. Phys. Rev. Lett. 107, 053602 (2011)
Shalibo, Y. et al. Direct Wigner tomography of a superconducting anharmonic oscillator. Preprint at http://arXiv.org/abs/1208.2441 (2012)
Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett. 76, 1796–1799 (1996)
Greiner, M., Mandel, O., Hänsch, T. W. & Bloch, I. Collapse and revival of the matter wave field of a Bose-Einstein condensate. Nature 419, 51–54 (2002)
Johnson, B. R. et al. Quantum non-demolition detection of single microwave photons in a circuit. Nature Phys. 6, 663–667 (2010)
Solano, E. Selective interactions in trapped ions: state reconstruction and quantum logic. Phys. Rev. A 71, 013813 (2005)
Milburn, G. Quantum and classical Liouville dynamics of the anharmonic-oscillator. Phys. Rev. A 33, 674–685 (1986)
Deléglise, S. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008)
Eichler, C., Bozyigit, D. & Wallraff, A. Characterizing quantum microwave radiation and its entanglement with superconducting qubits using linear detectors. Phys. Rev. A 86, 032106 (2012)
Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996)
Leghtas, Z. et al. Hardware-efficient autonomous quantum error correction. Preprint at http://arXiv.org/abs/1207.0679 (2012)
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).
The authors declare no competing financial interests.
This file contains Supplementary Text and Data, Supplementary Figures 1-5 and Supplementary References. (PDF 1186 kb)
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)
About this article
Cite this article
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). https://doi.org/10.1038/nature11902
Nature Physics (2020)
npj Quantum Information (2020)
Nature Physics (2020)