Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Deterministic creation of entangled atom–light Schrödinger-cat states

Abstract

Quantum physics allows for entanglement between microscopic and macroscopic objects, described by discrete and continuous variables, respectively. As in Schrödinger’s famous cat gedanken experiment, a box enclosing the objects can keep the entanglement alive. For applications in quantum information processing, however, it is essential to access the objects and manipulate them with suitable quantum tools. Here we reach this goal and deterministically generate entangled light–matter states by reflecting a coherent light pulse with up to four photons on average from an optical cavity containing one atom. The quantum light propagates freely and reaches a remote receiver for quantum state tomography. We produce a plethora of quantum states and observe negative-valued Wigner functions, a characteristic sign of non-classicality. As a first application, we demonstrate a quantum-logic gate between an atom and a light pulse, with the photonic qubit encoded in the phase of the light field.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Experimental set-up.
Fig. 2: Cat state generation protocol and Wigner functions of experimentally measured cat states.
Fig. 3: Non-classical properties of measured cat states.
Fig. 4: Control over cat state degrees of freedom.
Fig. 5: Entanglement between atom and cat state.
Fig. 6: Truth table of the atom–cat gate.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Schrödinger, E. Die gegenwärtige situation in der Quantenmechanik. Naturwissenschaften 23, 807–812 (1935).

    Article  ADS  Google Scholar 

  2. Glancy, S. & Vasconcelos, H. Md Methods for producing optical coherent state superpositions. J. Opt. Soc. Am. B 25, 712–733 (2008).

    Article  ADS  Google Scholar 

  3. Wineland, D. J. Nobel lecture: superposition, entanglement, and raising Schrödinger’s cat. Rev. Mod. Phys. 85, 1103–1114 (2013).

    Article  ADS  Google Scholar 

  4. Kienzler, D. et al. Observation of quantum interference between separated mechanical oscillator wave packets. Phys. Rev. Lett. 116, 140402 (2016).

    Article  ADS  Google Scholar 

  5. Deleglise, S. et al. Reconstruction of non-classical cavity field states with snapshots of their decoherence. Nature 455, 510–514 (2008).

    Article  ADS  Google Scholar 

  6. Haroche, S. Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083–1102 (2013).

    Article  ADS  Google Scholar 

  7. Vlastakis, B. et al. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 342, 607–610 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  8. Pfaff, W. et al. Controlled release of multiphoton quantum states from a microwave cavity memory. Nat. Phys. 13, 882–887 (2017).

    Article  Google Scholar 

  9. Morin, O. et al. Remote creation of hybrid entanglement between particle-like and wave-like optical qubits. Nat. Photon. 8, 570–574 (2014).

    Article  ADS  Google Scholar 

  10. Jeong, H. et al. Generation of hybrid entanglement of light. Nat. Photon. 8, 564–569 (2014).

    Article  ADS  Google Scholar 

  11. Ulanov, A. E., Sychev, D., Pushkina, A. A., Fedorov, I. A. & Lvovsky, A. I. Quantum teleportation between discrete and continuous encodings of an optical qubit. Phys. Rev. Lett. 118, 160501 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  12. Jeannic, H. L., Cavaillès, A., Raskop, J., Huang, K. & Laurat, J. Remote preparation of continuous-variable qubits using loss-tolerant hybrid entanglement of light. Optica 5, 1012–1015 (2018).

    Article  Google Scholar 

  13. Ourjoumtsev, A., Tualle-Brouri, R., Laurat, J. & Grangier, P. Generating optical Schrödinger kittens for quantum information processing. Science 312, 83–86 (2006).

    Article  ADS  Google Scholar 

  14. Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R. & Grangier, P. Generation of optical ‘Schrödinger cats’ from photon number states. Nature 448, 784–796 (2007).

    Article  ADS  Google Scholar 

  15. Neergaard-Nielsen, J. S., Nielsen, B. M., Hettich, C., Mølmer, K. & Polzik, E. S. Generation of a superposition of odd photon number states for quantum information networks. Phys. Rev. Lett. 97, 083604 (2006).

    Article  ADS  Google Scholar 

  16. Takahashi, H. et al. Generation of large-amplitude coherent-state superposition via ancilla-assisted photon subtraction. Phys. Rev. Lett. 101, 233605 (2008).

    Article  ADS  Google Scholar 

  17. Lvovsky, A. I. & Raymer, M. G. Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81, 299–332 (2009).

    Article  ADS  Google Scholar 

  18. Namekata, N. et al. Non-Gaussian operation based on photon subtraction using a photon-number-resolving detector at a telecommunications wavelength. Nat. Photon. 4, 655–660 (2010).

    Article  ADS  Google Scholar 

  19. Gerrits, T. et al. Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum. Phys. Rev. A 82, 031802 (2010).

    Article  ADS  Google Scholar 

  20. Yoshikawa, J.-i, Makino, K., Kurata, S., van Loock, P. & Furusawa, A. Creation, storage, and on-demand release of optical quantum states with a negative Wigner function. Phys. Rev. X 3, 041028 (2013).

    Google Scholar 

  21. Wang, B. & Duan, L.-M. Engineering superpositions of coherent states in coherent optical pulses through cavity-assisted interaction. Phys. Rev. A 72, 022320 (2005).

    Article  ADS  Google Scholar 

  22. Ralph, T. C., Gilchrist, A., Milburn, G. J., Munro, W. J. & Glancy, S. Quantum computation with optical coherent states. Phys. Rev. A 68, 042319 (2003).

    Article  ADS  Google Scholar 

  23. Gilchrist, A. et al. Schrödinger cats and their power for quantum information processing. J. Opt. B 6, S828–S833 (2004).

    Article  Google Scholar 

  24. Cochrane, P. T., Milburn, G. J. & Munro, W. J. Macroscopically distinct quantum-superposition states as a bosonic code for amplitude damping. Phys. Rev. A 59, 2631–2634 (1999).

    Article  ADS  Google Scholar 

  25. Leghtas, Z. et al. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett. 111, 120501 (2013).

    Article  ADS  Google Scholar 

  26. Bergmann, M. & van Loock, P. Quantum error correction against photon loss using multicomponent cat states. Phys. Rev. A 94, 042332 (2016).

    Article  ADS  Google Scholar 

  27. Lund, A. P., Ralph, T. C. & Haselgrove, H. L. Fault-tolerant linear optical quantum computing with small-amplitude coherent states. Phys. Rev. Lett. 100, 030503 (2008).

    Article  ADS  Google Scholar 

  28. Duan, L.-M. & Kimble, H. J. Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92, 127902 (2004).

    Article  ADS  Google Scholar 

  29. Reiserer, A. & Rempe, G. Cavity-based quantum networks with single atoms and optical photons. Rev. Mod. Phys. 87, 1379–1418 (2015).

    Article  ADS  Google Scholar 

  30. Jeong, H. & Kim, M. S. Efficient quantum computation using coherent states. Phys. Rev. A 65, 042305 (2002).

    Article  ADS  Google Scholar 

  31. Schleich, W., Pernigo, M. & Kien, F. L. Nonclassical state from two pseudoclassical states. Phys. Rev. A 44, 2172–2187 (1991).

    Article  ADS  Google Scholar 

  32. D’Ariano, G. M., Leonhardt, U. & Paul, H. Homodyne detection of the density matrix of the radiation field. Phys. Rev. A 52, R1801–R1804 (1995).

    Article  ADS  Google Scholar 

  33. Bužek, V., Vidiella-Barranco, A. & Knight, P. L. Superpositions of coherent states: squeezing and dissipation. Phys. Rev. A 45, 6570–6585 (1992).

    Article  ADS  Google Scholar 

  34. Spagnolo, N., Vitelli, C., De Angelis, T., Sciarrino, F. & De Martini, F. Wigner-function theory and decoherence of the quantum-injected optical parametric amplifier. Phys. Rev. A 80, 032318 (2009).

    Article  ADS  Google Scholar 

  35. Vlastakis, B. et al. Characterizing entanglement of an artificial atom and a cavity cat state with Bell’s inequality. Nat. Commun. 6, 8970 (2015).

    Article  Google Scholar 

  36. Vidal, G. & Werner, R. F. Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002).

    Article  ADS  Google Scholar 

  37. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).

  38. Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

    Article  ADS  Google Scholar 

  39. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    Article  ADS  Google Scholar 

  40. Teo, C. et al. Realistic loophole-free Bell test with atom–photon entanglement. Nat. Commun. 4, 2104 (2013).

    Article  Google Scholar 

  41. Kwon, H. & Jeong, H. Violation of the Bell–Clauser–Horne–Shimony–Holt inequality using imperfect photodetectors with optical hybrid states. Phys. Rev. A 88, 052127 (2013).

    Article  ADS  Google Scholar 

  42. Kalb, N., Reiserer, A., Ritter, S. & Rempe, G. Heralded storage of a photonic quantum bit in a single atom. Phys. Rev. Lett. 114, 220501 (2015).

    Article  ADS  Google Scholar 

  43. Andersen, U. L., Neergaard-Nielsen, J. S., Van Loock, P. & Furusawa, A. Hybrid discrete- and continuous-variable quantum information. Nat. Phys. 11, 713–719 (2015).

    Article  Google Scholar 

  44. 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  ADS  Google Scholar 

  45. Lvovsky, A. I. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B 6, S556–S559 (2004).

    Article  ADS  Google Scholar 

  46. Banaszek, K., D’Ariano, G. M., Paris, M. G. A. & Sacchi, M. F. Maximum-likelihood estimation of the density matrix. Phys. Rev. A 61, 010304 (1999).

    Article  Google Scholar 

  47. Kuhn, A. in Engineering the Atom–Photon Interaction (eds Predojević, A. & Mitchell, M. W.) 3–38 (Springer, Cham, 2015).

Download references

Acknowledgements

The authors thank J.I. Cirac, S. Dürr and O. Morin for valuable ideas and discussions. This work was supported by the Deutsche Forschungsgemeinschaft via the excellence cluster Nanosystems Initiative Munich (NIM) and the EU flagship project Quantum Internet Alliance (QIA). S.W. was supported by Elitenetzwerk Bayern (ENB) through the doctoral program Exploring Quantum Matter (ExQM).

Author information

Authors and Affiliations

Authors

Contributions

Experimental data were taken and analysed by B.H., S.W., S.D. and L.L. The homodyne detection set-up was built by B.H., S.W., S.D., A.S., S.R. and L.L. The manuscript was written by B.H., S.W. and G.R., with input from all authors.

Corresponding author

Correspondence to Bastian Hacker.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary notes and figures

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hacker, B., Welte, S., Daiss, S. et al. Deterministic creation of entangled atom–light Schrödinger-cat states. Nature Photon 13, 110–115 (2019). https://doi.org/10.1038/s41566-018-0339-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-018-0339-5

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing