A dissipatively stabilized Mott insulator of photons

An Author Correction to this article was published on 27 May 2019

This article has been updated

Abstract

Superconducting circuits are a competitive platform for quantum computation because they offer controllability, long coherence times and strong interactions—properties that are essential for the study of quantum materials comprising microwave photons. However, intrinsic photon losses in these circuits hinder the realization of quantum many-body phases. Here we use superconducting circuits to explore strongly correlated quantum matter by building a Bose–Hubbard lattice for photons in the strongly interacting regime. We develop a versatile method for dissipative preparation of incompressible many-body phases through reservoir engineering and apply it to our system to stabilize a Mott insulator of photons against losses. Site- and time-resolved readout of the lattice allows us to investigate the microscopic details of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. Our experiments demonstrate the power of superconducting circuits for studying strongly correlated matter in both coherent and engineered dissipative settings. In conjunction with recently demonstrated superconducting microwave Chern insulators, we expect that our approach will enable the exploration of topologically ordered phases of matter.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Dissipative stabilization of incompressible many-body states.
Fig. 2: Building a Bose–Hubbard lattice in a superconducting circuit.
Fig. 3: Dissipative stabilization of a single lattice site.
Fig. 4: Dissipative stabilization of a Mott insulator.
Fig. 5: Dynamics of a hole defect in the Mott insulator.

Data availability

The experimental data and numerical simulations presented in this manuscript are available from the corresponding author upon request.

Change history

  • 27 May 2019

    Change history: In this Article, two additional references (now added as refs 12 and 14) should have been cited at the end of the sentence “Recently, photonic systems have emerged as a platform of interest for the exploration of synthetic quantum matter.”. This has been corrected online.

References

  1. 1.

    Bakr, W. S., Gillen, J. I., Peng, A., Folling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Anderson, M. H. et al. Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Davis, K. B. et al. Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    ADS  CAS  Article  Google Scholar 

  6. 6.

    Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    He, Y.-C., Grusdt, F., Kaufman, A., Greiner, M. & Vishwanath, A. Realizing and adiabatically preparing bosonic integer and fractional quantum Hall states in optical lattices. Phys. Rev. B 96, 201103 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Gring, M. et al. Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  11. 11.

    Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Hartmann, M. J., Brandão, F. G. S. L. & Plenio, M. B. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849–855 (2006).

    Google Scholar 

  13. 13.

    Greentree, A. D., Tahan, C., Cole, J. H. & Hollenberg, L. C. L. Quantum phase transitions of light. Nat. Phys. 2, 856–861 (2006).

    CAS  Article  Google Scholar 

  14. 14.

    Angelakis, D. G., Santos, M. F. & Bose, S. Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays. Phys. Rev. A 76, 031805 (2007).

    Google Scholar 

  15. 15.

    Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Prog. Phys. 80, 016401 (2016).

    ADS  Article  Google Scholar 

  16. 16.

    Hartmann, M. J. Quantum simulation with interacting photons. J. Opt. 18, 104005 (2016).

    ADS  Article  Google Scholar 

  17. 17.

    Gu, X., Kockum, A. F. & Miranowicz, A., Liu, Y. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1–102 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  18. 18.

    Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Salathé, Y. et al. Digital quantum simulation of spin models with circuit quantum electrodynamics. Phys. Rev. X 5, 021027 (2015).

    Google Scholar 

  20. 20.

    Barends, R. et al. Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6, 7654 (2015).

    CAS  Article  Google Scholar 

  21. 21.

    O’Malley, P. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).

    Google Scholar 

  22. 22.

    Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Underwood, D. L., Shanks, W. E., Koch, J. & Houck, A. A. Low-disorder microwave cavity lattices for quantum simulation with photons. Phys. Rev. A 86, 023837 (2012).

    ADS  Article  Google Scholar 

  24. 24.

    Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146–151 (2017).

    CAS  Article  Google Scholar 

  25. 25.

    Owens, C. et al. Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array. Phys. Rev. A 97, 013818 (2018).

    ADS  CAS  Article  Google Scholar 

  26. 26.

    Raftery, J., Sadri, D., Schmidt, S., Türeci, H. E. & Houck, A. A. Observation of a dissipation-induced classical to quantum transition. Phys. Rev. X 4, 031043 (2014).

    Google Scholar 

  27. 27.

    Fitzpatrick, M., Sundaresan, N. M., Li, A. C., Koch, J. & Houck, A. A. Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Phys. Rev. X 7, 011016 (2017).

    Google Scholar 

  28. 28.

    Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  29. 29.

    Poyatos, J., Cirac, J. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996).

    ADS  CAS  Article  Google Scholar 

  30. 30.

    Plenio, M. B., Huelga, S. F., Beige, A. & Knight, P. L. Cavity-loss-induced generation of entangled atoms. Phys. Rev. A 59, 2468–2475 (1999).

    ADS  CAS  Article  Google Scholar 

  31. 31.

    Biella, A. et al. Phase diagram of incoherently driven strongly correlated photonic lattices. Phys. Rev. A 96, 023839 (2017).

    ADS  Article  Google Scholar 

  32. 32.

    Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).

    ADS  CAS  Article  Google Scholar 

  33. 33.

    Lu, Y. et al. Universal stabilization of a parametrically coupled qubit. Phys. Rev. Lett. 119, 150502 (2017).

    ADS  Article  Google Scholar 

  34. 34.

    Shankar, S. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419–422 (2013).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Kapit, E., Chalker, J. T. & Simon, S. H. Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric. Phys. Rev. A 91, 062324 (2015).

    ADS  Article  Google Scholar 

  36. 36.

    Kapit, E. Hardware-efficient and fully autonomous quantum error correction in superconducting circuits. Phys. Rev. Lett. 116, 150501 (2016).

    ADS  Article  Google Scholar 

  37. 37.

    Albert, V. V. et al. Pair-cat codes: autonomous error-correction with low-order nonlinearity. Preprint at https://arxiv.org/abs/1801.05897 (2018).

  38. 38.

    Ma, R., Owens, C., Houck, A., Schuster, D. I. & Simon, J. Autonomous stabilizer for incompressible photon fluids and solids. Phys. Rev. A 95, 043811 (2017).

    ADS  Article  Google Scholar 

  39. 39.

    Kapit, E., Hafezi, M. & Simon, S. H. Induced self-stabilization in fractional quantum Hall states of light. Phys. Rev. X 4, 031039 (2014).

    Google Scholar 

  40. 40.

    Hafezi, M., Adhikari, P. & Taylor, J. Chemical potential for light by parametric coupling. Phys. Rev. B 92, 174305 (2015).

    ADS  Article  Google Scholar 

  41. 41.

    Lebreuilly, J., Wouters, M. & Carusotto, I. Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping. C. R. Phys. 17, 836–860 (2016).

    ADS  CAS  Article  Google Scholar 

  42. 42.

    Lebreuilly, J. et al. Stabilizing strongly correlated photon fluids with non-Markovian reservoirs. Phys. Rev. A 96, 033828 (2017).

    ADS  Article  Google Scholar 

  43. 43.

    Hacohen-Gourgy, S., Ramasesh, V. V., De Grandi, C., Siddiqi, I. & Girvin, S. M. Cooling and autonomous feedback in a Bose–Hubbard chain with attractive interactions. Phys. Rev. Lett. 115, 240501 (2015).

    ADS  CAS  Article  Google Scholar 

  44. 44.

    Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    ADS  Article  Google Scholar 

  45. 45.

    Leek, P. et al. Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79, 180511 (2009).

    ADS  Article  Google Scholar 

  46. 46.

    Ma, R. et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett. 107, 095301 (2011).

    ADS  Article  Google Scholar 

  47. 47.

    Gemelke, N., Zhang, X., Hung, C.-L. & Chin, C. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460, 995 (2009).

    ADS  CAS  Article  Google Scholar 

  48. 48.

    Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633–636 (2009).

    CAS  Article  Google Scholar 

  49. 49.

    Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).

    ADS  CAS  Article  Google Scholar 

  50. 50.

    Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015).

    ADS  CAS  Article  Google Scholar 

  51. 51.

    Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014).

    ADS  Article  Google Scholar 

  52. 52.

    Umucalilar, R. & Carusotto, I. Fractional quantum Hall states of photons in an array of dissipative coupled cavities. Phys. Rev. Lett. 108, 206809 (2012).

    ADS  CAS  Article  Google Scholar 

  53. 53.

    Anderson, B. M., Ma, R., Owens, C., Schuster, D. I. & Simon, J. Engineering topological many-body materials in microwave cavity arrays. Phys. Rev. X 6, 041043 (2016).

    Google Scholar 

  54. 54.

    Ningyuan, J., Owens, C., Sommer, A., Schuster, D. & Simon, J. Time- and site-resolved dynamics in a topological circuit. Phys. Rev. X 5, 021031 (2015).

    Google Scholar 

  55. 55.

    Barkeshli, M. & Qi, X.-L. Topological nematic states and non-Abelian lattice dislocations. Phys. Rev. X 2, 031013 (2012).

    Google Scholar 

Download references

Acknowledgements

We thank M. Hafezi and A. Houck for discussions. This work was supported by Army Research Office grant W911NF-15-1-0397 and by the University of Chicago Materials Research Science and Engineering Center (MRSEC), which is funded by the National Science Foundation (NSF) under award number DMR-1420709. D.I.S. acknowledges support from the David and Lucile Packard Foundation; R.M. acknowledges support from the MRSEC-funded Kadanoff-Rice Postdoctoral Research Fellowship; C.O. is supported by the NSF Graduate Research Fellowships Program. This work made use the Pritzker Nanofabrication Facility at the University of Chicago, which receives support from NSF ECCS-1542205.

Reviewer information

Nature thanks A. Daley, K. Hazzard and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Affiliations

Authors

Contributions

R.M., B.S., C.O., J.S. and D.I.S. designed and developed the experiments. R.M. and B.S. performed the device fabrication, measurements and analysis, with assistance from N.L. and Y.L. All authors contributed to the preparation of the manuscript.

Corresponding author

Correspondence to Ruichao Ma.

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

This file contains Supplementary Sections A-G, including Supplementary Figures 1-12, Supplementary Tables 1-3 and Supplementary references – see contents page for details

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ma, R., Saxberg, B., Owens, C. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019). https://doi.org/10.1038/s41586-019-0897-9

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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