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Disorder-assisted assembly of strongly correlated fluids of light

Nature volume 612, pages 435–441 (2022)Cite this article

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Abstract

Guiding many-body systems to desired states is a central challenge of modern quantum science, with applications from quantum computation1,2 to many-body physics3 and quantum-enhanced metrology4. Approaches to solving this problem include step-by-step assembly5,6, reservoir engineering to irreversibly pump towards a target state7,8 and adiabatic evolution from a known initial state9,10. Here we construct low-entropy quantum fluids of light in a Bose–Hubbard circuit by combining particle-by-particle assembly and adiabatic preparation. We inject individual photons into a disordered lattice for which the eigenstates are known and localized, then adiabatically remove this disorder, enabling quantum fluctuations to melt the photons into a fluid. Using our platform11, we first benchmark this lattice melting technique by building and characterizing arbitrary single-particle-in-a-box states, then assemble multiparticle strongly correlated fluids. Intersite entanglement measurements performed through single-site tomography indicate that the particles in the fluid delocalize, whereas two-body density correlation measurements demonstrate that they also avoid one another, revealing Friedel oscillations characteristic of a Tonks–Girardeau gas12,13. This work opens new possibilities for the preparation of topological and otherwise exotic phases of synthetic matter3,14,15.

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Fig. 1: Individually addressed many-body states in the Bose–Hubbard circuit.
Fig. 2: Adiabatic assembly of single-particle eigenstates.
Fig. 3: Adiabatic preparation of strongly correlated fluids of light.
Fig. 4: Microscopy of the strongly correlated fluid—anti-bunching and delocalization.

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Data availability

The experimental data presented in this manuscript are available from the corresponding author upon request, due to the proprietary file formats used in the data collection process.

Code availability

The source code for simulations throughout are available from the corresponding author upon request.

References

  1. Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198–201 (1996).

    Article  CAS  ADS  Google Scholar 

  2. Devitt, S. J., Munro, W. J. & Nemoto, K. Quantum error correction for beginners. Rep. Prog. Phys. 76, 076001 (2013).

    Article  ADS  Google Scholar 

  3. Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).

    Article  CAS  Google Scholar 

  4. Pezze, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  5. Grusdt, F., Letscher, F., Hafezi, M. & Fleischhauer, M. Topological growing of Laughlin states in synthetic gauge fields. Phys. Rev. Lett. 113, 155301 (2014).

    Article  ADS  Google Scholar 

  6. Dallaire-Demers, P.-L., Romero, J., Veis, L., Sim, S. & Aspuru-Guzik, A. Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer. Quantum Sci. Technol. 4, 045005 (2019).

    Article  ADS  Google Scholar 

  7. 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 

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

    Article  ADS  Google Scholar 

  9. Albash, T. & Lidar, D. A. Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  10. Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).

    Article  ADS  Google Scholar 

  11. Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).

    Article  CAS  ADS  Google Scholar 

  12. Tonks, L. The complete equation of state of one, two and three-dimensional gases of hard elastic spheres. Phys. Rev. 50, 955–963 (1936).

    Article  CAS  MATH  ADS  Google Scholar 

  13. Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. 1, 516–523 (1960).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  14. Goldman, N., Budich, J. C. & Zoller, P. Topological quantum matter with ultracold gases in optical lattices. Nat. Phys. 12, 639–645 (2016).

    Article  CAS  Google Scholar 

  15. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  16. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    Article  CAS  Google Scholar 

  17. Bloch, I., Dalibard, J. & Nascimbene, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Article  CAS  Google Scholar 

  18. Clark, L. W., Schine, N., Baum, C., Jia, N. & Simon, J. Observation of Laughlin states made of light. Nature 582, 41–45 (2020).

    Article  CAS  ADS  Google Scholar 

  19. Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS–BEC crossover: from high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1–88 (2005).

    Article  CAS  ADS  Google Scholar 

  20. 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).

    Article  CAS  ADS  Google Scholar 

  21. Cooper, N., Dalibard, J. & Spielman, I. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).

    Article  MathSciNet  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  23. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  25. Karamlou, A. H. et al. Quantum transport and localization in 1d and 2d tight-binding lattices. npj Quantum Inform. 8, 35 (2022).

    Article  ADS  Google Scholar 

  26. Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).

    Article  CAS  ADS  Google Scholar 

  27. Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).

    Article  CAS  ADS  Google Scholar 

  28. Choi, J.-Y. et al. Exploring the many-body localization transition in two dimensions. Science 352, 1547–1552 (2016).

    Article  MathSciNet  CAS  MATH  ADS  Google Scholar 

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

    Article  MathSciNet  CAS  ADS  Google Scholar 

  30. Bluvstein, D. et al. Controlling quantum many-body dynamics in driven Rydberg atom arrays. Science 371, 1355–1359 (2021).

    Article  MathSciNet  CAS  MATH  ADS  Google Scholar 

  31. Brown, P. T. et al. Bad metallic transport in a cold atom Fermi–Hubbard system. Science 363, 379–382 (2019).

    Article  CAS  ADS  Google Scholar 

  32. McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020).

    Article  CAS  Google Scholar 

  33. Choi, S., Bao, Y., Qi, X.-L. & Altman, E. Quantum error correction in scrambling dynamics and measurement-induced phase transition. Phys. Rev. Lett. 125, 030505 (2020).

    Article  MathSciNet  CAS  ADS  Google Scholar 

  34. Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  37. 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).

    Article  ADS  Google Scholar 

  38. Bak, P. Commensurate phases, incommensurate phases and the devil’s staircase. Rep. Prog. Phys. 45, 587 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  39. Umucalílar, R., Simon, J. & Carusotto, I. Autonomous stabilization of photonic Laughlin states through angular momentum potentials. Phys. Rev. A 104, 023704 (2021).

    Article  MathSciNet  ADS  Google Scholar 

  40. Gemelke, N., Zhang, X., Hung, C.-L. & Chin, C. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460, 995–998 (2009).

    Article  CAS  ADS  Google Scholar 

  41. Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).

    Article  MathSciNet  ADS  Google Scholar 

  42. Kinoshita, T., Wenger, T. & Weiss, D. S. Observation of a one-dimensional Tonks–Girardeau gas. Science 305, 1125–1128 (2004).

    Article  CAS  ADS  Google Scholar 

  43. Paredes, B. et al. Tonks–Girardeau gas of ultracold atoms in an optical lattice. Nature 429, 277–281 (2004).

    Article  CAS  ADS  Google Scholar 

  44. Cazalilla, M. A., Citro, R., Giamarchi, T., Orignac, E. & Rigol, M. One dimensional bosons: from condensed matter systems to ultracold gases. Rev. Mod. Phys. 83, 1405–1466 (2011).

    Article  ADS  Google Scholar 

  45. Meyer, D. A. & Wallach, N. R. Global entanglement in multiparticle systems. J. Math. Phys. 43, 4273 (2002).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  46. Chandran, A., Erez, A., Gubser, S. S. & Sondhi, S. L. Kibble–Zurek problem: universality and the scaling limit. Phys. Rev. B 86, 064304 (2012).

    Article  ADS  Google Scholar 

  47. Owens, J. C. et al. Chiral cavity quantum electrodynamics. Nat. Phys. 18, 1048–1052 (2022).

    Article  CAS  Google Scholar 

  48. Swingle, B., Bentsen, G., Schleier-Smith, M. & Hayden, P. Measuring the scrambling of quantum information. Phys. Rev. A 94, 040302 (2016).

    Article  MathSciNet  ADS  Google Scholar 

  49. Grusdt, F., Yao, N. Y., Abanin, D., Fleischhauer, M. & Demler, E. Interferometric measurements of many-body topological invariants using mobile impurities. Nat. Commun. 7, 11994 (2016).

    Article  CAS  ADS  Google Scholar 

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

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Acknowledgements

This work was supported by ARO MURI grant W911NF-15-1-0397, AFOSR MURI grant FA9550-19-1-0399 and by NSF Eager grant 1926604. Support was also provided by the Chicago MRSEC, which is funded by NSF through grant DMR-1420709. G.R. and M.G.P. acknowledge support from the NSF GRFP. A.V. acknowledges support from the MRSEC-funded Kadanoff–Rice Postdoctoral Research Fellowship. Devices were fabricated in the Pritzker Nanofabrication Facility at the University of Chicago, which receives support from Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205), a node of the National Science Foundation’s National Nanotechnology Coordinated Infrastructure.

Author information

Author notes

  1. These authors contributed equally: Brendan Saxberg, Andrei Vrajitoarea, Gabrielle Roberts

Authors and Affiliations

  1. The Department of Physics and James Frank Institute, University of Chicago, Chicago, IL, USA

    Brendan Saxberg, Andrei Vrajitoarea, Gabrielle Roberts, Margaret G. Panetta, Jonathan Simon & David I. Schuster

  2. The Department of Physics, Stanford University, Stanford, CA, USA

    Jonathan Simon

  3. The Department of Applied Physics, Stanford University, Stanford, CA, USA

    Jonathan Simon & David I. Schuster

  4. The Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA

    Jonathan Simon & David I. Schuster

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Contributions

The experiments were designed by B.S., A.V., G.R., J.S. and D.I.S. The apparatus was built by B.S., A.V. and G.R. The collection of data was handled by B.S., A.V. and G.R. All authors analysed the data and contributed to the manuscript.

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Correspondence to Brendan Saxberg.

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Extended data figures and tables

Extended Data Fig. 1 Adiabaticity Curves for All \(\bar{n}\) Fillings.

Adiabaticity is given by the average number of photons that return to the originally excited sites as a function of ramp length. Here, we measure adiabaticity curves for the highest energy eigenstate for all \(\bar{n}\) fillings, revealing the minimum ramp length needed to be adiabatic when preparing these many-body states. As particle number increases, we start to suffer more from loss and no longer fully recover the initial starting population.

Extended Data Fig. 2 Profiles for \(\bar{n}\) Fillings.

Density profiles for the highest energy eigenstates, corresponding to fluid ground states, for filling \(\bar{n}\)=\(\frac{1}{7}\) through \(\frac{6}{7}\). For 5 and 6 particles, our results suffer from particle loss.

Extended Data Fig. 3 Entanglement for \(\bar{n}\) Fillings.

Measure of entanglement vs disorder, for filling \(\bar{n}\)=\(\frac{1}{7}\) through \(\frac{6}{7}\). Error bars reflect S.E.M.; here they are smaller than markers.

Supplementary information

Supplementary Information

Supplementary Sections A–J, Table 1, Figs. 1–7 and references.

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Saxberg, B., Vrajitoarea, A., Roberts, G. et al. Disorder-assisted assembly of strongly correlated fluids of light. Nature 612, 435–441 (2022). https://doi.org/10.1038/s41586-022-05357-x

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