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.
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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).
Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).
Anderson, M. H. et al. Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995).
Davis, K. B. et al. Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).
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).
Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).
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).
Gring, M. et al. Relaxation and prethermalization in an isolated quantum system. Science 337, 1318–1322 (2012).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Kaufman, A. M. et al. Quantum thermalization through entanglement in an isolated many-body system. Science 353, 794–800 (2016).
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).
Greentree, A. D., Tahan, C., Cole, J. H. & Hollenberg, L. C. L. Quantum phase transitions of light. Nat. Phys. 2, 856–861 (2006).
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).
Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Prog. Phys. 80, 016401 (2016).
Hartmann, M. J. Quantum simulation with interacting photons. J. Opt. 18, 104005 (2016).
Gu, X., Kockum, A. F. & Miranowicz, A., Liu, Y. & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. 718–719, 1–102 (2017).
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).
Salathé, Y. et al. Digital quantum simulation of spin models with circuit quantum electrodynamics. Phys. Rev. X 5, 021027 (2015).
Barends, R. et al. Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6, 7654 (2015).
O’Malley, P. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).
Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).
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).
Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nat. Phys. 13, 146–151 (2017).
Owens, C. et al. Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array. Phys. Rev. A 97, 013818 (2018).
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).
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).
Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).
Poyatos, J., Cirac, J. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996).
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).
Biella, A. et al. Phase diagram of incoherently driven strongly correlated photonic lattices. Phys. Rev. A 96, 023839 (2017).
Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).
Lu, Y. et al. Universal stabilization of a parametrically coupled qubit. Phys. Rev. Lett. 119, 150502 (2017).
Shankar, S. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419–422 (2013).
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).
Kapit, E. Hardware-efficient and fully autonomous quantum error correction in superconducting circuits. Phys. Rev. Lett. 116, 150501 (2016).
Albert, V. V. et al. Pair-cat codes: autonomous error-correction with low-order nonlinearity. Preprint at https://arxiv.org/abs/1801.05897 (2018).
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).
Kapit, E., Hafezi, M. & Simon, S. H. Induced self-stabilization in fractional quantum Hall states of light. Phys. Rev. X 4, 031039 (2014).
Hafezi, M., Adhikari, P. & Taylor, J. Chemical potential for light by parametric coupling. Phys. Rev. B 92, 174305 (2015).
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).
Lebreuilly, J. et al. Stabilizing strongly correlated photon fluids with non-Markovian reservoirs. Phys. Rev. A 96, 033828 (2017).
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).
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
Leek, P. et al. Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79, 180511 (2009).
Ma, R. et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett. 107, 095301 (2011).
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).
Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633–636 (2009).
Cheneau, M. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012).
Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77–83 (2015).
Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014).
Umucalilar, R. & Carusotto, I. Fractional quantum Hall states of photons in an array of dissipative coupled cavities. Phys. Rev. Lett. 108, 206809 (2012).
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).
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).
Barkeshli, M. & Qi, X.-L. Topological nematic states and non-Abelian lattice dislocations. Phys. Rev. X 2, 031013 (2012).
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.
Nature thanks A. Daley, K. Hazzard and the other anonymous reviewer(s) for their contribution to the peer review of this work.
The authors declare no competing interests.
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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
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