Photonic synthetic materials provide an opportunity to explore the role of microscopic quantum phenomena in determining macroscopic material properties. There are, however, fundamental obstacles to overcome — in vacuum, photons not only lack mass, but also do not naturally interact with one another. Here, we review how the superconducting quantum circuit platform has been harnessed in the last decade to make some of the first materials from light. We describe the structures that are used to imbue individual microwave photons with matter-like properties such as mass, the nonlinear elements that mediate interactions between these photons, and quantum dynamic/thermodynamic approaches that can be used to assemble and stabilize strongly correlated states of many photons. We then describe state-of-the-art techniques to generate synthetic magnetic fields, engineer topological and non-topological flat bands and explore the physics of quantum materials in non-Euclidean geometries — directions that we view as some of the most exciting for this burgeoning field. Finally, we discuss upcoming prospects, and in particular opportunities to probe novel aspects of quantum thermalization and detect quasi-particles with exotic anyonic statistics, as well as potential applications in quantum information science.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Nature Communications Open Access 15 October 2022
Communications Physics Open Access 11 June 2021
npj Quantum Information Open Access 16 February 2021
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Walls, D. & Milburn, G. Quantum Optics (Springer, 2008).
Aspect, A., Dalibard, J. & Roger, G. Experimental test of bell’s inequalities using time-varying analyzers. Phys. Rev. Let. 49, 1804–1807 (1982).
Weihs, G., Jennewein, T., Simon, C., Weinfurter, H. & Zeilinger, A. Violation of Bell’s inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81, 5039–5043 (1998).
Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013). A review of quantum fluids of light from an interdisciplinary perspective, from exciton-polariton in microcavities to circuit-QED.
Kavokin, A., Baumberg, J., Malpuech, G. & Laussy, F. Microcavities (Oxford Univ. Press, 2017).
Deng, H., Haug, H. & Yamamoto, Y. Exciton-polariton Bose-Einstein condensation. Rev. Mod. Phys. 82, 1489–1537 (2010).
Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics—photon by photon. Nat. Photon. 8, 685–694 (2014).
Schuster, D. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).
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).
Reagor, M. et al. Quantum memory with millisecond coherence in circuit QED. Phys. Rev. B 94, 014506 (2016).
Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012). An authoritative earlier review on many-body physics in arrays of superconducting circuits.
Schmidt, S. & Koch, J. Circuit QED lattices: towards quantum simulation with superconducting circuits. Ann. Phys. 525, 395–412 (2013).
Hartmann, M. J. Quantum simulation with interacting photons. J. Opt. 18, 104005 (2016).
Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Prog. Phys. 80, 016401 (2016).
Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011).
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).
Grusdt, F., Letscher, F., Hafezi, M. & Fleischhauer, M. Topological growing of Laughlin states in synthetic gauge fields. Phys. Rev. Lett. 113, 155301 (2014).
Sørensen, A. S., Demler, E. & Lukin, M. D. Fractional quantum Hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).
Hartmann, M. J., Brandao, F. G. & 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. 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 x y spin models in coupled cavity arrays. Phys. Rev. A 76, 031805 (2007).
Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).
Klaers, J., Schmitt, J., Vewinger, F. & Weitz, M. Bose–Einstein condensation of photons in an optical microcavity. Nature 468, 545–548 (2010).
Altman, E., Sieberer, L. M., Chen, L., Diehl, S. & Toner, J. Two-dimensional superfluidity of exciton polaritons requires strong anisotropy. Phys. Rev. X 5, 011017 (2015).
Ji, K., Gladilin, V. N. & Wouters, M. Temporal coherence of one-dimensional nonequilibrium quantum fluids. Phys. Rev. B 91, 045301 (2015).
Dagvadorj, G. et al. Nonequilibrium phase transition in a two-dimensional driven open quantum system. Phys. Rev. X 5, 041028 (2015).
Squizzato, D., Canet, L. & Minguzzi, A. Kardar-Parisi-Zhang universality in the phase distributions of one-dimensional exciton-polaritons. Phys. Rev. B 97, 195453 (2018).
Gerace, D., Türeci, H. E., Imamoglu, A., Giovannetti, V. & Fazio, R. The quantum-optical Josephson interferometer. Nat. Phys. 5, 281–284 (2009).
Carusotto, I. et al. Fermionized photons in an array of driven dissipative nonlinear cavities. Phys. Rev. Lett. 103, 033601 (2009). The first proposal for a scheme to exploit driving and dissipation to generate strongly-correlated state of photons in a cavity array.
Umucalılar, R. & Carusotto, I. Fractional quantum Hall states of photons in an array of dissipative coupled cavities. Phys. Rev. Lett. 108, 206809 (2012).
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).
Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217–220 (2017).
Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221–225 (2017).
Fausti, D. et al. Light-induced superconductivity in a stripe-ordered cuprate. Science 331, 189–191 (2011).
Eisert, J., Friesdorf, M. & Gogolin, C. Quantum many-body systems out of equilibrium. Nat. Phys. 11, 124–130 (2015).
Kapit, E., Hafezi, M. & Simon, S. H. Induced self-stabilization in fractional quantum hall states of light. Phys. Rev. X 4, 031039 (2014). Together with refs. 39,41–44, this work has theoretically pioneered the idea of dissipative stabilization of a non-equilibrium many-body system by means of engineered driving and losses.
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).
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).
Biella, A. et al. Phase diagram of incoherently driven strongly correlated photonic lattices. Phys. Rev. A 96, 023839 (2017).
Lebreuilly, J. et al. Stabilizing strongly correlated photon fluids with non-Markovian reservoirs. Phys. Rev. A 96, 033828 (2017).
Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).This represents first experimental realization of a strongly interacting fluid of impenetrable photons.
Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004).
Gu, X., Kockum, A. F., Miranowicz, A., Liu, Y.-x & Nori, F. Microwave photonics with superconducting quantum circuits. Phys. Rep. https://doi.org/10.1016/j.physrep.2017.10.002 (2017).
Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).
Imamoḡlu, A., Schmidt, H., Woods, G. & Deutsch, M. Strongly interacting photons in a nonlinear cavity. Phys. Rev. Lett. 79, 1467–1470 (1997).
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).
Kollár, A. J., Fitzpatrick, M. & Houck, A. A. Hyperbolic lattices in circuit quantum electrodynamics. Nature 571, 45–50 (2019).This work has reported the first experimental realization of an array with an intrinsically non-Euclidean geometry.
Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling. Phys. Rev. Lett. 113, 220502 (2014).
Roushan, P. et al. Chiral ground-state currents of interacting photons in a synthetic magnetic field.Nat. Phys. 13, 146–151 (2017).This work has reported the first experimental study of the interplay of a synthetic magnetic field and strong interactions for photons in a simplest geometry.
Pitaevskii, L. P. & Stringari, S. Bose-Einstein Condensation and Superfluidity (Oxford Univ. Press, 2016).
Amo, A. & Bloch, J. Exciton-polaritons in lattices: a non-linear photonic simulator. C. R. Phys. 17, 934–945 (2016).
Togan, E., Lim, H.-T., Faelt, S., Wegscheider, W. & Imamoglu, A. Enhanced interactions between dipolar polaritons. Phys. Rev. Lett. 121, 227402 (2018).
Muñoz-Matutano, G. et al. Emergence of quantum correlations from interacting fibre-cavity polaritons. Nat. Mater. 18, 213–218 (2019).
Delteil, A. et al. Towards polariton blockade of confined exciton–polaritons. Nat. Mater. 18, 219–222 (2019).
Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012).
Jia, N. et al. A strongly interacting polaritonic quantum dot. Nat. Phys. 14, 550–554 (2018).
Sommer, A., Büchler, H. P. & Simon, J. Quantum crystals and Laughlin droplets of cavity Rydberg polaritons. Preprint at https://arxiv.org/abs/1506.00341 (2015).
Clark, L. W. et al. Interacting Floquet polaritons. Nature 571, 532–536 (2019).
Clark, L. W., Schine, N., Baum, C., Jia, N. & Simon, J. Observation of Laughlin states made of light. Preprint at https://arxiv.org/abs/1907.05872 (2019).
Reed, M. et al. High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity. Phys. Rev. Lett. 105, 173601 (2010).
Walter, T. et al. Rapid high-fidelity single-shot dispersive readout of superconducting qubits. Phys. Rev. Appl. 7, 054020 (2017).
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).
Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68–72 (2010).
Roushan, P. et al. Spectroscopic signatures of localization with interacting photons in superconducting qubits. Science 358, 1175–1179 (2017).This work has studied the temporal dynamics of systems of few strongly interacting photons in a disordered landscape.
Cooper, K. et al. Observation of quantum oscillations between a Josephson phase qubit and a microscopic resonator using fast readout. Phys. Rev. Lett. 93, 180401 (2004).
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).
Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).
Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013).
Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006).
Houck, A. A. et al. Generating single microwave photons in a circuit. Nature 449, 328–331 (2007).
Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009).
Tangpanitanon, J. & Angelakis, D. G. Many-body physics and quantum simulations with strongly interacting photons. Preprint at https://arxiv.org/abs/1907.05030 (2019). A very recent set of lecture notes giving another perspective on strongly interacting photons.
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).This work, inspired by the theoretical investigation in the next reference, provides experimental evidence of a dynamical localization transition in a dimer geometry, from an oscillatory behaviour to a self-trapped state.
Schmidt, S., Gerace, D., Houck, A. A., Blatter, G. & Türeci, H. E. Nonequilibrium delocalization-localization transition of photons in circuit quantum electrodynamics. Phys. Rev. B 82, 100507 (2010).
Albiez, M. et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005).
Abbarchi, M. et al. Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons. Nat. Phys. 9, 275–279 (2013).
Yan, Z. et al. Strongly correlated quantum walks with a 12-qubit superconducting processor. Science 364, 753–756 (2019).
Ye, Y. et al. Propagation and localization of collective excitations on a 24-qubit superconducting processor. Phys. Rev. Lett. 123, 050502 (2019).
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).
Umucalılar, R. & Carusotto, I. Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity. Phys. Rev. A 96, 053808 (2017).
Biondi, M., Blatter, G. & Schmidt, S. Emergent light crystal from frustration and pump engineering. Phys. Rev. B 98, 104204 (2018).
Mamaev, M., Govia, L. C. G. & Clerk, A. A. Dissipative stabilization of entangled cat states using a driven Bose-Hubbard dimer. Quantum 2, 58 (2018).
Lebreuilly, J., Aron, C. & Mora, C. Stabilizing arrays of photonic cat states via spontaneous symmetry breaking. Phys. Rev. Lett. 122, 120402 (2019).
Bardyn, C.-E. & İmamoǧlu, A. Majorana-like modes of light in a one-dimensional array of nonlinear cavities. Phys. Rev. Lett. 109, 253606 (2012).
Liu, Y. & Houck, A. A. Quantum electrodynamics near a photonic bandgap. Nat. Phys. 13, 48–52 (2017).
Tomadin, A. et al. Signatures of the superfluid-insulator phase transition in laser-driven dissipative nonlinear cavity arrays. Phys. Rev. A 81, 061801 (2010).
Le Hur, K. et al. Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light. C. R. Phys. 17, 808–835 (2016).
Biondi, M., Blatter, G., Türeci, H. E. & Schmidt, S. Nonequilibrium gas-liquid transition in the driven-dissipative photonic lattice. Phys. Rev. A 96, 043809 (2017).
Foss-Feig, M. et al. Emergent equilibrium in many-body optical bistability. Phys. Rev. A 95, 043826 (2017).
Rota, R., Minganti, F., Ciuti, C. & Savona, V. Quantum critical regime in a quadratically driven nonlinear photonic lattice. Phys. Rev. Lett. 122, 110405 (2019).
Vicentini, F., Minganti, F., Rota, R., Orso, G. & Ciuti, C. Critical slowing down in driven-dissipative Bose-Hubbard lattices. Phys. Rev. A 97, 013853 (2018).
Tangpanitanon, J. et al. Hidden order in quantum many-body dynamics of driven-dissipative nonlinear photonic lattices. Phys. Rev. A 99, 043808 (2019).
Le Boité, A., Orso, G. & Ciuti, C. Bose-Hubbard model: Relation between driven-dissipative steady states and equilibrium quantum phases. Phys. Rev. A 90, 063821 (2014).
Wouters, M. & Carusotto, I. Absence of long-range coherence in the parametric emission of photonic wires. Phys. Rev. B 74, 245316 (2006).
Dalla Torre, E. G., Demler, E., Giamarchi, T. & Altman, E. Quantum critical states and phase transitions in the presence of non-equilibrium noise. Nat. Phys. 6, 806–810 (2010).
Sieberer, L. M., Buchhold, M. & Diehl, S. Keldysh field theory for driven open quantum systems. Rep. Prog. Phys. 79, 096001 (2016).
Marino, J. & Diehl, S. Driven Markovian quantum criticality. Phys. Rev. Lett. 116, 070407 (2016).
Lebreuilly, J., Chiocchetta, A. & Carusotto, I. Pseudothermalization in driven-dissipative non-Markovian open quantum systems. Phys. Rev. A 97, 033603 (2018).
Jin, J., Rossini, D., Fazio, R., Leib, M. & Hartmann, M. J. Photon solid phases in driven arrays of nonlinearly coupled cavities. Phys. Rev. Lett. 110, 163605 (2013).
Finazzi, S., Le Boité, A., Storme, F., Baksic, A. & Ciuti, C. Corner-space renormalization method for driven-dissipative two-dimensional correlated systems. Phys. Rev. Lett. 115, 080604 (2015).
Vicentini, F., Minganti, F., Biella, A., Orso, G. & Ciuti, C. Optimal stochastic unraveling of disordered open quantum systems: Application to driven-dissipative photonic lattices. Phys. Rev. A 99, 032115 (2019).
Yoshioka, N. & Hamazaki, R. Constructing neural stationary states for open quantum many-body systems. Phys. Rev. B 99, 214306 (2019).
Hartmann, M. J. & Carleo, G. Neural-network approach to dissipative quantum many-body dynamics. Phys. Rev. Lett. 122, 250502 (2019).
Strathearn, A., Kirton, P., Kilda, D., Keeling, J. & Lovett, B. W. Efficient non-Markovian quantum dynamics using time-evolving matrix product operators. Nat. Commun. 9, 3322 (2018).
Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).
Xu, K. et al. Emulating many-body localization with a superconducting quantum processor. Phys. Rev. Lett. 120, 050507 (2018).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010).
Cooper, N., Dalibard, J. & Spielman, I. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).
Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).This article reviews the field of topological photonics from a cross-platform perspective, highlighting the links with other areas of topological condensed-matter physics.
Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).Together with the experimental implementation in ref. 112, this work has highlighted that the quantum Hall effect is not restricted to fermionic electrons, thus opening the field of topological photonics.
Wang, Z., Chong, Y., Joannopoulos, J. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).
Koch, J., Houck, A. A., Le Hur, K. & Girvin, S. Time-reversal-symmetry breaking in circuit-QED-based photon lattices. Phys. Rev. A 82, 043811 (2010).
Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).
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).
Albert, V. V., Glazman, L. I. & Jiang, L. Topological properties of linear circuit lattices. Phys. Rev. Lett. 114, 173902 (2015).
Lu, Y. et al. Probing the Berry curvature and fermi arcs of a Weyl circuit. Phys. Rev. B 99, 020302 (2019).
Imhof, S. et al. Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14, 925–929 (2018).
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).
Owens, C. et al. Quarter-flux Hofstadter lattice in a qubit-compatible microwave cavity array. Phys. Rev. A 97, 013818 (2018).This work has reported the experimental realization of an ɑ = 1/4 Harper-Hofstadter model for photons on a qubit compatible platform.
Tai, M. E. et al. Microscopy of the interacting Harper–Hofstadter model in the two-body limit. Nature 546, 519–523 (2017).
Cai, W. et al. Observation of topological magnon insulator states in a superconducting circuit. Phys. Rev. Lett. 123, 080501 (2019).
Cho, J., Angelakis, D. G. & Bose, S. Fractional quantum Hall state in coupled cavities. Phys. Rev. Lett. 101, 246809 (2008).
de Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775–780 (2019).An experimental study of topological states in synthetic quantum matter using an alternative platform consisting of a gas of spin excitations in an array of Rydberg atoms trapped by optical tweezers.
Boada, O., Celi, A., Rodríguez-Laguna, J., Latorre, J. I. & Lewenstein, M. Quantum simulation of non-trivial topology. N. J. Phys. 17, 045007 (2015).
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Sarma, S. D. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).
Leykam, D., Andreanov, A. & Flach, S. Artificial flat band systems: from lattice models to experiments. Adv. Phys. X 3, 1473052 (2018).
Casteels, W., Rota, R., Storme, F. & Ciuti, C. Probing photon correlations in the dark sites of geometrically frustrated cavity lattices. Phys. Rev. A 93, 043833 (2016).
Kollár, A. J., Fitzpatrick, M., Sarnak, P. & Houck, A. A. Line-graph lattices: Euclidean and non-Euclidean flat bands, and implementations in circuit quantum electrodynamics. Commun. Math. Phys. https://doi.org/10.1007/s00220-019-03645-8 (2019).
Biggs, N. Algebraic Graph Theory 2nd edn (Cambridge Univ. Press, 1993).
Shirai, T. The spectrum of infinite regular line graphs. Trans. Am. Math. Soc. 352, 115–132 (1999).
Irvine, W. T., Vitelli, V. & Chaikin, P. M. Pleats in crystals on curved surfaces. Nature 468, 947–951 (2010).
Kinsey, L. C. Topology of Surfaces (Springer, 1997).
Can, T., Laskin, M. & Wiegmann, P. Fractional quantum hall effect in a curved space: Gravitational anomaly and electromagnetic response. Phys. Rev. Lett. 113, 046803 (2014).
Schine, N., Chalupnik, M., Can, T., Gromov, A. & Simon, J. Electromagnetic and gravitational responses of photonic landau levels. Nature 565, 173–179 (2019).
Ozawa, T. & Price, H. M. Topological quantum matter in synthetic dimensions. Nat. Rev. Phys. 1, 349–357 (2019).This work reviews the perspectives of using the synthetic dimension concept to investigate new states of topological quantum matter using either atoms or photons.
Irvine, W. T. & Vitelli, V. Geometric background charge: dislocations on capillary bridges. Soft Matter 8, 10123–10129 (2012).
Breuckmann, N. P. & Terhal, B. M. Constructions and noise threshold of hyperbolic surface codes. IEEE Trans. Inf. Theory 62, 3731–3744 (2016).
Abuwasib, M., Krantz, P. & Delsing, P. Fabrication of large dimension aluminum air-bridges for superconducting quantum circuits. J. Vac. Sci. Technol. B 31, 031601 (2013).
Foxen, B. et al. Qubit compatible superconducting interconnects. Quantum Sci. Technol. 3, 014005 (2018).
Berkley, A. J., Johnson, M. W. & Bunyk, P. I. Systems and methods for superconducting integrated circuits. US Patent 9,355,365 (2016).
Holland, E. T. et al. Single-photon-resolved cross-Kerr interaction for autonomous stabilization of photon-number states. Phys. Rev. Lett. 115, 180501 (2015).
Collodo, M. C. et al. Observation of the crossover from photon ordering to delocalization in tunably coupled resonators. Phys. Rev. Lett. 122, 183601 (2019).
Burnell, F., Parish, M. M., Cooper, N. & Sondhi, S. L. Devil’s staircases and supersolids in a one-dimensional dipolar bose gas. Phys. Rev. B 80, 174519 (2009).
Sameti, M., Poto c čnik, A., Browne, D. E., Wallraff, A. & Hartmann, M. J. Superconducting quantum simulator for topological order and the toric code. Phys. Rev. A 95, 042330 (2017).
Marcos, D., Rabl, P., Rico, E. & Zoller, P. Superconducting circuits for quantum simulation of dynamical gauge fields. Phys. Rev. Lett. 111, 110504 (2013).
Sterdyniak, A., Regnault, N. & Möller, G. Particle entanglement spectra for quantum Hall states on lattices. Phys. Rev. B 86, 165314 (2012).
Gerster, M., Rizzi, M., Silvi, P., Dalmonte, M. & Montangero, S. Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks. Phys. Rev. B 96, 195123 (2017).
Rosson, P., Lubasch, M., Kiffner, M. & Jaksch, D. Bosonic fractional quantum Hall states on a finite cylinder. Phys. Rev. A 99, 033603 (2019).
Macaluso, E. et al. Charge and statistics of lattice quasiholes from density measurements: a tree tensor network study. Phys. Rev. Res. 2, 013145 (2020).This work reports a numerical study of a fractional quantum Hall state in a lattice of realistic size, highlighting schemes to detect the anyonic statistics of quasi-holes.
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).
Umucalılar, R. & Carusotto, I. Many-body braiding phases in a rotating strongly correlated photon gas. Phys. Lett. A 377, 2074–2078 (2013).
Umucalılar, R., Macaluso, E., Comparin, T. & Carusotto, I. Time-of-flight measurements as a possible method to observe anyonic statistics. Phys. Rev. Lett. 120, 230403 (2018).
Macaluso, E., Comparin, T., Mazza, L. & Carusotto, I. Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements. Phys. Rev. Lett. 123, 266801 (2019).
Stern, A. Anyons and the quantum Hall effect—a pedagogical review. Ann. Phys. 323, 204–249 (2008).
Song, C. et al. Demonstration of topological robustness of anyonic braiding statistics with a superconducting quantum circuit. Phys. Rev. Lett. 121, 030502 (2018).
Alicki, R. & Kosloff, R. Thermodynamics in the Quantum Regime (eds Binder F. et al) Ch. 1 (Springer, 2018).
Leviatan, E., Pollmann, F., Bardarson, J. H., Huse, D. A. & Altman, E. Quantum thermalization dynamics with matrix-product states. Preprint at https://arxiv.org/abs/1702.08894 (2017).
Zurek, W. H. in Quantum Decoherence (eds Duplantier B., Raimond J. M. & Rivasseau V.) Ch. 1 (Birkhäuser, 2006).
Gardner, G. C., Fallahi, S., Watson, J. D. & Manfra, M. J. Modified MBE hardware and techniques and role of gallium purity for attainment of two dimensional electron gas mobility >35×106 cm2/V s in AlGaAs/GaAs quantum wells grown by MBE. J. Cryst. Growth 441, 71–77 (2016).
Dean, C. et al. Intrinsic gap of the ν = 5/2 fractional quantum Hall state. Phys. Rev. Lett. 100, 146803 (2008).
Dial, O. et al. Bulk and surface loss in superconducting transmon qubits. Supercond. Sci. Tech. 29, 044001 (2016).
A.K. and A.H. acknowledge financial support from the National Science Foundation via the Princeton Center for Complex Materials DMR-1420541 and by the ARO MURI W911NF-15-1-0397. I.C. acknowledges financial support from the Provincia Autonoma di Trento and from the FET-Open Grant MIR-BOSE (737017) and Quantum Flagship Grant PhoQuS (820392) of the European Union. The work of J.S. and D.I.S. was partially supported by the University of Chicago Materials Research Science and Engineering Center, which is funded by the National Science Foundation under award number DMR-1420709. J.S. and D.I.S. also acknowledge support from ARO MURI grant W911NF-15-1-0397.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Carusotto, I., Houck, A.A., Kollár, A.J. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020). https://doi.org/10.1038/s41567-020-0815-y
This article is cited by
Nature Communications (2022)
Nature Reviews Physics (2022)
Nature Physics (2022)
Nature Physics (2022)
Nature Physics (2022)