Abstract
Understanding and characterizing phase transitions in driven-dissipative systems constitutes a new frontier for many-body physics1,2,3,4,5,6,7,8. A generic feature of dissipative phase transitions is a vanishing gap in the Liouvillian spectrum9, which leads to long-lived deviations from the steady state as the system is driven towards the transition. Here, we show that photon correlation measurements can be used to characterize the corresponding critical slowing down of non-equilibrium dynamics. We focus on the extensively studied phenomenon of optical bistability in GaAs cavity polaritons10,11, which can be described as a first-order dissipative phase transition12,13,14. Increasing the excitation strength towards the bistable range results in an increasing photon-bunching signal along with a decay time that is prolonged by more than nine orders of magnitude as compared with that of single polaritons. In the limit of strong polariton interactions leading to pronounced quantum fluctuations, the mean-field bistability threshold is washed out. Nevertheless, the functional form with which the Liouvillian gap closes as the thermodynamic limit is approached provides a signature of the emerging dissipative phase transition. Our results establish photon correlation measurements as an invaluable tool for studying dynamical properties of dissipative phase transitions without requiring phase-sensitive interferometric measurements.
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References
Diehl, S. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008).
Verstraete, F., Wolf, M. M. & Cirac, J. I. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633–636 (2009).
Diehl, S., Tomadin, A., Micheli, A., Fazio, R. & Zoller, P. Dynamical phase transitions and instabilities in open atomic many-body systems. Phys. Rev. Lett. 105, 015702 (2010).
Le Boité, A., Orso, G. & Ciuti, C. Steady-state phases and tunneling-induced instabilities in the driven dissipative bose-hubbard model. Phys. Rev. Lett. 110, 233601 (2013).
Carmichael, H. J. Breakdown of photon blockade: a dissipative quantum phase transition in zero dimensions. Phys. Rev. X 5, 031028 (2015).
Fink, J. M., Dombi, A., Vukics, A., Wallra, A. & Domokos, P. Observation of the photon-blockade breakdown phase transition. Phys. Rev. X 7, 011012 (2017).
Wilson, R. M. et al. Collective phases of strongly interacting cavity photons. Phys. Rev. A 94, 033801 (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).
Kessler, E. M. et al. Dissipative phase transition in a central spin system. Phys. Rev. A 86, 012116 (2012).
Baas, A., Karr, J. P., Eleuch, H. & Giacobino, E. Optical bistability in semiconductor microcavities. Phys. Rev. A 69, 023809 (2004).
Boulier, T. et al. Polariton-generated intensity squeezing in semiconductor micropillars. Nat. Commun. 5, 3260 (2014).
Drummond, P. D. & Walls, D. F. Quantum theory of optical bistability. I. Nonlinear polarisability model. J. Phys. A. Math. Gen. 13, 725–741 (1980).
Casteels, W., Storme, F., Le Boité, A. & Ciuti, C. Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators. Phys. Rev. A 93, 033824 (2016).
Casteels, W., Fazio, R. & Ciuti, C. Critical dynamical properties of a first-order dissipative phase transition. Phys. Rev. A 95, 012128 (2017).
Gibbs, H. M., McCall, S. L. & Venkatesan, T. N. C. Differential gain and bistability using a sodium-filled Fabry-Perot interferometer. Phys. Rev. Lett. 36, 1135–1138 (1976).
Almeida, V. R. & Lipson, M. Optical bistability on a silicon chip. Opt. Lett. 29, 2387–2389 (2004).
Wurtz, G. A., Pollard, R. & Zayats, A. V. Optical bistability in nonlinear surface-plasmon polaritonic crystals. Phys. Rev. Lett. 97, 057402 (2006).
Kheruntsyan, K. V. Wigner function for a driven anharmonic oscillator. J. Opt. B 1, 225–233 (1999).
Risken, H., Savage, C., Haake, F. & Walls, D. F. Quantum tunneling in dispersive optical bistability. Phys. Rev. A 35, 1729–1739 (1987).
Lett, P., Christian, W., Singh, S. & Mandel, L. Macroscopic quantum fluctuations and first-order phase transition in a laser. Phys. Rev. Lett. 47, 1892–1895 (1981).
Letscher, F., Thomas, O., Niederprüm, T., Fleischhauer, M. & Ott, H. Bistability versus metastability in driven dissipative Rydberg gases. Phys. Rev. X 7, 021020 (2017).
Rodriguez, S. R. K. et al. Probing a dissipative phase transition via dynamical optical hysteresis. Phys. Rev. Lett. 118, 247402 (2017).
Kasprzak, J. et al. Bose-Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).
Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).
Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).
Amo, A. et al. Exciton-polariton spin switches. Nat. Photon. 4, 361–366 (2010).
Ballarini, D. et al. All-optical polariton transistor. Nat. Commun. 4, 1778 (2013).
Hartmann, M. J. Quantum simulation with interacting photons. J. Optics 18, 104005 (2016).
Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Prog. Phys. 80, 016401 (2017).
Carusotto, I. Linear and Nonlinear Optics in Bose Fields: Light Waves in Dielectric Structures, Matter Waves in Optical Lattices PhD thesis, Scuola Normale Superiore di Pisa (2000).
Goldsztein, G. H., Broner, F. & Strogatz, S. H. Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions. SIAM. J. Appl. Math. 57, 1163–1187 (1997).
Sachdev, S. Quantum Phase Transitions. 2nd edn, (Cambridge Univ. Press, Cambridge, 2011).
Jin, J., Rossini, D., Leib, M., Hartmann, M. J. & Fazio, R. Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities. Phys. Rev. A 90, 023827 (2014).
Mendoza-Arenas, J. J. et al. Beyond mean-field bistability in driven-dissipative lattices: bunching-antibunching transition and quantum simulation. Phys. Rev. A 93, 023821 (2016).
Foss-Feig, M. et al. Emergent equilibrium in many-body optical bistability. Phys. Rev. A 95, 043826 (2017).
Besga, B. et al. Polariton boxes in a tunable fiber cavity. Phys. Rev. Appl. 3, 014008 (2015).
Acknowledgements
We would like to thank A. Reinhard, T. Volz and J. Reichel for early work that led to the development of the semiconductor fibre cavity structure used in this work. We also acknowledge fruitful discussions with C. Ciuti and S. Zeytinoğlu. This work was supported by the Swiss National Science Foundation (SNSF) through the National Centre of Competence in Research - Quantum Science and Technology (NCCR QSIT). A.S., C.S. and S.H. acknowledge support by the State of Bavaria and the Deutsche Forschungsgemeinschaft within the Project Schn1376/3–1.
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T.F. and A.I. designed and supervised the experiment. T.F. carried out the measurements. A.S., S.H., and C.S. grew the sample. T.F. and A.I. wrote the manuscript.
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Fink, T., Schade, A., Höfling, S. et al. Signatures of a dissipative phase transition in photon correlation measurements. Nature Phys 14, 365–369 (2018). https://doi.org/10.1038/s41567-017-0020-9
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DOI: https://doi.org/10.1038/s41567-017-0020-9
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