We prove that the observable telegraph signal accompanying the bistability in the photon-blockade-breakdown regime of the driven and lossy Jaynes–Cummings model is the finite-size precursor of what in the thermodynamic limit is a genuine first-order phase transition. We construct a finite-size scaling of the system parameters to a well-defined thermodynamic limit, in which the system remains the same microscopic system, but the telegraph signal becomes macroscopic both in its timescale and intensity. The existence of such a finite-size scaling completes and justifies the classification of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition.
Bistability in certain small quantum systems has been identified as signature of first order quantum phase transitions, however, this identification is problematic: a randomly switching telegraph signal between two well-resolved attractors can also be observed in quantum dynamics distinct from phase transitions. For example, the famous electron-shelving scheme – used in atomic clocks or for qubit measurement in ion-trap quantum computers – produces a similar signal without any connection to phase transitions.
There is a missing element to support the interpretation of bistability as a first-order quantum phase transition: it must be shown that bistability is only a finite-size effect, and there exists an idealized thermodynamic limit, where temporal bistability is replaced by hysteresis. This idealized thermodynamic limit can be introduced such that the physical system remains a small quantum system with a few degrees of freedom, that is, the passage to the thermodynamic limit does not involve a quantum-to-classical transition. In this paper, we present a prototype of this procedure by constructing a finite-size scaling for the recently-observed photon-blockade-breakdown effect to justify its classification as a first-order dissipative quantum phase transition.
 Carr C, Ritter R, Wade C G, Adams C S and Weatherill K J 2013 Phys. Rev. Lett. 111(11) 113901 URL https://doi.org/10.1103/PhysRevLett.111.113901.
 Marcuzzi M, Levi E, Diehl S, Garrahan J P and Lesanovsky I 2014 Phys. Rev. Lett. 113(21) 210401 URL https://doi.org/10.1103/PhysRevLett.113.210401.
 Malossi N, Valado M M, Scotto S, Huillery P, Pillet P, Ciampini D, Arimondo E and Morsch O 2014 Phys. Rev. Lett. 113(2) 023006 URL https://doi.org/10.1103/PhysRevLett.113.023006.
 Labouvie R, Santra B, Heun S and Ott H 2016 Phys. Rev. Lett. 116(23) 235302 URL https://doi.org/10.1103/PhysRevLett.116.235302.
 Le Boité A, Orso G and Ciuti C 2013 Phys. Rev. Lett. 110(23) 233601 URL https://doi.org/10.1103/PhysRevLett.110.233601.
 Rodriguez S R K, Casteels W, Storme F, Carlon Zambon N, Sagnes I, Le Gratiet L, Galopin E, Lemaı̂tre A, Amo A, Ciuti C and Bloch J 2017 Phys. Rev. Lett. 118(24) 247402 URL https://doi.org/10.1103/PhysRevLett.118.247402.
 Pályi A, Struck P R, Rudner M, Flensberg K and Burkard G 2012 Phys. Rev. Lett. 108(20) 206811 URL https://doi.org/10.1103/PhysRevLett.108.206811.
 Sachdev S 2011 Quantum Phase Transitions (Cambridge University Press) ISBN 978-0-521-51468-2.
 Marino J and Diehl S 2016 Phys. Rev. Lett. 116(7) 070407 URL https://doi.org/10.1103/PhysRevLett.116.070407.
 Brennecke F, Mottl R, Baumann K, Landig R, Donner T and Esslinger T 2013 Proceedings of the National Academy of Sciences 110 11763–11767 URL https://doi.org/10.1073/pnas.1306993110.
 Pietikäinen I, Danilin S, Kumar K S, Vepsäläinen A, Golubev D S, Tuorila J and Paraoanu G S 2017 Phys. Rev. B 96(2) 020501 URL https://doi.org/10.1103/PhysRevB.96.020501.
 Hwang M J, Puebla R and Plenio M B 2015 Phys. Rev. Lett. 115(18) 180404 URL https://doi.org/10.1103/PhysRevLett.115.180404.
 Hwang M J and Plenio M B 2016 Phys. Rev. Lett. 117(12) 123602 URL https://doi.org/10.1103/PhysRevLett.117.123602.
 Alsing P and Carmichael H 1991 Quantum Optics: Journal of the European Optical Society Part B 3 13 URL https://doi.org/10.1088/0954-8998/3/1/003.
 Paul Brookes, Giovanna Tancredi, Andrew D. Patterson, Joseph Rahamim, Martina Esposito, Themistoklis K. Mavrogordatos, Peter J. Leek, Eran Ginossar, and Marzena H. Szymanska, "Critical slowing down in circuit quantum electrodynamics", Science Advances 7 21, eabe9492 (2021).
 Xin H. H. Zhang and Harold U. Baranger, "Driven-dissipative phase transition in a Kerr oscillator: From semiclassical PT symmetry to quantum fluctuations", Physical Review A 103 3, 033711 (2021).
 Bruno O. Goes and Gabriel T. Landi, "Entropy production dynamics in quench protocols of a driven-dissipative critical system", Physical Review A 102 5, 052202 (2020).
 Bin-Bin Mao, Liangsheng Li, Wen-Long You, and Maoxin Liu, "Superradiant phase transition in quantum Rabi dimer with staggered couplings", Physica A: Statistical Mechanics and its Applications 564, 125534 (2021).
 Jonathan B. Curtis, Igor Boettcher, Jeremy T. Young, Mohammad F. Maghrebi, Howard Carmichael, Alexey V. Gorshkov, and Michael Foss-Feig, "Critical theory for the breakdown of photon blockade", Physical Review Research 3 2, 023062 (2021).
 Ricardo Gutiérrez-Jáuregui, "Breaking barriers: photon-blockade breakdown from the few quanta to the thermodynamic limit", Quantum Views 3, 14 (2019).
 I. Pietikäinen, J. Tuorila, D. S. Golubev, and G. S. Paraoanu, "Photon blockade and the quantum-to-classical transition in the driven-dissipative Josephson pendulum coupled to a resonator", Physical Review A 99 6, 063828 (2019).
 Bruno O. Goes, Carlos E. Fiore, and Gabriel T. Landi, "Quantum features of entropy production in driven-dissipative transitions", Physical Review Research 2 1, 013136 (2020).
 Th. K. Mavrogordatos, "Strong-coupling limit of the driven dissipative light-matter interaction", Physical Review A 100 3, 033810 (2019).
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