Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition

A. Vukics1, A. Dombi1, J. M. Fink2, and P. Domokos1

1Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49., Hungary
2Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria

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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.

The dataset of simulations may be found here.

First-order phase transitions characterized by the coexistence of phases are commonly observed in the surrounding world, e.g. in the freezing of water. Continuous – second-order – phase transitions also exist in classical physics, e.g. the transition between ferro- and paramagnetism at the Curie temperature. Whereas the latter class has seen straightforward generalizations to quantum systems for decades, the notion of a first-order quantum phase transition remains to be elucidated.

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.

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[1] B. Gábor, D. Nagy, A. Dombi, T. W. Clark, F. I. B. Williams, K. V. Adwaith, A. Vukics, and P. Domokos, "Ground-state bistability of cold atoms in a cavity", Physical Review A 107 2, 023713 (2023).

[2] 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).

[3] Ricardo Gutiérrez-Jáuregui, "Breaking barriers: photon-blockade breakdown from the few quanta to the thermodynamic limit", Quantum Views 3, 14 (2019).

[4] 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).

[5] T. W. Clark, A. Dombi, F. I. B. Williams, Á. Kurkó, J. Fortágh, D. Nagy, A. Vukics, and P. Domokos, "Time-resolved observation of a dynamical phase transition with atoms in a cavity", Physical Review A 105 6, 063712 (2022).

[6] 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).

[7] 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).

[8] Hong Li, Ming Liu, Feng Yang, Siqi Zhang, and Shengping Ruan, "Phase-Controlled Tunable Unconventional Photon Blockade in a Single-Atom-Cavity System", Micromachines 14 11, 2123 (2023).

[9] 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).

[10] B. Gábor, D. Nagy, A. Vukics, and P. Domokos, "Quantum bistability in the hyperfine ground state of atoms", Physical Review Research 5 4, L042038 (2023).

[11] 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).

[12] Andrus Giraldo, Stuart J. Masson, Neil G. R. Broderick, and Bernd Krauskopf, "Semiclassical bifurcations and quantum trajectories: a case study of the open Bose–Hubbard dimer", The European Physical Journal Special Topics 231 3, 385 (2022).

[13] Riya Sett, Farid Hassani, Duc Phan, Shabir Barzanjeh, Andras Vukics, and Johannes M. Fink, "Emergent Macroscopic Bistability Induced by a Single Superconducting Qubit", PRX Quantum 5 1, 010327 (2024).

[14] 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).

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The above citations are from Crossref's cited-by service (last updated successfully 2024-04-12 13:59:56) and SAO/NASA ADS (last updated successfully 2024-04-12 13:59:57). The list may be incomplete as not all publishers provide suitable and complete citation data.

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