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

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

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.

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.

► BibTeX data

► References

[1] Ates C, Olmos B, Garrahan J P and Lesanovsky I 2012 Phys. Rev. A 85(4) 043620 URL https:/​/​doi.org/​10.1103/​PhysRevA.85.043620.
https:/​/​doi.org/​10.1103/​PhysRevA.85.043620

[2] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.113901

[3] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.210401

[4] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.113.023006

[5] Overbeck V R, Maghrebi M F, Gorshkov A V and Weimer H 2017 Phys. Rev. A 95(4) 042133 URL https:/​/​doi.org/​10.1103/​PhysRevA.95.042133.
https:/​/​doi.org/​10.1103/​PhysRevA.95.042133

[6] Letscher F, Thomas O, Niederprüm T, Fleischhauer M and Ott H 2017 Phys. Rev. X 7(2) 021020 URL https:/​/​doi.org/​10.1103/​PhysRevX.7.021020.
https:/​/​doi.org/​10.1103/​PhysRevX.7.021020

[7] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.116.235302

[8] Le Boité A, Orso G and Ciuti C 2013 Phys. Rev. Lett. 110(23) 233601 URL https:/​/​doi.org/​10.1103/​PhysRevLett.110.233601.
https:/​/​doi.org/​10.1103/​PhysRevLett.110.233601

[9] Casteels W and Ciuti C 2017 Phys. Rev. A 95(1) 013812 URL https:/​/​doi.org/​10.1103/​PhysRevA.95.013812.
https:/​/​doi.org/​10.1103/​PhysRevA.95.013812

[10] Casteels W, Fazio R and Ciuti C 2017 Phys. Rev. A 95(1) 012128 URL https:/​/​doi.org/​10.1103/​PhysRevA.95.012128.
https:/​/​doi.org/​10.1103/​PhysRevA.95.012128

[11] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.118.247402

[12] Fink T, Schade A, Höfling S, Schneider C and Imamoglu A 2018 Nature Physics 14 365–369 URL https:/​/​doi.org/​10.1038/​s41567-017-0020-9.
https:/​/​doi.org/​10.1038/​s41567-017-0020-9

[13] Carmichael H J 2015 Phys. Rev. X 5(3) 031028 URL https:/​/​doi.org/​10.1103/​PhysRevX.5.031028.
https:/​/​doi.org/​10.1103/​PhysRevX.5.031028

[14] Dombi, András, Vukics, András and Domokos, Peter 2015 Eur. Phys. J. D 69 60 URL https:/​/​doi.org/​10.1140/​epjd/​e2015-50861-9.
https:/​/​doi.org/​10.1140/​epjd/​e2015-50861-9

[15] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.108.206811

[16] Fink J M, Dombi A, Vukics A, Wallraff A and Domokos P 2017 Phys. Rev. X 7(1) 011012 URL https:/​/​doi.org/​10.1103/​PhysRevX.7.011012.
https:/​/​doi.org/​10.1103/​PhysRevX.7.011012

[17] Bergquist J C, Hulet R G, Itano W M and Wineland D J 1986 Phys. Rev. Lett. 57(14) 1699–1702 URL https:/​/​doi.org/​10.1103/​PhysRevLett.57.1699.
https:/​/​doi.org/​10.1103/​PhysRevLett.57.1699

[18] Sachdev S 2011 Quantum Phase Transitions (Cambridge University Press) ISBN 978-0-521-51468-2.

[19] Marino J and Diehl S 2016 Phys. Rev. Lett. 116(7) 070407 URL https:/​/​doi.org/​10.1103/​PhysRevLett.116.070407.
https:/​/​doi.org/​10.1103/​PhysRevLett.116.070407

[20] Gutiérrez-Jáuregui R and Carmichael H J 2018 Phys. Rev. A 98(2) 023804 URL https:/​/​doi.org/​10.1103/​PhysRevA.98.023804.
https:/​/​doi.org/​10.1103/​PhysRevA.98.023804

[21] Reiter F, Nguyen T L, Home J P and Yelin S F 2018 arXiv preprint arXiv:1807.06026.
arXiv:1807.06026

[22] Nagy D, Szirmai G and Domokos P 2011 Phys. Rev. A 84(4) 043637 URL https:/​/​doi.org/​10.1103/​PhysRevA.84.043637.
https:/​/​doi.org/​10.1103/​PhysRevA.84.043637

[23] 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.
https:/​/​doi.org/​10.1073/​pnas.1306993110

[24] Bonifacio R, Gronchi M and Lugiato L A 1978 Phys. Rev. A 18(5) 2266–2279 URL https:/​/​doi.org/​10.1103/​PhysRevA.18.2266.
https:/​/​doi.org/​10.1103/​PhysRevA.18.2266

[25] 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.
https:/​/​doi.org/​10.1103/​PhysRevB.96.020501

[26] Pietikäinen I, Tuorila J, Golubev D and Paraoanu G 2019 arXiv preprint arXiv:1901.05655.
arXiv:1901.05655

[27] 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.
https:/​/​doi.org/​10.1103/​PhysRevLett.115.180404

[28] Hwang M J and Plenio M B 2016 Phys. Rev. Lett. 117(12) 123602 URL https:/​/​doi.org/​10.1103/​PhysRevLett.117.123602.
https:/​/​doi.org/​10.1103/​PhysRevLett.117.123602

[29] Larson J and Irish E K 2017 Journal of Physics A: Mathematical and Theoretical 50 174002 URL https:/​/​doi.org/​10.1088/​1751-8121/​aa65dc.
https:/​/​doi.org/​10.1088/​1751-8121/​aa65dc

[30] Hwang M J, Rabl P and Plenio M B 2018 Phys. Rev. A 97(1) 013825 URL https:/​/​doi.org/​10.1103/​PhysRevA.97.013825.
https:/​/​doi.org/​10.1103/​PhysRevA.97.013825

[31] Alsing P, Guo D S and Carmichael H 1992 Physical Review A 45 5135 URL https:/​/​doi.org/​10.1103/​PhysRevA.45.5135.
https:/​/​doi.org/​10.1103/​PhysRevA.45.5135

[32] 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.
https:/​/​doi.org/​10.1088/​0954-8998/​3/​1/​003

[33] Gutiérrez-Jáuregui R and Carmichael H J 2018 Phys. Rev. A 98(2) 023804 URL https:/​/​doi.org/​10.1103/​PhysRevA.98.023804.
https:/​/​doi.org/​10.1103/​PhysRevA.98.023804

[34] Vukics A and Ritsch H 2007 European Physical Journal D 44 585–599 URL https:/​/​doi.org/​10.1140/​epjd/​e2007-00210-x.
https:/​/​doi.org/​10.1140/​epjd/​e2007-00210-x

[35] Vukics A 2012 Computer Physics Communications 183 1381–1396 URL https:/​/​doi.org/​10.1016/​j.cpc.2012.02.004.
https:/​/​doi.org/​10.1016/​j.cpc.2012.02.004

[36] Sandner R and Vukics A 2014 Computer Physics Communications 185 2380 – 2382 URL https:/​/​doi.org/​10.1016/​j.cpc.2014.04.011.
https:/​/​doi.org/​10.1016/​j.cpc.2014.04.011

Cited by

[1] 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).

[2] 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).

[3] 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).

[4] 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).

[5] 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).

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

[7] 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).

[8] 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).

[9] Th. K. Mavrogordatos, "Strong-coupling limit of the driven dissipative light-matter interaction", Physical Review A 100 3, 033810 (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2021-10-19 21:10:17). The list may be incomplete as not all publishers provide suitable and complete citation data.

On SAO/NASA ADS no data on citing works was found (last attempt 2021-10-19 21:10:17).

1 thought on “Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition

  1. Pingback: Perspective in Quantum Views by Ricardo Gutiérrez-Jáuregui "Breaking barriers: photon-blockade breakdown from the few quanta to the thermodynamic limit"