Finite-size scaling of the photon-blockade breakdown dissipative quantum phase transition
1Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49., Hungary
2Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria
| Published: | 2019-06-03, volume 3, page 150 |
| Eprint: | arXiv:1809.09737v2 |
| Doi: | https://doi.org/10.22331/q-2019-06-03-150 |
| Citation: | Quantum 3, 150 (2019). |
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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.
Featured image: Montage: phase diagram (left) level scheme (top right) and time-resolved quantum jumps (bottom right) in the photon-blockade breakthrough effect.
The dataset of simulations may be found here.
Popular summary
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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[9] Ricardo Gutiérrez-Jáuregui, "Breaking barriers: photon-blockade breakdown from the few quanta to the thermodynamic limit", Quantum Views 3, 14 (2019).
[10] 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).
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