Quantum Phase Transition and Universal Dynamics in the Rabi Model

Physical Review Letters
Myung-Joong HwangMartin B Plenio

Abstract

We consider the Rabi Hamiltonian, which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in the unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal; that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.

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Citations

Dec 30, 2017·Physical Review Letters·Maoxin LiuHai-Qing Lin
Jan 20, 2018·Physical Review. E·Wassilij KopylovTobias Brandes
Jan 5, 2019·Physical Review Letters·Nicolò DefenuGiovanna Morigi
May 23, 2019·Nature Communications·Balázs DóraRoderich Moessner
Feb 15, 2020·Physical Review Letters·Simone Felicetti, Alexandre Le Boité
Mar 7, 2020·Physical Review Letters·C J ZhuG S Agarwal
Apr 26, 2020·Scientific Reports·Jun JingLian-Ao Wu
Apr 14, 2020·Physical Review Letters·Louis GarbeSimone Felicetti
Jun 25, 2020·Physical Review. E·Sascha WaldFernando L Semião
Mar 4, 2017·Physical Review Letters·Ricardo PueblaMartin B Plenio
Nov 16, 2019·Scientific Reports·Alejandro R UrzúaHéctor M Moya-Cessa
Dec 5, 2019·Scientific Reports·Liwei DuanQing-Hu Chen
Oct 22, 2019·Physical Review Letters·Vasiliy MakhalovSylvain Nascimbene
Jul 1, 2020·Physical Review Letters·Ricardo PueblaMartin B Plenio
Jul 9, 2020·Physical Review Letters·Fernando J Gómez-RuizAdolfo Del Campo
Aug 17, 2020·Physical Review Letters·Paraj Titum, Mohammad F Maghrebi
Dec 15, 2016·Physical Review. E·Armando RelañoJorge Dukelsky
Dec 30, 2017·Physical Review Letters·Mehdi AbdiMartin B Plenio
Oct 1, 2016·Physical Review Letters·Myung-Joong Hwang, Martin B Plenio
Aug 17, 2020·Physical Review Letters·Han-Jie ZhuWu-Ming Liu
Sep 24, 2016·Optics Express·Z C ShiX X Yi
Jan 23, 2021·Physical Review Letters·Yaoming ChuJianming Cai
Apr 18, 2021·Physical Review. E·Zakaria MzaoualiSteve Campbell
Aug 24, 2021·Physical Review Letters·Yu-Yu ZhangXue-Feng Zhang

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