Characterizing Superradiant Phase of the Quantum Rabi Model
Yun-Tong Yang1,2 and Hong-Gang Luo1,2,3*
1School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China 2Lanzhou Center for Theoretical Physics & Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China 3Beijing Computational Science Research Center, Beijing 100084, China
Abstract：Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalizations to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus, one is able to see how the phase transition occurs and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition takes place and further exhibits the statistics of Gaussian unitary ensemble with increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.
. [J]. 中国物理快报, 2023, 40(2): 20502-.
Yun-Tong Yang and Hong-Gang Luo. Characterizing Superradiant Phase of the Quantum Rabi Model. Chin. Phys. Lett., 2023, 40(2): 20502-.
Monroe C, Campbell W C, Duan L M, Gong Z X, Gorshkov A V, Hess P W, Islam R, Kim K, Linke N M, Pagano G, Richerme P, Senko C, and Yao N Y 2021 Rev. Mod. Phys.93 025001
The Supplemental Material provides the detailed comparison of the energies of the ground state and excited states with those obtained by numerically ED and the detailed fittings of the photons population in various cases.
2023, Vol. 40 
