02137nas a2200133 4500008004100000245009800041210006900139260001400208520167400222100001801896700002501914700002701939856003701966 2019 eng d00aOn the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model0 anature of the nonequilibrium phase transition in the nonMarkovia c2019/10/93 a
The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this work, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents, including those, such as the dynamical critical exponent, that have not been previously considered. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely non-equilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that capture the system's long-time memory as well as its non-equilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.
1 aLundgren, Rex1 aGorshkov, Alexey, V.1 aMaghrebi, Mohammad, F. uhttps://arxiv.org/abs/1910.04319