Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model
159
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 systems 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.
rate research
Read More
We study the ergodic -- non-ergodic transition in a generalized Dicke model with independent co- and counter rotating light-matter coupling terms. By studying level statistics, the average ratio of consecutive level spacings, and the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we show that the ergodic -- non-ergodic transition in the Dicke model is a consequence of the proximity to the integrable limit of the model when one of the couplings is set to zero. This can be interpreted as a hint for the existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser theorem. Besides, we show that there is no intrinsic relation between the ergodic -- non-ergodic transition and the precursors of the normal -- superradiant quantum phase transition.
We study the quantum phase transition of the Dicke model in the classical oscillator limit, where it occurs already for finite spin length. In contrast to the classical spin limit, for which spin-oscillator entanglement diverges at the transition, entanglement in the classical oscillator limit remains small. We derive the quantum phase transition with identical critical behavior in the two classical limits and explain the differences with respect to quantum fluctuations around the mean-field ground state through an effective model for the oscillator degrees of freedom. With numerical data for the full quantum model we study convergence to the classical limits. We contrast the classical oscillator limit with the dual limit of a high frequency oscillator, where the spin degrees of freedom are described by the Lipkin-Meshkov-Glick model. An alternative limit can be defined for the Rabi case of spin length one-half, in which spin frequency renormalization replaces the quantum phase transition.
The quantum phase transition of the Dicke-model has been observed recently in a system formed by motional excitations of a laser-driven Bose--Einstein condensate coupled to an optical cavity [1]. The cavity-based system is intrinsically open: photons can leak out of the cavity where they are detected. Even at zero temperature, the continuous weak measurement of the photon number leads to an irreversible dynamics towards a steady-state which exhibits a dynamical quantum phase transition. However, whereas the critical point and the mean field is only slightly modified with respect to the phase transition in the ground state, the entanglement and the critical exponents of the singular quantum correlations are significantly different in the two cases.
We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate age, related to the time one has spent holding the same state, as a part of the description. We show that, in some cases, the model can be reduced to an effective Markovian process, where the age distribution of the population rapidly equilibrates to a quasi-steady state, while the global state of the system is out of equilibrium. This effective Markovian process shares the same phenomenology of the non-linear noisy-voter model and we establish a clear parallelism between these two extensions of the noisy-voter model.
Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
