@phdthesis{Bakemeier2014,
author = {Lutz Bakemeier},
title = {Quantum to classical crossover in cavity QED and optomechanical systems},
journal = {{\"U}bergang von der Quantenmechanik zur klassischen Physik in Systemen der Quantenelektrodynamik in Kavit{\"a}ten und Optomechanik},
url = {https://nbn-resolving.org/urn:nbn:de:gbv:9-002089-6},
year = {2014},
abstract = {Modern cavity QED and cavity optomechanical systems realize the interaction of light with mesoscopic devices, which exhibit discrete (atom-like) energy spectra or perform micromechanical motion. In this thesis we have studied the crossover from the quantum regime to the classical limit of two prototypical models, the Dicke model and the generic optomechanical model. The physical problems considered in this approach range from a ground state phase transition, its dynamical response to general nonequilibrium dynamics including Hamiltonian and driven dissipative chaotic motion. The classical limit of these models follows from the classical limit of at least one of its subsystems. The classical equations of motion result from the respective quantum equations through the application of the semiclassical approximation, i.e., the neglect of quantum correlations. The approach of the results from quantum mechanics to the prediction of the classical equations can be obtained by subsequently decreasing the respective scaling parameter. In order to obtain exact results we have utilized advanced numerical methods, e.g., the Lanczos diagonalization method for ground state calculations, the Kernel Polynomial Method for dynamical response functions, Chebyshev recursion for time propagation, and quantum state diffusion for open system dynamics. We have studied the quantum phase transition of the Dicke model in the classical oscillator limit. Our work shows that in this limit the transition occurs already for finite spin length but with the same critical behavior as in the classical spin limit. We have derived an effective model for the oscillator degrees of freedom and have discussed the differences of both classical limits with respect to quantum fluctuations around the mean-field ground state and spin-oscillator entanglement. In this thesis we have proposed a variational ansatz for the Dicke model which extends the mean-field description through the inclusion of spin-oscillator correlations. The ansatz becomes correct in the limit of large oscillator frequency and in the limit of a large spin. For the latter it captures the leading quantum corrections to the classical limit exactly including the spin-oscillator entanglement entropy. We have studied the dynamics of spin and oscillator coherent states in the nonresonant Dicke model at weak coupling. In this regime periodic collapses and revivals of Rabi oscillations occur, which are accompanied by the buildup and decay of atom-field entanglement. The spin-oscillator wave function evolves into a superposition of multiple field coherent states that are correlated with the spin configuration. In our work we provide a description of the underlying dynamical mechanism based on perturbation theory. Our analysis shows that collapse and revival at nonresonance is distinguished from the resonant case treated within the rotating wave approximation by the appearance of two time scales instead of one. We have extended our study of the Dicke dynamics to the case of increasing spin length, as the system approaches the classical spin limit. We described the emergence of collective excitations above the ground state that converge to the coupled spin-oscillator oscillations observed in the classical limit. With increased spin length the corresponding Green functions thus reveal quantum dynamical signatures of the quantum phase transition. For the dynamics at larger coupling and energy, classical phase space drift and quantum diffusion hinders the direct comparison of quantum and classical observables. As we show in our work, signatures of classical quasiperiodic orbits can be identified in the Husimi phase-space functions of the propagated wave function and individual eigenstates with energies close to that of the quasiperiodic orbits. The analysis of the generic optomechanical system complements our study of cavity QED systems by a quantum dissipative system. In this thesis we have shown for the first time, how the route to chaos in the classical optomechanical system takes place, given as a sequence of consecutive period doubling bifurcations of self-induced cantilever oscillations. In addition to the semiclassical dynamics we have analyzed the possibility of chaotic motion in the quantum regime. Our results showed that quantum mechanics protects the optomechanical system against irregular dynamics. In sufficient distance to the semiclassical limit simple periodic orbits reappear and replace the classically chaotic motion. In this way direct observation of the dynamical properties of an optomechanical system makes it possible to pin down the crossover from quantum to classical mechanics.},
language = {en}
}