Abstract:
In this Thesis we consider various quantum systems in a resonator where coherent feedback of one of the output fields into another input channel is applied without any measurements performed on the field. A finite time delay associated with propagation is considered as an important control parameter. In the short-delay regime, where the output field is fed back before the resonator field decays away, most properties are determined by the interference between the returning and the emitted field. Constructive and destructive interference results in an enhanced or suppressed decay of the resonator field, respectively. The reduced emission of the resonator is found to cause enhanced quantum behaviour of the system, such as the preservation of atomic coherence, enhanced negativity in the Wigner function or the recovery of revivals after a coherent-state collapse. In the long-delay regime, where all the resonator field decays away before the output field is fed back, the specific value of the time delay has a much greater impact. Altered dynamics e.g., emergence of stable periodic solutions, and modified characteristic properties such as frequency or strength of inherent quantum features, e.g., squeezing or entanglement are demonstrated. The specific structure of the feedback reservoir also influences the observed characteristics. Continuous-mode feedback is intrinsically lossy, and thus, the fine balance created between the loss and the feedback gain results in recovered Rabi oscillations for an open Jaynes-Cummings system. A discrete-mode structure, on the other hand, can preserve the atomic excitation in the same setup. The coupled system scheme where two Fabry-Perot cavities containing atoms are coupled by an optical fibre inherently involves a discrete-mode time-delayed coherent feedback. The transmission and reflection spectra of such a setup has been studied experimentally by Prof. Takao Aoki’s group in the weak-driving regime. These results can mostly be recovered using the normal modes of the single-mode master equation. For a more accurate description we consider a transfer matrix approach which applies even for long cavity lengths and reduced mirror reflectances. Finally, a numerical method based on matrix product states is applied to study the non-Markovian features of the dynamics in this system.