Two-state systems with non-Markovian thermal and squeezed quantum noise inputs
The effect of quantum noise on the two-state system is studied in the context of (i) coherent quantum tunnelling in a double-well system subject to low temperature quantum noise, and (ii) the two-level atom subject to finite bandwidth squeezed noise. Our approach to these problems is based on the adjoint equation, which describes the evolution of a quantum stochastic density operator. This equation is amenable to solution by ordinary stochastic methods, of which numerical simulation plays the most significant role in our calculations. The dissipative double-well system is relevant to the search for macroscopic quantum coherence in superconducting quantum interference devices, and previous work, starting from a two-state model and using path integral methods, has established the so-called “noninteracting-blip approximation” as a central result. The adjoint equation, applied to this problem in the weak coupling limit, is shown to closely reproduce this result. The noninteracting-blip approximation entails a Markovian-type assumption about the noise, and, by means of stochastic simulation, we are able to check, and confirm, the validity of this assumption, even for the case of a zero-temperature bath. Squeezed light, which has reduced quantum fluctuations in one quadrature phase, has been produced experimentally, and possible applications are under active consideration. Analyses of the effect of squeezed light on fundamental radiative processes in simple atoms have revealed interesting possibilities, most notably line-narrowing in the fluorescence spectrum. The original analyses in this field of research have been based on the assumption of broad bandwidth squeezing, and we review the primary results found in this limit. Also in this limit, we study in more detail the phenomenon of squeezed-light-induced photon echoes. For broad bandwidth squeezing, line-narrowing in resonance fluorescence is restricted to the central fluorescence peak, while the Rabi sidebands exhibit broadening. We examine strongly driven resonance fluorescence for the case in which squeezing is confined to relatively small regions of frequency space about individual fluorescence peaks. It is shown that the noisy component associated with the unsqueezed quadrature phase can be effectively decoupled from the atomic dynamics, which allows narrowing to occur in all three peaks of the spectrum. Finally, we address the practical problem of producing an effective coupling between an atom and a realistic three-dimensional squeezed field of modest angular spread. We show that this can be achieved, in principle, inside a microscopic plane mirror cavity, provided the injected squeezed field is suitably mode-matched to the cavity.
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