Directional pumping of a two-level system by a fluctuation-regulated quantum source

Abstract

A resonant classical field drives a two-level system coherently and, with ordinary relaxation, produces saturation rather than directional population transfer. Here we show that directionality emerges when the excitation source is retained as a quantum subsystem and subsequently traced out. We model the source as a single-excitation degree of freedom, or equivalently a stream of two-level ancillas, exchange-coupled to a target two-level system. The source first moment generates the usual coherent drive, while its second moments produce upward and downward dissipative channels. For a number-diagonal, fully excited source, the first moment vanishes and only the upward channel remains, yielding monotonic pumping of the target. The same structure follows from both an exact collision map and a fluctuation-regulated second-order quantum master equation. For exponentially decaying source correlations, the pumping rate shows a Lorentzian detuning dependence governed by the correlation time $τ_c$, accompanied by a dispersive frequency shift. In the presence of thermal relaxation, the steady-state excited-state population can exceed the resonantly driven optical-Bloch limit of one half. Within the fluctuation-regulated master equation, this directional pumping arises as a drive-induced dissipative contribution whose strength and spectral response are controlled by $τ_c$.