Pulse propagation in maser-type traveling-wave amplifiers with a homogeneously broadened transition is treated by a formalism analogous to the Bloch equations. Phenomenological dephasing (T2) and recovery (T1) times are defined, and a linear (nonsaturable) loss mechanism is included. In the numerical calculations, only the case of negligible excitation during the time it takes a pulse to pass is considered. When pulses are allowed to grow until the amplifier is ``saturated,'' steady-state pulses having a unique shape and intensity independent of the initial pulse are found. The parameters of these steady-state pulses depend only on the ratio of the linear loss and gain coefficients. Steady-state pulses have a peak intensity that decreases monotonically from infinity to zero as the linear loss coefficient varies from zero to the gain coefficient, while the pulse width correspondingly varies from zero to infinity, and the pulse energy varies from a finite value to zero. Steady-state pulses propogate at a velocity less than that of the small signal velocity in the medium.
The use of entanglement in sensing is often motivated by improved sensitivity arising from non-classical correlations among probes. For static signals, however, this quantum advantage in Ramsey spectroscopy with N probes is known to be highly susceptible to dephasing, which severely limits the possible gain from entanglement. In contrast, we consider sensing of signals that vary in time. Considering the simplest example of dephasing by classical white noise, we show that entanglement allows a large increase in bandwidth when estimating the frequency components of a time-dependent signal. Without sacrificing any sensitivity, entanglement allows for an increase in bandwidth by a factor of N. Alternatively, when interrogation times are limited by the signal bandwidth rather than by dephasing, the average estimation uncertainty over a fixed bandwidth is reduced by a factor of N compared with separable states.
We analyze the steady state entanglement generated in a coherently coupled dimer system subject to dephasing noise as a function of the degree of Markovianity of the evolution. By keeping fixed the effective noise strength while varying the memory time of the environment, we demonstrate that non-Markovianity is an essential, quantifiable resource that may support the formation of steady state entanglement whereas purely Markovian dynamics governed by Lindblad master equations lead to separable steady states. This result illustrates possible mechanisms leading to long-lived entanglement in purely decohering, possibly local, environments. We present a feasible experimental demonstration of this noise assisted phenomenon using a system of trapped ions.