Abstract
Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.
Highlights
Quantum evolution speed determines how quickly a quantum system needs to evolve between an initial state and a target state in a given process
Some methods have been provided to speed up quantum evolution for open systems, such as by engineering multiple environments[11], driving the system by an external classical field[12], and using the periodic dynamical decoupling pulse[13]
We have studied a classically driven qubit that is coupled to a photonic crystal (PC) waveguide
Summary
The end of the waveguide can be considered a perfect mirror, which can lead to form the systemenvironment bound state[24] and giant Lamb shift[25]. In this case, the photon dispersion relationship around the atomic frequency is of the form[26] ωk = ω0 + υ(k − k0),. In order to obtain the measure of dynamical speed in an explicit form, we can rewrite the evolved state ρt in tMhoerfoozromva-oČf eintscosvp-ePcettrzaflodrmecaolimsmp,otshietiionns,taρnt=tan∑keopuk sφskpeφedk. Any contractive Riemannian metric can be employed to evaluate the speed of evolution with a different type of MC function f(t).
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