Quantum Speedup Of A Two-level Atom’s Evolution In Memory Environment

The number of orthogonal states passed through by a quantum system in unit time is the origin of quantum speed limit. Quantum speed limit is the basic problem of quantum measurement, quantum calculation and quantum communication, it concerns quantum computer’s physical extreme, the faster quantum system evolves, the faster corresponding computer process information. How to realize quantum speedup is attracting more and more attention. However, most of the current relevant literatures focus on the closed quantum system, studies of the open quantum system is necessary for realistic quantum system is affected by environment inevitably.The open quantum system dynamic has two classes, i.e. the markovian dynamics and the non-markovian dynamics. In markovian situation, there’s hardly any information exchange between atom and environment, it’s meaningless for realization of quantum speedup. In non-markovian situation, the environment can reserve the system’s information and feedback to it, cause its current state affected by its historical state, this affection maybe lead to quantum speedup, so it’s the emphasis in this article. Using a physical model of a two-level atom couple with a Bose bath, we have derived the system’s speed limit time in strong coupling situation and weak coupling situation, and display the relation of the QSL time and decay rate in ?gures by numerical integration. In addition, in view of the possible in?uence of driving time, we also calculate the QSL time in different driving time.The result shows that the memory effect can speedup quantum states’ evolution,stronger coupling lead to more obvious speedup, so is the situation when driving time is longer. Via further theoretical analysis, we found that it’s the coe?cient of environment’s non-Markovianity and atom’s excited states population result in quantum speedup.