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The European Physical Journal Plus

Quantum speed limit time and purity of open two-level atom without rotating wave approximation

Kalim Ullah Khan, Salman Khan

Published Aug 10, 2024• 1 citation
Publisher
DOI
10.1140/epjp/s13360-024-05498-0

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Scientific Reports•Feb 13, 2015•107 citations
Dynamics of quantum speed limit (QSL) time, under the scenario of frequent measurements on the system, of a two-level atom interacting with the vacuum electromagnetic field without the rotating wave approximation (RWA) are studied. The effects of three different interacting spectra, namely, super-ohmic, ohmic, and sub-ohmic, are analyzed. The behavior of QSL time shows control switching from quantum Zeno effect (QZE) to quantum anti-Zeno effect (QAZE) for certain choices of the parameter space of the Hamiltonian of the system. Graphical analysis of our results shows that the super-ohmic spectrum might be a better choice for certain quantum information tasks than the other two spectra considered here.
We derive an easily computable quantum speed limit (QSL) time bound for open systems whose initial states can be chosen as either pure or mixed states. Moreover, this QSL time is applicable to either Markovian or non-Markovian dynamics. By using of a hierarchy equation method, we numerically study the QSL time bound in a qubit system interacting with a single broadened cavity mode without rotating-wave, Born and Markovian approximation. By comparing with rotating-wave approximation (RWA) results, we show that the counter-rotating terms are helpful to increase evolution speed. The problem of non-Markovianity is also considered. We find that for non-RWA cases, increasing system-bath coupling can not always enhance the non-Markovianity, which is qualitatively different from the results with RWA. When considering the relation between QSL and non-Markovianity, we find that for small broadening widths of the cavity mode, non-Markovianity can increase the evolution speed in either RWA or non-RWA cases, while, for larger broadening widths, it is not true for non-RWA cases.