Trade-off between speed and cost in shortcuts to adiabaticity

2016/09/30 by Steve Campbell, Sebastian Deffner · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physrevlett.118.100601

published as Phys. Rev. Lett. 118, 100601 (2017) · 7 pages, 2 figures. Close to published version. v4 corrects minor errors in figures

arxiv created 2017/08/07 · arxiv updated 2017/08/09

Abstract

Achieving effectively adiabatic dynamics is a ubiquitous goal in almost all areas of quantum physics. Here, we study the speed with which a quantum system can be driven when employing transitionless quantum driving. As a main result, we establish a rigorous link between this speed, the quantum speed limit, and the (energetic) cost of implementing such a shortcut to adiabaticity. Interestingly, this link elucidates a trade-off between speed and cost, namely that instantaneous manipulation is impossible as it requires an infinite cost. These findings are illustrated for two experimentally relevant systems - the parametric oscillator and the Landau-Zener model - which reveal that the spectral gap governs the quantum speed limit as well as the cost for realizing the shortcut.

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