The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

doi:10.1088/1674-1056/28/8/080301

Abstract The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.

Keywords: adiabatic dynamics parametric driving upper bound function

Received: 16 March 2019
Revised: 29 May 2019
Accepted manuscript online:

PACS:	03.65.Ca	(Formalism)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	03.65.Vf	(Phases: geometric; dynamic or topological)

Fund: Project supported by the National Natural Science Foundation of China (Emergency Project, Grant Nos. 11447025 and 11847308).

Corresponding Authors: Lin Zhang
E-mail: zhanglincn@snnu.edu.cn

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Lin Zhang(张林), Junpeng Liu(刘军鹏) The upper bound function of nonadiabatic dynamics in parametric driving quantum systems 2019 Chin. Phys. B 28 080301

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The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

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