Parameters Drive The Adiabatic Conditions And Adiabatic Shortcuts Of Quantum Systems

The adiabatic control is a powerful technique for many practical applications in quan-tum state engineering,light-driven chemical reactions and geometrical quantum compu-tations.This thesis 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 in unit time 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.As the research hotspot over the past decade in quantum control field,shortcut to adiabaticity(STA)has been extensively applied in each domain,because it overcomes the requirements of quantum adiabatic process which needs a slow driving for long time,while keeps a good robustness,although the description of theory for STA is still lack in details.In this paper,STA of inverse control method based on invariants is explained in depth.The natural advantages of the Lie transformation method lead to obtain the exact solutions of the Schrodinger equation and design the invariants conveniently,so that the boundary of the design scheme for STA is given.Finally,a typical harmonic oscillator model and an infinite well with a moving boundary are combined to demonstrate the design process in detail.