Generating Three-dimensional Entanglement Via Shortcuts To Adiabaticity

High-dimensional entanglement has been paid more and more attention in recent decade because of its more superiorities than qubit entanglement.In recent years,in order to speed up the slow quantum adiabatic process,researchers have proposed and been developing shortcut-to-adiabaticity techniques.In order to fast and accurately obtain robust high-dimensional entanglement,we propose a series of shortcut-to-adiabaticity schemes to generate three-dimensional entanglement.(1)A scheme is proposed for the fast generation of three-dimensional entangle-ment between two atoms trapped in two cavities connected by a fiber via invariant-based shortcut to adiabaticity.We pick appropriate parameters and discuss robust-ness and feasibility of the scheme by numerical simulations.(2)We propose Lewis-Riesenfeld-invariant scheme and transitionless-quantum-driving scheme for the preparation of three-atom tree-type three-dimensional en-tanglement.Numerical simulations show that the parameters we choose can guar-antee high-fidelity three-atom tree-type three-dimensional entangled states.The two schemes are both robust against the variations in the parameters,atomic spon-taneous emissions and the cavity-fiber photon leakages.In addition,we discuss shortcomings and disadvantages of the two schemes.(3)In order to address the problems during generating three-atom tree-type three-dimensional entanglement by using the Lewis-Riesenfeld-invariant scheme and the transitionless-quantum-driving scheme,we propose superadiabatic-shortcut scheme for optimizing the fast generation of three-atom tree-type 3D entanglement.Su-per adiabatic pulses are easily-implemented double-peak Gaussian pulses,and the resulting population transfer is almost perfect.(4)In order to depress the populations of excited states,we investigate a new method to construct shortcut to adiabaticity.We propose the chosen-path scheme for fast generating three-dimensional entanglement between a single atom and a BEC.The target state can be rapidly obtained,and the population of the lossy intermediate state can be controlled by setting proper parameters.