Shortcuts To Adiabaticity For Controlling Population Transfer In Multiple-level Systems And Their Applications

Fast and accurate quantum state preparation and manipulation is a hot topic in the fields of quantum information processing and quantum computing.It has potential application in quantum information,quantum communication,quantum measurement and quantum sensing.It is well known that the quantum adiabatic process has been widely used due to its robustness.However,its long operating time will significantly enhance the destruction of quantization due to decoherence effect.Therefore,in order to achieve fast and robust quantum state manipulation,people have developed the “shortcut to adiabaticity(STA)” technique to accelerate the adiabatic process,so that the system can achieve the same dynamic evolution result as quantum adiabatic process in short time.In this thesis,we select atomic or ionic internal states as the physical carriers of qubit to study the implementations of STA in effective two-and multiple-level systems and their application for quantum state controlling and preparation.The results achieved are as follows:Firstly,we start from the stimulated Raman adiabatic passage(STIRAP)in the three-level system by using the counter-diabatic driving method.In the cases of large detuning and single-photon resonance,we both reduce the three-level systems to the effective two-level systems and apply the counter-diabatic terms to obtain the corrected Raman laser fields,which achieves the experiment-feasible stimulated Raman shortcutto-adiabatic passage(STIRSAP).This protocol has been finally verified in atomic experimental system.Secondly,for the rare-earth ions qubit system,by combining the inverse engineering technique based on Lewis-Riesenfeld quantum invariant and optimization algorithm,we design the STA pulses to manipulate qubits closely spaced in frequency spectrum with a high fidelity.This protocol is robust against the fluctuations in frequency detuning and Rabi frequencies,and simultaneously avoid disturbance caused by excitation of off-resonance ions.Thirdly,by parameterizing the real part of Hamiltonian and evolution operator via geometric four-dimensional rotation and the quaternion,we study the STA inverse engineering method in the four-level system.Combined with cold atoms,optical lattices and quantum dot systems,the three common structures-N-type,inverted tripod type and diamond type-are exemplified.We achieve the arbitrary manipulation of quantum states in short time.Furthermore,in particular,a single-electron spin in a double quantum dot system with strong spin-orbit coupling effect is studied.We apply the above four-level system STA protocol to design the intensities of tunneling rates and spin-orbit couplings respectively with taking into account the perturbation of spin controlling caused by disturbance of electric field in practice.Finally we achieve the robust single electron transportation between double quantum dots while flipping the spin in short time.