Research On Non-adiabatic Control Of Two-level And Three-level Systems Based On Shortcuts To Adiabaticity

Quantum information processing is the process of controlled quantum evolution.Quantum adiabaticity is one of the non-dissipative mode of evolution process,the disadvantage of it is need a long runtime.Rapid pulse control can implement the necessary quantum operations in a short period of time,while it is sensitive to the changes of pulse intensity and area,and it will result in non-accurate control and appear unwanted deviation.Based on this,researchers try to find the method of quantum control to speed up the quantum adiabatic process and achieve fast quantum information processing.The shortcuts to adiabaticity provide protocols that speed up quantum adiabatic process.They have been widely used to implement fast and robust quantum information processing,such as quantum state transfer,quantum gates and quantum entanglement generation,and so on,by designing an experimental feasible Hamiltonian.This paper control the process of quantum evolution with two-level and three-level quantum systems by using inverse engineering based on Lewis-Riesenfeld quantum invariants method,and discusses the influence of boundary conditions on the fidelity for population transfer.The original shortcuts to adiabaticity will introduce additional coupling and detuning for the process of constructing the Hamiltonian.In order to overcome this defect we also find an experimental feasible counterdiabatic term through the method of superadiabatic iterations for two-level and three-level systems.For the three-level systems,we find a suitable alternative counterdiabatic terms HcdS(1)(t)based on the transitionless quantum driving with superadiabatic iterations,the structure of conterdiabatic terms shares the same form as the initial Hamiltonian,so it is simple in forms and does not have extra coupling and detuning and this makes the scheme easy to implement in the experiment and applies to general three-level systems.It can control quantum systems in the shortest possible time,we simulation population transfer in three-level quantum system.We acquire a perfect result through simulation preparation of superposition states throng this methods.It is also more robust against control parameter fluctuations for achieve population transfer when we increase the Rabi frequency of time delay and consider errors of system.Our work provides a useful method to control the evolution of quantum state for two and three-level systems,and enriches the method for quantum state control.It will be beneficial for quantum information processing.