Population Transfer In Non-hermitian Quantum Systems By Shortcuts To Adiabaticity

Quantum adiabatic theory has a very important position in quantum mechanics,which has extensive practical application in the fields of quantum optics and quantum information.The quantum adiabatic process refers to the process of regulating the Hamiltonian to make the system evolve along its own eigenstate,which is very effective in the preparation and regulation of the quantum state.But in the real world,the adiabatic process needs to satisfy the adiabatic condition,compared with the time of Rabi oscillation period of the same quantum system,the adiabatic process is slow,which requires long operation time.In order to overcome these difficulties,people are trying to find ways to speed up the quantum adiabatic process and the same effect as the quantum adiabatic process.Through unremitting efforts,shortcuts to adiabaticity(STA)technology are proposed.The quantum shortcuts to adiabaticity solves the slow problem of adiabatic process effectively.According to the difference of deriving auxiliary Hamiltonian,the shortcuts to adiabaticity can be divided into three kinds: transitionless quantum driving algorithm,counterdiabatic field algorithm and reverse engineering algorithm.The transitionless quantum driving algorithm is proposed by Berry.Demirplak and Rice proposed the counterdiabatic field algorithm.The reverse engineering algorithm is proposed by Lewis and Riesenfeld,so also known as the LR invariant theory.The STA technique has proved to be successful in designing control scheme for closed quantum systems.But there are still many places to be perfected and expanded.In practice,however,interactions between a quantum system and its surroundings is not avoidable,leading to coherence loss of the closed systems.Such a system can be described by a non-Hermitian Hamiltonian,non-Hermitian STA technique worthy of attention.The rotating wave approximation is valid in the weak coupling regime with small detuning and weak field amplitude,in this case the contribution of the counter-rotating term to the evolution of the system is quite small.In recent experiments,efforts are made to reach a promising method for studying strong and ultrastrong-coupling physics,where the RWA is no longer valid.The theory of shortcuts to adiabaticity without the rotating wave approximation are also important.Based on the above two points,this paper further improved the theory of shortcuts to adiabaticity in non-Hermitian quantum systems without RWA.The results are as follows:Firstly,we propose a renewed STA technique for non-Hermitian quantum systems beyond RWA.By using transitionless quantum driving method,we determine the exact control to speed up the adiabatic population transfer.Then,we apply it into the two-and three-level systems with decay and without RWA.We numerically calculate the population transfer dynamics with and without CR terms.The results show that the population transfer with the CR term is more steady.On the other hand,we also find that the decay of the excited state has small effect on the population transfer in the three-level system.This is attributed to the fact that,in the stimulated Raman adiabatic passage,the excited state remains unpopulated during the evolution.In the case of large detuning,we reduce the three-level system to an effective two-level system.The STA technique is then applied to the effective two-level system,which might shed more light on the present scheme.Secondly,we concentrate on a approach which is to use a shortcut to adiabaticity by adding unbalanced imaginary terms in the diagonal terms of the Hamiltonian which aim to nullify the nonadiabatic coupling.We find that the ratio between the gain and loss can control the transfer time and may become a new freedom to speed up the adiabatic transfer process.As an application example,we put this method into use the popular Landau-Zener model for the realization of fast population inversion.Numerical simulations indicate that the population transfer method is very robust against the change of parameters.We also find that the time of the evolution can be shortened when the ratio between the gain and loss raised.It provides a fast and robust approach to population control.We further show that the unbalanced gain and loss effect can speed up quantum evolution and therefore lead to a smaller quantum evolution time.