Optimal Nonadiabatic Quantum Control Of Cold Atoms

With the development of cold atoms and their applications in the field of precise measurement,quantum sensing,atom interferometry and quantum simulation,fast and high-fidelity quantum control becomes the hot research topic in physics.As far as we know,the quantum adiabatic theorem,that is,the wave function of system(the solution of time-dependent Schrodinger equation)evolves along the instan-taneous eigenstates when the parameters changes slowly enough,provides an impor-tant method to manipulate or prepare quantum states,particularly,for atom cooling,ion transport,and adiabatic quantum computing.However,adiabatic processes take typi-cally long time,which may spoil the desired final state and lead to lower accuracy of quantum computing and control,or even unachievable repetitions,in presence of deco-herence,noise,and perturbations.Motivated by this,one would like to speed up slow adiabatic processes,and finally achieve accurate,and high-fidelity control or prepara-tion of quantum states.Therefore,the concept of "Shortcut to adiabaticity"(STA)has been proposed in recent years.The Ph.D thesis is devoted to shortcuts to adiabaticity and their optimization,for achieving fast and accurate quantum manipulation of internal and orbit states in the system of cold atoms.Main results are as follows:(i)Starting from the equation of transport in classical mechanics,we engineer inversely the fast and robust transport of cold atoms in anharmonic traps,and the further optimization with respect to final residual energy and robustness against anharmonicity.(ii)Based on the dynamic invariant,we combine the reverse engineering,time-dependent perturbation theory and optimal control theory,to minimize the anharmonic energy for optimal shortcuts to adiabatic transport.(iii)Following the approaches of reverse engineering in two-level system,we achieve fast and robust generation of superposition state or entangled states for a single spin,two or more interacting spins,and optimize engineering with respect to dissipation and noise.(iv)Comparison between the shortcuts to adiabaticity and optimal control theory for atom transport,cooling,and spin control,illustrates that the shortcuts designed from reverse engineering can approach the results from optimal control theory,and shows the advantages of feasibility and simplicity of implementation.