Experimental Research On Adiabatic Quantum Control Based On Trapped Ion

The trapped ion system has the long coherence time with no need of the extreme cooling conditions,i.e.it can work in room temperature environment,and it has inter-nal electron spin and external motion degrees of freedom which is easy to control,so it is an ideal system for studying the quantum optics,quantum electrodynamics,and performing the precision measurements,quantum simulation and quantum information processing.We built an experimental system that uses the RF field to trap 171Yb+ ions,and use the laser to achieve the Doppler cooling,optical pumping quantum state initialization,and quantum fluorescence detection of the ions.We use microwave to implement the single qubit quantum state control and quantum state tomography,and use the stimulated Raman transition to couple the spin state and the motion state,successfully cool the ions to the motion ground state,measured the heating rate,and demonstrated that we can prepare the motion state as a coherent state.Adiabatic evolution is a very common and important evolutionary process in quan-tum mechanics,and the adiabatic theorem is a necessary and sufficient condition for adi-abatic evolution,which has significant influence in the development of physics.How-ever,the oscillating Hamiltonian found in recent years,due to the resonance transition between the energy levels,causes the adiabatic conditions to be inconsistent with the adiabatic theorem.At the same time,the adiabatic theorem applies only to closed sys-tems,so how to define it in an open system.Based on the trapped ion system we built,we have carried out a series of experimental and theoretical studies around the above-mentioned problems:1.Using the trapped ion qubit,we designed an oscillating Hamiltonian and exam-ined several related adiabatic conditions,confirming that these adiabatic condi-tions are no longer applicable.Then,by introducing a non-inertial rotation frame,the above-mentioned relevant adiabatic conditions are tested again.These adia-batic conditions are good predictive of adiabatic behavior,both at the resonance point and away from the resonance point.Finally,we also give the equivalent conditions for the verification mechanism to describe the adiabatic behavior in inertial and non-inertial frame.2.In the open quantum system,the non-unitary evolution under the control of the master equation determined by the super-operator can directly generalize the adi-abatic theorem.In order to achieve the target master equation,we introduce a Gaussian noise to frequency-modulate the microwaves that drive the qubit,and achieve a highly controllable high-quality decoherence channel.Different from the situation in the closed system,the adiabatic condition is consistent with the adiabatic theorem as the evolution time increases,and the adiabatic validity con-dition is robust to the resonance phenomenon.Moreover,we have also proved that the Deutsch algorithm in open systems has a optimal time windows.3.We experimentally verified he ability of the inertia theorem and the protocol to implement the theorem,confirming the robustness of the inertial solution.For the case where the deviation inertia theorem is small,theoretical simulation can well support the above conclusions.For the case where the deviation inertia theorem is large,the amplitude of the inertial solution first appears to be an error,but the phase is still accurate.By adding amplitude correction,we have solved this problem very well,and the phase information can also be used for parameter estimation of inertia limit accidents.The experimental verification of the inertial solution lays the foundation for fast and high precision quantum control.