Optimization of conveyance of quantum particles by moving potential well

Abstract

Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of a particle trapping in a potential well, i.e., survival probability in the process carrying of the particle for a given length within a given fixed time. For the actual motion of conveyance, we need to accelerate the particle to move and then decelerate it to stop at the destination. First, the relaxation of the survival probability in a constant acceleration rate is studied in detail by direct numerical calculation, the Wentzel-Kramers-Brillouin method, and a method of the resonance states. The survival probability was found to show an exponential decay in a long time, which is analyzed from a viewpoint of eigenvalue problem. An important source of dropoff comes from a non-analytic change of velocity at the starting point. When the rested particle begins to move, the ground state of the rest frame is redistributed to eigenstates of the moving frame, and then each eigenstate of the moving frame evolves in time. The dephasing of wave functions of the distributed populations reduces the probability of successful conveyance. In general, a smooth start gives a small initial disturbance but requires a large acceleration during the process to reach the destination in the fixed time which causes a larger dropoff in the process. Considering these conflicting facts, we study the survival probability in concrete conveyance schemes. We observe the time evolution of the trapped probability and the population distribution during the conveyance process. In cases that the potential well has several bound states, we propose a method to select the particle trapped at the ground state by making use of the difference of survival probabilities of bound states.