Tracking Quantum Evolution

Lou Yuesheng, Shuang Cong

The effect of control fields is analyzed based on Bloch sphere representation of a single qubit, the conditions which parameters obey are given under two different requirements in order to achieve the transition from a arbitrary initial state to a target state, and numerical simulation is also be done to get the track of evolution on Bloch sphere. The relationship between the parameters and the track is analyzed.

Adam E. Rothman, Tak‐San Ho, HERSCHEL A. RABITZ

This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.

Diederik Aerts, Massimiliano Sassoli de Bianchi

Gil Katz, Mark A. Ratner, Ronnie Kosloff

Enviroment - caused dissipation disrupts the hamiltonian evolution of all quantum systems not fully isolated from any bath. We propose and examine a feedback-control scheme to eliminate such dissipation, by tracking the free hamiltonian evolution. We determine a driving-field that maximizes the projection of the actual molecular system onto the freely propagated one. The evolution of a model two level system in a dephasing bath is followed, and the driving field that overcomes the decoherence is calculated. An implementation of the scheme in the laboratory using feedback control is suggested.