Reverse engineering of a Hamiltonian for a three-level system via the Rodrigues’ rotation formula
Yi‐Hao Kang, Bi‐Hua Huang, Pei-Min Lu, Yan Xia · Laser Physics Letters · 2016
Abstract We propose a scheme to reversely construct a three-level Hamiltonian via the Rodrigues’ rotation formula and an auxiliary unitary transformation. The main goal of the scheme is designing feasible pulses to drive a three-level system to evolve rapidly from an arbitrary initial state to a desired final state. Numerical simulations demonstrate that the scheme is not only fast but also robust against the decoherence caused by fluctuations of control parameters and some dissipation factors. Besides, we apply the idea to implement a Hadamard gate in a three-level system, and the results show the present scheme is much faster compared with stimulated Raman adiabatic passage (STIRAP). Therefore, the scheme may be useful to find out an effective shortcut to the adiabatic passage in a three-level system.