Number-Operator-Based Inverse Engineering Technique for the Shortcut to Adiabaticity in Two Level Quantum Mechanical System

In general, the conventional Lewis-Riesenfeld invariant-based inverse engineering is a nonadiabatic process that results in the adiabatic final states to achieve the shortcut to adiabaticity, which does not provide complete suppression of non-adiabaticity throughout the evolution. We propose a new method to accomplish the shortcut to adiabaticity through an entirely adiabatic path. This new method is developed using the number operator as an invariant of the Hamiltonian. This paper discusses the mathematical framework of the new method in two-level quantum system and analyzes its performance compared to the conventional Lewis-Riesenfeld invariant-based inverse engineering method.