Fast-forward generation of non-equilibrium steady states of a charged particle under the magnetic field

Abstract

Abstract The fast-forward (FF) is one of the ideas to speed up the dynamics of given systems, and reproduces series of events on a shortened time scale, just like rapid projection of movie films on a screen. Considering a charged particle under the electromagnetic field, we present a scheme of FF generation of its non-equilibrium steady state, which realizes with complete fidelity the underlying quantum adiabatic dynamics throughout the FF protocol. We then apply the scheme to Landau states of a clean spin-less electron gas in a 2D x − y plane under the constant magnetic field B in the z direction. We have found how the electric field should be applied in rapid preparation of the quantum-mechanical Hall state as a non-equilibrium steady state. The FF electric field expressed in terms of the time-scaling function is found to be common to both the ground and excited Landau states. The FF driving avoids the decoherence inevitable in slow adiabatic procedures and eliminates the undesired mixing among Landau states with different quantum numbers that usually occurs in fast control.