Fast-forward of adiabatic dynamics in quantum mechanics

TL;DR

This paper introduces a method to accelerate adiabatic quantum processes, enabling rapid state transformations like transport, splitting, and squeezing without residual disturbance, applicable to both linear and nonlinear quantum systems.

Contribution

It extends the fast-forward theory to adiabatic quantum dynamics, providing a way to achieve rapid, controlled quantum state manipulations in finite time.

Findings

Successfully fast-forwarded adiabatic transport of wave functions.

Achieved accelerated splitting and squeezing of wave functions.

Applicable to both linear and nonlinear quantum systems.

Abstract

We propose a way to accelerate adiabatic dynamics of wave functions in quantum mechanics to obtain a final adiabatic state except for the spatially uniform phase in any desired short time. We develop the previous theory of fast-forward (Masuda & Nakamura 2008) so as to derive a driving potential for the fast-forward of the adiabatic dynamics. A typical example is the fast-forward of adiabatic transport of a wave function which is the ideal transport in the sense that a stationary wave function is transported to an aimed position in any desired short time without leaving any disturbance at the final time of the fast-forward. As other important examples we show accelerated manipulations of wave functions such as their splitting and squeezing. The theory is also applicable to macroscopic quantum mechanics described by the nonlinear Schroedinger equation.