Fast-forward scaling theory

Abstract

Speed is the key to further advances in technology. For example, quantum technologies, such as quantum computing, require fast manipulations of quantum systems in order to overcome the effect of decoherence. However, controlling the speed of quantum dynamics is often very difficult due to both the lack of a simple scaling property in the dynamics and the infinitely large parameter space to be explored. Therefore, protocols for speed control based on understanding of the dynamical properties of the system, such as non-trivial scaling property, are highly desirable. Fast-forward scaling theory (FFST) was originally developed to provide a way to accelerate, decelerate, stop and reverse the dynamics of quantum systems. FFST has been extended in order to accelerate quantum and classical adiabatic dynamics of various systems including cold atoms, internal state of molecules, spins and solid-state artificial atoms. This paper describes the basic concept of FFST and reviews the recent developments and its applications such as fast state-preparations, state protection and ion sorting. We introduce a method, called inter-trajectory travel, recently derived from FFST. We also point out the significance of deceleration in quantum technology. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Keywords: fast-forward scaling theory; shortcuts to adiabaticity; speed control of quantum dynamics.

Figure 1.

(a) FFST and STA have overlap. FFST for quantum adiabatic dynamics can be categorized to STA. (b,c) Running forms of one of the authors (S.M.), jogging (b) and sprinting (c). (Online version in colour.)

Figure 2.

Illustration of the role of the speed-control factor $\alpha$. The speed-control factor characterizes the degree of speed control and is time dependent. The original dynamics is accelerated for $\alpha (t)>1$, slowed for $0<\alpha (t)<1$, driven backward for $\alpha (t)<0$, and stopped for $\alpha (t)=0$. $|\alpha |\gg 1$ can be used for STA. (Online version in colour.)

Figure 3.

(a) Schematic of successive transport of wave function under spatially random potential [54]. Schematic of rotation of the orientation of wave function distribution (b) and sorting of trapped ions with the fast-forward driving field (c) [32]. (Online version in colour.)

Figure 4.

Illustration of inter-trajectory travel (ITT). A virtual trajectory interconnects two FF trajectories in order to connect the initial and target states. (Online version in colour.)