Shortcuts to adiabaticity using flow fields

Abstract

A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.

Focus on Shortcuts to Adiabaticity

“…Patra and Jarzynski have introduced a novel technique to engineer STA using flow fields [11]. They consider a reference adiabatic trajectory for a system with Hamiltonian H 0 (t).…”

Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance

“…The potential diverges to negative infinity where the amplitude of the order parameter is small. Now we simulate evolution of the state driven from the ground state in the harmonic potential in equation (15) to a WPUM for the same ω and η 0 as in figure 1. In the following simulation we use the approximate potential of which…”

“…Protection of quantum states from the disturbance due to fluctuating background potential with the sequential manipulation [14] and sorting of trapped ions [12] were proposed using the fast-forward driving potential. A scheme encompassing quantum, classical and stochastic dynamics was proposed utilizing flow fields providing compact expressions for counter-diabaitc Hamiltonians and fast-forward potentials [15]. Recently a scheme of fast-forward of adiabatic control of stationary tunneling states has been proposed, which allows the acceleration of both the amplitude and phase of wave functions throughout the fast-forward time range.…”

Swift heat transfer by fast-forward driving in open quantum systems

“…The ideas of shortcuts to adiabaticity were recently generalized to speed up equilibration and isothermal processes in open systems [35][36][37][38][39][40][41]. Such protocols assume Markovian baths and are effective when the protocol duration is much longer than the bath relaxation time.…”