From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

TL;DR

This paper connects classical nonlinear integrable systems with quantum shortcuts to adiabaticity, providing exact counterdiabatic terms for certain quantum systems through Lax pairs and soliton solutions.

Contribution

It introduces a systematic method to derive exact counterdiabatic terms using classical integrable equations and classifies solvable quantum systems via Lax pairs.

Findings

Exact counterdiabatic terms derived for specific models.

Unified classification of solvable systems using Lax pairs.

Application to multisoliton potentials and spin chains.

Abstract

Using shortcuts to adiabaticity, we solve the time-dependent Schroedinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic XY spin chains from the Toda equations are studied in detail.