Shortcuts to adiabaticity across a separatrix

TL;DR

This paper develops a method to extend classical shortcuts to adiabaticity, enabling crossing of phase-space separatrices with fixed energy cost and fidelity, which was previously not possible with standard protocols.

Contribution

It introduces a novel Hamiltonian control technique that allows crossing phase-space separatrices during fast driving, expanding the applicability of shortcuts to adiabaticity.

Findings

Successfully crossing a separatrix with fixed energy cost.

Design of an erasure procedure with protocol-duration-independent fidelity.

Extension of classical shortcuts to adiabaticity to non-adiabatic regimes.

Abstract

Shortcuts to adiabaticity are strategies for conserving adiabatic invariants under non-adiabatic (i.e. fast-driving) conditions. Here, we show how to extend classical, Hamiltonian shortcuts to adiabaticity to allow the crossing of a phase-space separatrix -- a situation in which a corresponding adiabatic protocol does not exist. Specifically, we show how to construct a time-dependent Hamiltonian that evolves one energy shell to another energy shell across a separatrix. Leveraging this method, we design an erasure procedure whose energy cost and fidelity do not depend on the protocol's duration.