Shortcuts to adiabatic population inversion via time-rescaling: stability and thermodynamic cost

TL;DR

This paper explores a time-rescaling method to create shortcuts to adiabatic population inversion in two-level quantum systems, maintaining high fidelity and thermodynamic properties without requiring detailed spectral information.

Contribution

It introduces a simple, eigenvalue-independent approach to generate adiabatic shortcuts, demonstrating its effectiveness and thermodynamic consistency in quantum control.

Findings

High fidelity in population inversion using the method

Comparable robustness against control parameter errors

Work distribution remains unchanged compared to slow protocols

Abstract

A shortcut to adiabaticity (STA) is concerned with the fast and robust manipulation of the dynamics of a quantum system that reproduces the effect of an adiabatic process. A recently proposed method enables the generation of shortcuts from a prescribed slow dynamics by simply rescaling the time variable of the quantum evolution operator [B. L. Bernardo, Phys. Rev. Research 2, 013133 (2020)]. This time-rescaling method does not demand knowledge about the eigenvalues and eigenstates of the Hamiltonian, and in many cases no additional coupling fields. Here, we use this approach to study the problem of speeding up the population inversion of a two-level quantum system. The fidelity of the dynamics versus systematic errors in the control parameters are shown to be comparable with other STA schemes. From a quantum thermodynamic viewpoint, we also demonstrate that the main properties of the distribution of work required to drive the system along the shortcuts are unchanged with respect to the reference (slow) protocol.