Single-Atom Verification of the Optimal Trade-Off between Speed and Cost in Shortcuts to Adiabaticity

TL;DR

This paper investigates the fundamental speed-cost trade-off in shortcuts to adiabaticity, experimentally verifying a tight bound using a single ultracold ion, and enhances understanding of quantum control limitations.

Contribution

It introduces a new theoretical trade-off bound between speed and cost in shortcuts to adiabaticity, verified experimentally with a single trapped ion.

Findings

The trade-off bound is tight for both eigenstates and thermal states.

Experimental verification confirms the theoretical speed-cost relationship.

The work highlights the role of phase space in quantum control constraints.

Abstract

The approach of shortcuts to adiabaticity enables the effective execution of adiabatic dynamics in quantum information processing with enhanced speed. Owing to the inherent trade-off between dynamical speed and the cost associated with the transitionless driving field, executing arbitrarily fast operations becomes impractical. To understand the accurate interplay between speed and energetic cost in this process, we propose theoretically and verify experimentally a new trade-off, which is characterized by a tightly optimized bound within $s$-parameterized phase spaces. Our experiment is carried out in a single ultracold $^{40}$Ca$^{+}$ ion trapped in a harmonic potential. By exactly operating the quantum states of the ion, we execute the Landau-Zener model as an example, where the quantum speed limit as well as the cost are governed by the spectral gap. We witness that our proposed trade-off is indeed tight in scenarios involving both initially eigenstates and initially thermal equilibrium states. Our work helps understanding the fundamental constraints in shortcuts to adiabaticity and illuminates the potential of under-utilized phase spaces that have been traditionally overlooked.