Validation of Quantum Adiabaticity through Non-Inertial Frames and Its Trapped-Ion Realization

TL;DR

This paper introduces a validation method for the quantum adiabatic approximation by analyzing the system in a non-inertial frame, demonstrating its effectiveness through theoretical analysis and an experimental trapped-ion setup.

Contribution

It proposes a novel validation mechanism for adiabaticity using non-inertial frames, applicable to multi-particle systems, and confirms its effectiveness experimentally with a trapped Ytterbium ion.

Findings

Adiabatic conditions fail in the inertial frame but succeed in the non-inertial frame.

The validation mechanism extends to multi-particle quantum systems.

Experimental results with a Ytterbium ion confirm the theoretical predictions.

Abstract

Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several relevant adiabatic approximation conditions previously derived and show that all of them fail by introducing a suitable oscillating Hamiltonian for a single quantum bit (qubit). Then, by evaluating the adiabatic condition in a rotated non-inertial frame, we show that all of these conditions, including the standard adiabatic condition, can correctly describe the adiabatic dynamics in the original frame, either far from resonance or at a resonant point. Moreover, we prove that this validation mechanism can be extended for general multi-particle quantum systems, establishing the conditions for the equivalence of the adiabatic behavior as described in inertial or non-inertial frames. In order to experimentally investigate our method, we consider a hyperfine qubit through a single trapped Ytterbium ion $^{171}$Yb$^{+}$, where the ion hyperfine energy levels are used as degrees of freedom of a two-level system. By monitoring the quantum evolution, we explicitly show the consistency of the adiabatic conditions in the non-inertial frame.