Adiabaticity violation under arbitrarily slow evolution

TL;DR

This paper demonstrates that quantum adiabaticity can be violated even during arbitrarily slow processes, challenging a fundamental principle and introducing new parameters and methods to control this phenomenon.

Contribution

The authors introduce the ITA and ITP parameters and the PDM method, providing a new framework and experimental evidence for adiabaticity violation in slow quantum evolutions.

Findings

Adiabaticity can be violated in arbitrarily slow processes.

New parameters (ITA and ITP) effectively describe adiabatic evolution.

Experimental demonstration in photonic waveguides confirms the phenomenon.

Abstract

The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this principle and show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, Instantaneous Transition Accumulation (ITA) and Instantaneous Transition Probability (ITP), to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new Phase Difference Manipulation (PDM) method, we control ITP and ITA to induce adiabaticity violation in a Landau-Zener (LZ) process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow LZ process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.