Density and state metrics to measure adiabaticity in quantum many-body systems at zero and finite temperature

Abstract

Adiabatic evolutions of many-body quantum systems are very important in many fields of physics, from quantum computing to quantum thermodynamics to atomic and molecular physics, to name a few. However, current methods for characterizing adiabaticity are designed for pure states at zero temperature, while most applications are based on many-body systems at finite temperature, and so new insights and techniques are needed. We demonstrate [1], [2] that appropriate metrics for the system state and for its corresponding local particle-density can be used to quantitatively determine the degree of adiabaticity of the dynamics of quantum many-body systems, at zero and finite temperature. This is important for quantum technologies and quantum thermodynamics related protocols. We show that the Bures and the trace distance, both well defined at finite temperatures, are reliable measures of adiabaticity, both qualitatively and quantitatively. In addition, adiabaticity can be characterized using only the local particle density distance. The local particle density is a much more accessible quantity, both experimentally and computationally, especially when handling many-body systems. Metrics retain memory effects, and the importance of considering them is discussed by comparing the metrics' results to the ones obtained by extending the quantum adiabatic criterion to finite temperatures: the latter may produce false readings being quasi-Markovian by construction. The possibility of characterizing the degree of adiabatic evolution via the system local particle densities, makes this method potentially applicable to very large many-body systems and to experiments. [1] A. H. Skelt, R. W. Godby, and I. D'Amico, Phys. Rev. A 98, 012104 (2018) [2] A. H. Skelt, and I. D'Amico, Adv. Quantum Technol. 3, 1900139 (2020)