en
Scientific article
Open access
English

Probing the Topology of Density Matrices

Published inPhysical Review X, vol. 8, no. 1, 011035
Publication date2018
Abstract

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the “ensemble geometric phase” (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities (“purity-gap” closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Research group
Citation (ISO format)
BARDYN, Charles et al. Probing the Topology of Density Matrices. In: Physical Review X, 2018, vol. 8, n° 1, p. 011035. doi: 10.1103/PhysRevX.8.011035
Main files (1)
Article (Published version)
accessLevelPublic
Identifiers
ISSN of the journal2160-3308
338views
183downloads

Technical informations

Creation02/04/2019 11:33:00 AM
First validation02/04/2019 11:33:00 AM
Update time03/15/2023 3:40:19 PM
Status update03/15/2023 3:40:18 PM
Last indexation01/17/2024 4:49:42 AM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack