Probing the Topology of Density Matrices - Kölner UniversitätsPublikationsServer

Bardyn, Charles-Edouard, Wawer, Lukas, Altland, Alexander ORCID: 0000-0002-2991-4805, Fleischhauer, Michael ORCID: 0000-0003-4059-7289 and Diehl, Sebastian (2018). Probing the Topology of Density Matrices. Phys. Rev. X, 8 (1). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2160-3308

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DOI:10.1103/PhysRevX.8.011035

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.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Bardyn, Charles-Edouard	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Wawer, Lukas	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Altland, Alexander	UNSPECIFIED	orcid.org/0000-0002-2991-4805	UNSPECIFIED
Fleischhauer, Michael	UNSPECIFIED	orcid.org/0000-0003-4059-7289	UNSPECIFIED
Diehl, Sebastian	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED