Bardyn, Charles-Edouard, Wawer, Lukas, Altland, Alexander, 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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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:
CreatorsEmailORCIDORCID Put Code
Bardyn, Charles-EdouardUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Wawer, LukasUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Altland, AlexanderUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Fleischhauer, MichaelUNSPECIFIEDorcid.org/0000-0003-4059-7289UNSPECIFIED
Diehl, SebastianUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-195482
DOI: 10.1103/PhysRevX.8.011035
Journal or Publication Title: Phys. Rev. X
Volume: 8
Number: 1
Date: 2018
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2160-3308
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
ULTRACOLD FERMIONS; PHASE; SYSTEMS; BANDSMultiple languages
Physics, MultidisciplinaryMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/19548

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