Journal
PHYSICAL REVIEW X
Volume 8, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.8.011035
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Funding
- DQMP at the University of Geneva
- Swiss National Science Foundation under Division II
- German Research Foundation (DFG) through the Institutional Strategy of the University of Cologne within the German Excellence Initiative [ZUK 81]
- European Research Council [647434]
- German Research Foundation (DFG) [SFB TRR 185]
- National Science Foundation [NSF PHY-1125915]
- [CRC 183]
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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.
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