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Probing the topology of density matrices | | Charles-Edouard Bardyn
; Lukas Wawer
; Alexander Altland
; Michael Fleischhauer
; Sebastian Diehl
; | | Date: |
8 Jun 2017 | | 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 adiabatic
protocols, the EGP provides a topologically quantized observable which 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. | | Source: | arXiv, 1706.2741 | | Services: | Forum | Review | PDF | Favorites | |
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