Weak-measurement-induced phases and dephasing: broken symmetry of the geometric phase

TL;DR

This paper explores how weak measurements induce phases in quantum states, revealing a broken symmetry in geometric phases, with topological transitions and dephasing effects, supported by proposed experimental observations.

Contribution

It uncovers a novel symmetry-breaking in geometric phases induced by weak measurements and links topological transitions to dephasing phenomena.

Findings

Identification of symmetric and antisymmetric phase components as non-dynamical and non-geometrical.

Discovery of topological phase transitions characterized by winding numbers.

Observation of diverging dephasing at phase transition points.

Abstract

Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and dynamical terms. Furthermore, considering the reversal of the order of the measurement sequence, such a phase comprises a symmetric and an antisymmetric term. Superseding common wisdom, we show that the symmetric and the antisymmetric components do not correspond to the dynamical and geometrical parts respectively. Addressing a broad class of measurement protocols, we further investigate the dependence of the induced phases on the measurement parameters (e.g., the measurement strength). We find transitions between different topologically distinct sectors, defined by integer-valued winding numbers, and show that the transitions are accompanied by diverging dephasing. We propose experimental protocols to observe these effects.