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.
Highlights
Geometrical phases are a cornerstone of modern physics [1]
We have demonstrated our theoretical framework via analyzing a specific protocol, calculating postselected and averaged measurement-induced phases, and investigating their dependence on various measurement parameters
We have shown that the projective-measurement-induced Pancharatnam phase and the Berry phase induced by adiabatic Hamiltonian evolution can be viewed as two limiting cases of the phases induced by quasicontinuous sequences of weak measurements
Summary
Geometrical phases are a cornerstone of modern physics [1]. The work of Berry [2] provided a unifying language that is key to understanding disparate phenomena including the quantum Hall effect [3,4] and topological insulators [5], sheds light on some features of graphene [6,7], and provides the basis for geometric [8,9] and topological [10] quantum computation platforms. We demonstrate that weak-measurement-induced phases generically involve both geometrical and dynamical components even in the absence of an additional Hamiltonian. This fact went unnoticed in earlier studies that focused on restricted classes of measurements. And superseding the common structure of phases generated by conventional adiabatic Hamiltonian dynamics, the symmetric and antisymmetric components do not coincide with the dynamical and geometrical components, respectively These general insights are demonstrated through the analysis of specific measurement protocols. Multiple distinct topological sectors exist, forming a rich phase diagram Transitions between such sectors are marked by (i) a vanishing probability of the corresponding postselected sequence (the case of postselective protocols) and (ii) diverging dephasing (the case of averaging protocols)..
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