Topological Transition in Measurement-Induced Geometric Phases
Topological transition in measurement-induced geometric phases Valentin Gebharta,b,1, Kyrylo Snizhko b,1 , Thomas Wellensa, Andreas Buchleitnera, Alessandro Romitoc, and Yuval Gefenb,2 aPhysikalisches Institut, Albert-Ludwigs-Universitat¨ Freiburg, 79104 Freiburg, Germany; bDepartment of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel; and cDepartment of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom Edited by Yakir Aharonov, Chapman University, Orange, CA, and approved February 4, 2020 (received for review July 10, 2019) The state of a quantum system, adiabatically driven in a cycle, may the Pancharatnam phase is equal to the Berry phase associated acquire a measurable phase depending only on the closed trajec- with the trajectory that connects the states j k i by the shortest tory in parameter space. Such geometric phases are ubiquitous geodesics in Hilbert space (6, 16). and also underline the physics of robust topological phenom- The Pancharatnam phase can quite naturally be interpreted ena such as the quantum Hall effect. Equivalently, a geometric as a result of a sequence of strong (projective) measurements phase may be induced through a cyclic sequence of quantum acting on the system and yielding specific measurement read- measurements. We show that the application of a sequence of outs (17). This interpretation is valid for optical experiments weak measurements renders the closed trajectories, hence the observing the Pancharatnam phase induced with sequences of geometric phase, stochastic. We study the concomitant probabil- polarizers (18). Such a phase can be consistently defined despite ity distribution and show that, when varying the measurement the fact that measurements (typically considered an incoher- strength, the mapping between the measurement sequence and ent process) are involved.
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