AIMR Math Group On-line Seminar

#1 FY2020

 

Date : April. 24th (Fri) 2020 10:00–12:00

Venue: Zoom

Speaker: Tomoki Ozawa
Title:Geometry of quantum states, its meaning, and how one can measure it

 

Abstract

Geometry plays important roles in quantum mechanics. The Berry curvature, a geometrical structure of quantum states in a parameter space, has been studied from various angles in relation to topological phases of matter. The Berry curvature is not the only geometrical property one can have for quantum states. In this talk, I start from discussing what we mean by "geometrical property of quantum states defined in a parameter space," and then introduce the quantum geometric tensor, whose imaginary part gives the Berry curvature and the real part gives the quantum metric. I then discuss physical meaning of the quantum metric in three different parameter spaces: a general parameter space for parameter estimation and quantum metrology, momentum space analogous to those studied in topological phases of matter, and the twist boundary condition space relevant for many-body systems. I also discuss some experiments where effects of quantum metric has been elucidated.

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