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  • Letter
  • Open Access

Quantum geometric tensor for the group SU(1,1)

Tharon Holdsworth1,2,* and Girish S. Agarwal1,2,3

  • 1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
  • 2Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA
  • 3Department of Biological and Agricultural Engineering, Texas A&M University, College Station, Texas 77843, USA

  • *Contact author: tharonholdsworth@tamu.edu
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Phys. Rev. Research 8, L032038 – Published 1 September, 2026

DOI: https://doi.org/10.1103/c1y9-q1wd

Abstract

The quantum geometric tensor sets the local relation between variations of external parameters and distances between states in Hilbert space. Its real and imaginary parts are, respectively, the quantum Fisher information matrix, which determines the ultimate precision bound in parameter estimation, and the Berry curvature. We study the geometry of SU(1,1) Hamiltonian eigenstates and propose two dynamical methods for extracting the components of the SU(1,1) quantum geometric tensor. A time-separated quench method extracts both the real and imaginary parts of the quantum geometric tensor from transition probabilities following two sudden parameter changes separated by free evolution, while a weak resonant modulation method relates quasiparticle production to the same geometric tensor. These results provide an operational method for measuring the local geometry of single-mode squeezed states and, in particular, for extracting the quantum Fisher information matrix directly from experimental observables.

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Phys. Rev. Research 8, L032038– Published 1 September, 2026
  • Received 10 April 2026
  • Accepted 10 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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