Dynamical structure factor from weak measurements

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Altuntaş, E. and Lena, R.G. and Flannigan, S. and Daley, A.J. and Spielman, I.B. (2025) Dynamical structure factor from weak measurements. Quantum Science and Technology, 10 (3). 035045. ISSN 2058-9565 (https://doi.org/10.1088/2058-9565/ade335)

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Abstract

Much of our knowledge of quantum systems is encapsulated in the expectation value of Hermitian operators, experimentally obtained by averaging projective measurements. However, dynamical properties are often described by products of operators evaluated at different times; such observables cannot be measured by individual projective measurements, which occur at a single time. For example, the dynamical structure factor (DSF) describes the propagation of density excitations, such as phonons, and is derived from the spatial density operator evaluated at different times. In equilibrium systems this can be obtained by first exciting the system at a specific wavevector and frequency, then measuring the response. Here, we describe an alternative approach using a pair of time-separated weak measurements, and analytically show that their cross-correlation function directly recovers the DSF, for all systems, even far from equilibrium. This general schema can be applied to obtain the cross-correlation function of any pair of weakly observable quantities. We provide numerical confirmation of this technique with a matrix product states simulation of the one-dimensional Bose–Hubbard model, weakly measured by phase contrast imaging. We explore the limits of the method and demonstrate its applicability to real experiments with limited imaging resolution.

ORCID iDs

Altuntaş, E., Lena, R.G., Flannigan, S., Daley, A.J. ORCID logoORCID: https://orcid.org/0000-0001-9005-7761 and Spielman, I.B.;
  • Item type:Article
    ID code:93284
    Dates:
    Date
    Event
    October 2025
    Published
    25 June 2025
    Published Online
    10 June 2025
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:27 Jun 2025 14:22
    Last modified:07 Jul 2026 03:45
    URI:https://strathprints.strath.ac.uk/id/eprint/93284
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