Critical Quantum Metrology with Fully-Connected Models: From Heisenberg
to Kibble-Zurek Scaling
- URL: http://arxiv.org/abs/2110.04144v2
- Date: Tue, 30 Jan 2024 15:59:17 GMT
- Title: Critical Quantum Metrology with Fully-Connected Models: From Heisenberg
to Kibble-Zurek Scaling
- Authors: Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla
- Abstract summary: Phase transitions represent a compelling tool for classical and quantum sensing applications.
Quantum sensors can saturate the Heisenberg scaling in the limit of large probe number and long measurement time.
Our analysis unveils the existence of universal precision-scaling regimes.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Phase transitions represent a compelling tool for classical and quantum
sensing applications. It has been demonstrated that quantum sensors can in
principle saturate the Heisenberg scaling, the ultimate precision bound allowed
by quantum mechanics, in the limit of large probe number and long measurement
time. Due to the critical slowing down, the protocol duration time is of utmost
relevance in critical quantum metrology. However, how the long-time limit is
reached remains in general an open question. So far, only two dichotomic
approaches have been considered, based on either static or dynamical properties
of critical quantum systems. Here, we provide a comprehensive analysis of the
scaling of the quantum Fisher information for different families of protocols
that create a continuous connection between static and dynamical approaches. In
particular, we consider fully-connected models, a broad class of quantum
critical systems of high experimental relevance. Our analysis unveils the
existence of universal precision-scaling regimes. These regimes remain valid
even for finite-time protocols and finite-size systems. We also frame these
results in a general theoretical perspective, by deriving a precision bound for
arbitrary time-dependent quadratic Hamiltonians.
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