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Critical quantum thermometry and its feasibility in spin systems

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Enes Aybar1, Artur Niezgoda1,2, Safoura S. Mirkhalaf3,4, Morgan W. Mitchell1,5, Daniel Benedicto Orenes1, and Emilia Witkowska6

1ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
2Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
3Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran
4School of Nano Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
5ICREA – Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
6Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland

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Abstract

In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the sensitivity in the temperature estimation, and apply a finite-size scaling framework to link this sensitivity to critical exponents of the system around critical points. We numerically calculate the QFI around the critical points for two experimentally-realizable systems: the spin-1 Bose-Einstein condensate and the spin-chain Heisenberg XX model in the presence of an external magnetic field. Our results confirm finite-size scaling properties of the QFI. Furthermore, we discuss experimentally-accessible observables that (nearly) saturate the QFI at the critical points for these two systems.

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