Quantum sensing of a quantum field, by Ricard Ravell Rodríguez, Martí Perarnau-Llobet, Pavel Sekatski

SciPost Physics Home Authoring Refereeing Submit a manuscript About Quantum sensing of a quantum field Ricard Ravell Rodríguez, Martí Perarnau-Llobet, Pavel Sekatski SciPost Phys. 20, 107 (2026) · published 10 April 2026 doi: 10.21468/SciPostPhys.20.4.107 pdf BiBTeX RIS Submissions/Reports Abstract Estimating a classical parameter encoded in the Hamiltonian of a quantum probe is a fundamental and well-understood task in quantum metrology. A textbook example is the estimation of a classical field’s amplitude using a two-level probe, as described by the semi-classical Rabi model. In this work, we explore the fully quantum analogue, where the amplitude of a coherent quantized field is estimated by letting it interact with a two-level atom. For both metrological scenarios, we focus on the quantum Fisher information (QFI) of the reduced state of the atomic probe. In the semi-classical Rabi model, the QFI is independent of the field amplitude and grows quadratically with the interaction time $\tau$. In contrast, when the atom interacts with a single coherent mode of the field, the QFI is bounded by 4, a constant dictated by the non-orthogonality of coherent states. We find that this bound can only be approached in the vacuum limit. In the limit of large amplitude $\alpha$, the QFI is found to attain its maximal value $1.47$ at $\tau =O(1)$ and $\tau =O(\alpha^2)$, and also shows periodic revivals at much later times. When the atom interacts with a sequence of coherent states, the QFI can increase with time but is bounded to scale linearly due to the production of entanglement between the atom and the radiation (back-action), except in the limit where the number of modes and their total energy diverge. Finally, in the continuous-field limit, where the atom interacts with a continuous source of weak coherent states, this back-action can be simply interpreted as spontaneous emission; we find that the optimal atomic QFI rate is finite, depends on the source intensity, and is upper bounded by the constant rate at which the QFI is emitted by the radiation source. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.4.107TI - Quantum sensing of a quantum fieldPY - 2026/04/10UR - https://scipost.org/SciPostPhys.20.4.107JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 4SP - 107A1 - Ravell Rodríguez, RicardAU - Perarnau-Llobet, MartíAU - Sekatski, PavelAB - Estimating a classical parameter encoded in the Hamiltonian of a quantum probe is a fundamental and well-understood task in quantum metrology. A textbook example is the estimation of a classical field’s amplitude using a two-level probe, as described by the semi-classical Rabi model. In this work, we explore the fully quantum analogue, where the amplitude of a coherent quantized field is estimated by letting it interact with a two-level atom. For both metrological scenarios, we focus on the quantum Fisher information (QFI) of the reduced state of the atomic probe. In the semi-classical Rabi model, the QFI is independent of the field amplitude and grows quadratically with the interaction time $\tau$. In contrast, when the atom interacts with a single coherent mode of the field, the QFI is bounded by 4, a constant dictated by the non-orthogonality of coherent states. We find that this bound can only be approached in the vacuum limit. In the limit of large amplitude $\alpha$, the QFI is found to attain its maximal value $1.47$ at $\tau =O(1)$ and $\tau =O(\alpha^2)$, and also shows periodic revivals at much later times. When the atom interacts with a sequence of coherent states, the QFI can increase with time but is bounded to scale linearly due to the production of entanglement between the atom and the radiation (back-action), except in the limit where the number of modes and their total energy diverge. Finally, in the continuous-field limit, where the atom interacts with a continuous source of weak coherent states, this back-action can be simply interpreted as spontaneous emission; we find that the optimal atomic QFI rate is finite, depends on the source intensity, and is upper bounded by the constant rate at which the QFI is emitted by the radiation source.ER - × @Article{10.21468/SciPostPhys.20.4.107, title={{Quantum sensing of a quantum field}}, author={Ricard Ravell Rodríguez and Martí Perarnau-Llobet and Pavel Sekatski}, journal={SciPost Phys.}, volume={20}, pages={107}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.4.107}, url={https://scipost.org/10.21468/SciPostPhys.20.4.107},} Ontology / Topics See full Ontology or Topics database. Quantum optics quantum sensing Authors / Affiliations: mappings to Contributors and Organizations See all Organizations. 1 2 Ricard Ravell Rodríguez, 3 Martí Perarnau-Llobet, 4 Pavel Sekatski 1 Institut de Ciències Fotòniques / Institute of Photonic Sciences [ICFO] 2 Universitat de les Illes Balears / Universitat de les Illes Balears [UIB] 3 Universitat Autònoma de Barcelona / Autonomous University of Barcelona [UAB] 4 Université de Genève / University of Geneva [UNIGE] Funders for the research work leading to this publication Agencia Estatal de Investigación FUNDACIÓ Privada MIR-PUIG Fundacion Cellex (through Organization: Fundació Privada Cellex) Generalitat de Catalunya / Government of Catalonia Govern de les Illes Balears Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España National Centres of Competence in Research SwissMAP NextGenerationEU Stiftelsen för Internationalisering av Högre Utbildning och Forskning / Swedish Foundation for International Cooperation in Research and Higher Education [STINT]