Quantum sensing of a quantum field

• URL: http://arxiv.org/abs/2509.22361v1
• Date: Fri, 26 Sep 2025 13:56:54 GMT
• Title: Quantum sensing of a quantum field
• Authors: Ricard Ravell Rodríguez, Martí Perarnau-Llobet, Pavel Sekatski,
• Abstract summary: We show that the amplitude of a coherent quantized field is estimated by letting it interact with a two-level atom.<n>For both metrological scenarios, we focus on the quantum Fisher information (QFI) of the reduced state of the atomic probe.<n>In the limit of large amplitude $alpha$, the QFI is found to attain its maximal value $1.47$ at $tau =O(1)$ and $tau =O(alpha2)$, and also shows periodic revivals at much later times.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 limit, where the atom interacts with many weak coherent states, this back-action can be simply interpreted as spontaneous emission, giving rise to the optimal interaction time and QFI rate.

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