Quantum sensing of a quantum field

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.

Improved clarity and corrected some typos

References in corpus (24)

• Quantum-enhanced measurements: beating the standard quantum limit
• Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
• Experimental realization of sub-shot-noise quantum imaging
• Individual quantum probes for optimal thermometry
• Fisher information under decoherence in Bloch representation
• Achieving the Heisenberg limit in quantum metrology using quantum error correction
• Squeezed-Light Optical Magnetometry
• Thermometry in the quantum regime: Recent theoretical progress
• Quantum-Enhanced Plasmonic Sensing
• Adaptive quantum metrology under general Markovian noise
• Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
• Discontinuities of the quantum Fisher information and the Bures metric
• Quantum metrology with full and fast quantum control
• Qubit-assisted thermometry of a quantum harmonic oscillator
• Bayesian parameter estimation by continuous homodyne detection
• Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system
• Cloning Entangled Qubits to Scales One Can See
• Optimal nonequilibrium thermometry in Markovian environments
• Control of Stochastic Quantum Dynamics by Differentiable Programming
• Quantum Cramér-Rao bound for quantum statistical models with parameter-dependent rank
• Optimal quantum estimation of the coupling constant of Jaynes-Cummings interaction
• Application of Abel-Plana formula for collapse and revival of Rabi oscillations in Jaynes-Cummings model
• Quantum-state transfer between atom and cavity field in Jaynes-Cummings model
• Inside the Jaynes-Cummings sum