Adiabatic Sensing Technique for Optimal Temperature Estimation using Trapped Ions

Abstract

We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition. We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cramér-Rao bound for quantum oscillator at thermal equilibrium.

8 pages, 7 figures

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• Optimal quantum sensing of the nonlinear bosonic interactions using Fock states
• Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions
• Thermometry of Trapped Ions Based on Bichromatic Driving