Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians

Abstract

We derive families of optimal and near-optimal probe states for quantum estimation of the coupling constants of a general two-mode number-conserving bosonic Hamiltonian describing one-body and two-body dynamics. We find that the optimal states for estimating the dephasing of the modes, the self-interaction strength, and the contact interaction strength are related to the NOON states, whereas the optimal states for estimation of the intermode single particle tunneling amplitude are superpositions of antipodal SU(2) coherent states. For estimation of the amplitude of pair tunneling and the amplitude of density-dependent single particle tunneling processes, respectively, we introduce classes of variational superposition probe states that provide near perfect saturation of the corresponding quantum Cramér-Rao bounds. We show that the ground state of the pair tunneling term in the Hamiltonian has a high fidelity with the optimal states for estimation of a single particle tunneling amplitude, suggesting that high-performance probes for tunneling amplitude estimation may be produced by tuning the two-mode system through a quantum phase transition.

arXiv comment12 pages

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• Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atomic interferometry
• Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout
• Many-body quantum metrology with scalar bosons in a single potential well
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
• Spatial distribution of superfluidity and superfluid distillation of Bose liquids
• Distillation of maximally correlated bosonic matter from many-body quantum coherence
• Efficient trainability of linear optical modules in quantum optical neural networks