Squeezing of high-dimensional metastable spins (qudits) in ⁴⁰Ca+

Maximally entangled states of spin ensembles, such as the Greenberger–Horne–Zeilinger (GHZ) states, are known to achieve Heisenberg limited (HL) measurement sensitivity. However, the experimental complexity of state generation and increased fragility of GHZ states has inhibited the deployment of large quantum-enhanced sensors for impactful applications. Therefore, simplified methods that minimize operational overhead are needed. Spin-squeezing, which refers to a broad class of techniques for generating entangled spins, enables quantum-enhanced sensing that is more robust. A recent proposal [1] suggests a novel approach to spin-squeezing that leverages two ubiquitous capabilities of ion trapping setups, namely the ability to squeeze the bosonic states of ion motion and the Tavis-Cummings interaction that couples the bosonic state to the internal spin degrees of freedom. Here we present an extension of this protocol that generates probe states composed of many d-dimensional spins (or qudits) with metrological utility beyond the Standard quantum limit that scales as (Δθ)² ∝ ((d-1)N)^-3/2. We quantify the advantages of qudits over qubits via the quantum Fisher information with respect to the spin-reduced and total spin-boson system and report preliminary results demonstrating the metrological gain achievable with qudits encoded in the D_5/2 manifold of trapped ⁴⁰Ca+ ions.