Quantum Confocal Microscopy in Fock Space with a 19 dB Metrological Gain

Quantum metrology promises measurement precision beyond classical limits by exploiting large-scale quantum states, yet realizing this advantage faces two fundamental challenges: the deterministic preparation of non-trivial quantum probes and the efficient extraction of metrological information in high-dimensional Hilbert spaces. Here, we introduce quantum confocal microscopy in Fock space that simultaneously resolves both challenges. Drawing a direct analogy between classical wave optics and quantum state evolution in a bosonic mode, we construct a confocal system with two Fock-space lenses. The first lens deterministically focuses a coherent state into a quantum probe with a tightly concentrated photon-number distribution, while the second lens maps the metrological information back to the vacuum state for efficient readout. Using a superconducting circuit QED platform, we prepare focused probe states with mean photon numbers up to {N} = 500, achieving a 21.5pm1.1 dB compression of the photon-number uncertainty relative to a coherent state, with a scalable quantum circuit of mathcal{O}(1) operational depth. We demonstrate a displacement sensitivity scaling as N^-0.416, approaching the Heisenberg scaling $N^-0.5$, and achieve a record metrological gain of 19.06pm0.13 dB beyond the standard quantum limit. This work establishes quantum confocal microscopy as a scalable and practical framework for quantum-enhanced precision measurement, readily extendable to other bosonic platforms and high-dimensional quantum many-body systems.