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

TL;DR

This paper introduces a quantum confocal microscopy technique in Fock space that enhances measurement precision beyond classical limits, achieving a 19 dB metrological gain using scalable quantum states on a superconducting circuit platform.

Contribution

It presents a novel quantum confocal microscopy method in Fock space that overcomes key challenges in quantum metrology with scalable, high-photon-number states and efficient information readout.

Findings

Achieved a 21.5 dB photon-number compression relative to coherent states.

Demonstrated displacement sensitivity approaching Heisenberg scaling.

Recorded a 19 dB metrological gain beyond the standard quantum limit.

Abstract

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 21.5$\pm$1.1 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 19.06$\pm$0.13 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.