Incoherent Imaging with Spatially Structured Quantum Probes

TL;DR

This work addresses the fundamental limits of incoherent, active imaging by introducing a universal quantum imaging module that leverages spatially structured probes. Through twin-beam echoes and structured Fock states, it achieves simultaneous absorption and fluorescence imaging with quantum-enhanced sensitivity and subdiffraction resolution, mapping the generalized imaging channel onto two distinct detection channels. The authors derive ultimate sensitivity bounds via quantum Fisher information for both subdiffraction and conventional imaging tasks, demonstrating near-optimal performance that persists under perturbative noise. The framework is broad in scope, applicable to quantum optical microscopy, phononic/acoustic imaging, and distributed sensor networks, and points to practical pathways for implementing quantum advantages in complex, multiparameter imaging problems.

Abstract

Incoherent imaging, including fluorescence and absorption microscopy, is often limited by weak signals and resolution constraints -- notoriously, Rayleigh's curse. We investigate how spatially structured quantum probes, combined with quantum detection strategies like spatial mode demultiplexing and photon counting, overcome these limitations. We propose a novel imaging protocol based on twin-beam echoes that maps the generalized incoherent-imaging model -- comprising both absorption and fluorescence -- onto distinct passive imaging channels that separately encode the absorption and fluorescence signatures. This enables (i) simultaneous absorption and fluorescence imaging and (ii) direct application of well-known results from passive imaging, all featuring quantum-enhanced measurement sensitivity. Remarkably, the same protocol supports displacement-field reconstruction of multiple quadratures (e.g., oscillators' positions) and works for both conventional and subdiffraction imaging, thereby functioning as a universal quantum imaging module. We also examine the utility of Fock states in a structured spatial mode basis, which offer comparable performance in principle. Though developed for optical imaging, our framework applies broadly to quantum-optical microscopy, phononic or acoustic imaging, and mapping stochastic forces, fields, or charge distributions using an array of mechanical oscillators.

Figures (8)

• Figure 1: Quantum imaging with bosonic modes. (a) Structured quantum-optical probes interrogate a sample of emitters/absorbers. Spatial information about the sample is imprinted onto the probes through incoherent quantum processes (e.g., absorption and emission) and then extracted from the reflected light via quantum processing and measurements, such as spatial-mode demultiplexing (SPADE) and photon counting. (b) Alternative setting subsumed by our framework where a stochastic field $f(x)$ drives an array of mechanical oscillators, such as trapped ions or nanomechanical resonators. A collective quantum state of the motional modes is prepared (squiggles represent entanglement) and measured to reveal properties hidden in the correlators $\mathbb{E}[f(x_i)f(x_j)]$. Collective heating (cooling) can be addressed as well.
• Figure 2: Pictorial construction of the quantum imaging model. Local interactions between emitters (subsystems $E_x$) and probes (subsystems $S_x$) encode emitter properties onto the probes, such as absorption, fluorescence, and emitter positions. Due to stochastic behavior of the emitters, this interaction induces incoherent evolution of the probes, described by a quantum-imaging channel acting on the probe state (reduced schematic). Propagation from the emitter plane to the detection plane (kernel $K$) spreads the encoded information across multiple "pixel" modes on the collection plane, yielding the observed mutual coherence $\Gamma_{\downarrow}(u,u')$ and absorption profile $\Gamma_{\uparrow}(u,u')$ [or displacement-field covariance kernel $\Gamma(u,u')$]. Propagation from the probe source to the emitter plane (kernel $\widetilde{K}$) included for completeness.
• Figure 3: Lineage of the grandfather equation [Eq. \ref{['eq:grandfather']}]. Descendants include absorption imaging, passive fluorescence imaging, and stochastic displacement imaging (a.k.a., displacement-field reconstruction).
• Figure 4: Quantum circuit for structured imaging. Quantum probes (twin beams or Fock states) are prepared in a structured mode basis $\Psi=\{\psi_k\}$. Idler modes (if present) are retained in storage, while the signal modes propagate to the emitter plane (via propagator $\widetilde{K}$), interact with the sample, then propagate to the collection plane (via propator $K$) for processing and measurement. Quantum processing refers to energy non-conserving operations, such as squeezing, as well as linear-optical operations, such as SPADE.
• Figure 5: Twin-beam echo. A metrological Loschmidt echo Macri2016:echoMetrology via two-mode squeezing between signal ($S$, annihilation operator $\hat{a}$) and idler ($I$, annihilation operator $\hat{b}$) maps absorption signatures to the idler while maintaining fluorescence signatures on the signal.