Bicolor Quantum Imaging & Sensing

• Bicolor quantum imaging and sensing is a dual-wavelength technique that exploits quantum correlations to boost spectral selectivity and sensitivity in photon-limited regimes.
• Integrated photonic circuits and nonlinear interferometric schemes enable precise separation and detection of optical signals, achieving sub-photon-level measurement precision.
• Applications span single-molecule fluorescence, FRET microscopy, and polarization sensing, advancing biomedical imaging and real-time spectroscopy.

Bicolor quantum imaging and sensing refers to methodologies that exploit quantum correlations or quantum detection architectures to simultaneously or selectively probe a system at two distinct optical wavelengths (often termed “colors”), with the aim of enhancing spectral selectivity, sensitivity, or information content in photon-limited regimes. This field combines advances in integrated photonics, single-photon detection, nonlinear optics, and quantum interferometry to produce platforms with sub-photon-level spectral discrimination, temporal resolution, and—via nonlinear interferometers or “undetected-photon” protocols—the capacity to interrogate samples at one wavelength while detecting at a different, often technologically favorable, wavelength.

1. Integrated Photonic Bicolor Imaging Platforms

Bicolor quantum imaging architectures are exemplified by hybrid superconducting–nanophotonic circuits in which a low-loss silicon nitride (Si₃N₄) waveguide provides strong modal confinement for photons at both visible (λ ≈ 738 nm) and telecommunication (λ ≈ 1550 nm) wavelengths (Kahl et al., 2016). These platforms utilize an arrayed waveguide grating (AWG), engineered for dual-color operation, to spatially demultiplex incoming photons into separate wavelength channels (Δλ ≈ 2.2 nm, FSR ≃ 25 nm). Each channel is terminated by a waveguide-integrated superconducting nanowire single-photon detector (SNSPD), with output timing jitter δt ≈ 47.6 ps (FWHM) and dark count rates consistently below 10 Hz per detector under full shielding. The architectural specifics—such as a 200 nm-thick Si₃N₄ core for visible and 450 nm for telecom arms with >90% modal confinement—enable true dual-wavelength single-photon spectroscopy and lifetime imaging, supporting simultaneous acquisition of fluorescence intensities at two target wavelengths and their associated decay profiles, e.g., I(λ₁) and τ_f(λ₁), I(λ₂) and τ_f(λ₂).

2. Nonlinear Interferometric (Undetected-Photon) Bicolor Schemes

Bicolor quantum imaging extends to nonlinear interferometric (SU(1,1)) architectures exploiting nondegenerate parametric down-conversion (PDC). In induced-coherence schemes, the idler mode interrogates the object—possibly in a mid-IR or THz region inaccessible to standard detectors—while the signal photon (at a second color, e.g., visible or NIR) is detected to reconstruct the sample-induced phase and amplitude modulations (Haase et al., 2022, Schaffrath et al., 2023, Oglialoro et al., 5 May 2025).

A Mach–Zehnder or three-mode SU(1,1) interferometer uses two sequentially pumped nonlinear crystals: the first seeds signal/idler pairs, with the idler passing through the sample before a second PDC stage coherently recombines the quantum amplitudes. Detection at the signal wavelength encodes both the phase φ and visibility V imparted by the sample at the idler wavelength, allowing phase and loss recovery via

$I(\phi) = A + V\cos(\phi + \varphi),$

with quadrature demodulation via polarization optics providing simultaneous access to both phase and amplitude in a single acquisition (Haase et al., 2022).

3. Quantum Sensing Performance and Regimes

The sensitivity and operating principles of bicolor quantum imaging differ between the spontaneous (low-gain) and high-gain PDC regimes. In the low-gain regime ($n_0 \ll 1$), phase sensitivity is shot-noise limited, $\delta \phi_{\text{SNL}} = 1/\sqrt{N}$, where $N$ is the detected photon count (Schaffrath et al., 2023). The detected photon number and associated variance follow

$$\langle n(\phi) \rangle \approx \eta n_0 [1 - \cos \phi], \quad \Delta n^2(\phi) \approx \eta n_0 [1 - \cos \phi] + \text{(noise)},$$

where $\eta$ is the detection efficiency. In the high-gain regime ($n_0 \gg 1$), Heisenberg scaling ($\delta \phi_{\text{HL}} \sim 1/N$) can be achieved—but only at the interferometer’s optimal “working point” (typically $\phi = \pi/2$), where all technical and thermal noise contributions are minimized (Schaffrath et al., 2023). Phase-shifting (“distillation”) algorithms that integrate over multiple phase points accumulate excess photon-number noise and cannot beat the standard quantum limit in high-gain operation.

Experimental implementations require high-efficiency detectors ($\eta \gtrsim 0.3$), low background counts ($n_n \ll \eta n_0$), and precise phase stabilization to maintain sub-shot-noise performance (Schaffrath et al., 2023). These criteria equally apply for dual-color, wavelength-multiplexed, and undetected-photon protocols.

4. Polarization and Birefringence Sensing in Bicolor Quantum Imaging

The bicolor nature of nonlinear interferometers enables simultaneous measurement of material birefringence (phase retardation) and diattenuation (polarization-dependent loss), which are critical in biological imaging applications (Oglialoro et al., 5 May 2025). By inserting waveplates (SU(2) elements) to control the polarization of the idler, the sample’s Jones matrix

$$J = R(-\gamma_2)\; \text{diag}(t_\parallel e^{i\phi_\parallel}, t_\perp e^{i\phi_\perp})\; R(\gamma_1)$$

(incorporating transmission amplitudes $t_{\parallel,\perp}$ and phase shifts $\phi_{\parallel,\perp}$ along principal axes) is coherently interrogated without detecting the probe wavelength. Analysis of low- and high-gain interference fringes reveals mean and differential fringe visibilities ($\overline{\mathcal{V}},\,\mathcal{V}_\delta$) which independently encode mean transmission and diattenuation, while phase offsets recover retardance. Two-dimensional Fourier analysis or quadrature demodulation permits single-shot extraction of all polarization properties, even without precise knowledge of interferometer phase or sample orientation.

5. Photon-Counting Bicolor Imaging with Quanta Image Sensors

Quanta Image Sensors (QIS) provide a photon-counting, bicolor imaging capability at the megapixel scale under extreme low-light conditions (Gnanasambandam et al., 2019). Each “jot” is an ultra-small (1.1 μm) photodiode with deep-trench isolation for channel cross-talk suppression and >86% quantum efficiency at 480 nm. A standard Bayer mosaic color filter array (CFA) or custom bicolor mask forms two color channels, with each jot resolving discrete photon arrivals modeled as Poisson or binomial processes. Image recovery leverages variance-stabilizing transforms (e.g., Anscombe-Poisson for multi-bit), followed by joint demosaicing-denoising via Plug-and-Play ADMM algorithms. Bicolor adaptation is immediate—replacing $S \in \mathbb{R}^{M \times 3M}$ with $S_{\text{bi}} \in \mathbb{R}^{M \times 2M}$—and results in either up to 50% faster readout or enhanced SNR for photon-starved applications. This is especially advantageous in dual-color fluorescence applications or scenarios favoring reduced photonic load per channel.

6. Applications of Bicolor Quantum Imaging and Sensing

Bicolor quantum imaging provides advanced measurement modalities in domains requiring simultaneous or differential spectral sampling at the single-photon level. Key applications include:

• Single-molecule and dual-color fluorescence lifetime imaging: Real-time acquisition of both emission spectrum (e.g., silicon vacancy center ZPL and phonon sideband) and temporal decay via SNSPDs on-chip, with timing jitter < 50 ps, and per-channel efficiency up to 25% (Kahl et al., 2016).
• FRET (Förster Resonance Energy Transfer) microscopy: On-chip AWG separates donor and acceptor bands for parallel intensity monitoring, enabling direct calculation of FRET efficiency:

$E_{\text{FRET}} \approx A/(A + \gamma D)$

where $A$, $D$ are acceptor/donor channel counts and $\gamma$ a correction factor (Kahl et al., 2016).

• Biosensing and polarization microscopy: Simultaneous measurement of birefringence (e.g., collagen alignment via $\delta \phi$) and diattenuation (e.g., chemical staining) on photo-sensitive tissue using low photon flux at the probe wavelength (Oglialoro et al., 5 May 2025).
• Dynamic phase and amplitude imaging with undetected photons: Real-time monitoring of mid-IR/THz absorption or refractive dynamics (e.g., isopropanol film drying, polymer deformation) by detecting only the visible/NIR signal with conventional cameras; phase and loss maps follow directly from quadrature-resolved interference patterns (Haase et al., 2022).

7. Future Directions and Implications

Bicolor quantum imaging continues to advance through improvements in integrated detector efficiency, waveguide engineering, high-gain PDC source development, and polarization control. Potential directions include:

• Expansion to multi-channel (“multicolor”) imaging via increased AWG channel count or spatial multiplexing, enabling simultaneous readout of multiple species or chemical environments (Kahl et al., 2016).
• Development of real-time, adaptive quantum-enhanced holography and feedback-tracked single-phase tracking for dynamic imaging (Schaffrath et al., 2023).
• Further reduction in technical noise and increased background immunity for robust operation in complex or photon-starved environments (Schaffrath et al., 2023).
• Broadened accessibility to spectral fingerprint regions (mid-IR, THz) for pharmaceutical, industrial, or biological analyses using undetected-photon protocols, with data acquisition and processing at visible/NIR wavelengths (Haase et al., 2022, Oglialoro et al., 5 May 2025).

A plausible implication is that as the technological maturity of hybrid quantum photonic platforms and nonlinear quantum interferometers increases, chip-scale bicolor quantum imagers will see widespread application in single-molecule detection, biomedical imaging, and label-free real-time spectroscopy, combining quantum measurement advantages with robust, scalable device integration.