⚛️ quantum physics

Simultaneous amplitude and phase spectroscopy using two-photon interference

This paper proposes and demonstrates a quantum spectroscopy technique using entangled photon pairs and two-photon interference to simultaneously measure both the absorption and phase shift of chemical and biological samples with high precision at extremely low optical intensities.

Original authors: Kyle M. Jordan (National Research Council Canada, Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics), Yingwen Zh

Published 2026-03-18

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CC BY 4.0

Original authors: Kyle M. Jordan (National Research Council Canada, Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics), Yingwen Zhang (National Research Council Canada, Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics), Frédéric Bouchard (National Research Council Canada), Duncan England (National Research Council Canada), Philip J. Bustard (National Research Council Canada), Benjamin J. Sussman (National Research Council Canada, Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics), Jeff S. Lundeen (Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics), Andrew H. Proppe (National Research Council Canada, Department of Physics and Nexus for Quantum Technology, University of Ottawa, University of Ottawa-NRC Joint Center for Extreme Photonics)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand a mysterious, delicate object—like a rare, fragile flower or a tiny quantum dot. You want to know two things about it:

How much light does it swallow? (Absorption)
How does it twist the light that passes through? (Phase shift)

Usually, scientists use bright lasers to figure this out. But here's the problem: bright lasers are like a firehose. If you spray a firehose on that fragile flower, you might burn it or change its shape before you even finish measuring it. This is called "photodamage."

The researchers in this paper invented a new way to measure these delicate objects using a "gentle whisper" of light instead of a firehose. They used entangled photons (pairs of light particles that are magically linked) to measure both absorption and phase simultaneously without hurting the sample.

Here is how they did it, explained with some everyday analogies:

1. The Magic Twin Pair (Entangled Photons)

Imagine you have a pair of magical twins, Red and Blue. They are born at the exact same time and are perfectly synchronized.

If Red is wearing a red hat, Blue is wearing a blue hat.
If Red is hungry, Blue is hungry.
They are so connected that if you know everything about Red, you instantly know everything about Blue, even if they are in different rooms.

In the lab, the scientists create these twins using a special crystal. One twin (the Probe) is sent to look at the sample (the flower). The other twin (the Herald) is sent to a detector to act as a "witness."

2. The "Herald" Trick (Measuring Absorption)

In traditional spectroscopy, you shine light on a sample and count how much comes out. But if your light source flickers (which lasers do slightly), you might think the sample absorbed light when it was actually just the light source dimming.

The scientists use the Herald to fix this.

The Analogy: Imagine you are counting how many apples fall from a tree. You can't see the tree well, so you count the apples hitting the ground. But sometimes the wind blows them away, or you miss a count.
The Quantum Fix: Instead, you have a magical twin apple that flies away from the tree in the opposite direction. Every time the twin apple flies away, you know exactly one apple was sent toward the tree.
By counting the "witness" twin, the scientists know exactly how many photons hit the sample. If the witness says "100 twins were sent," but the detector on the sample side only sees "80," then the sample absorbed 20. This removes all the guesswork and noise, allowing them to use incredibly low light levels (a few photons) and still get a perfect count.

3. The "Dance Floor" (Measuring Phase with HOM Interference)

Measuring the "phase" (how the light is twisted or delayed) is harder. It's like trying to measure if a dancer is slightly out of step without seeing them clearly.

The scientists use a trick called Hong-Ou-Mandel (HOM) interference.

The Analogy: Imagine two identical dancers (the twins) running toward a crossroads with a traffic cop (a beam splitter).
- If they arrive at the exact same time and are perfectly identical, quantum mechanics says they will always dance together. They will either both turn left or both turn right. They will never split up (one left, one right).
- However, if the sample (the flower) delays one of the dancers slightly, they arrive at the crossroads at slightly different times. Now, they might split up.
The Measurement: By watching how often the twins split up versus how often they stay together, the scientists can calculate exactly how much the sample delayed the light. This delay is the "phase shift."

4. The Super-Sensitive Camera

To see all this, they used a special camera that can see individual photons and record exactly when they arrived (down to a billionth of a second).

They send the twins through the sample.
They mix them at the crossroads (beam splitter).
The camera takes a "snapshot" of where the twins ended up and what color they were.

Why is this a big deal?

Gentle Touch: Because they use such low light (picojoules, which is a tiny fraction of a watt), they can measure light-sensitive things like organic molecules or biological cells without burning them.
Two-in-One: Previous quantum methods could only measure absorption or phase. This method measures both at the same time with a single probe.
Speed: They can get a full spectrum (a complete picture of the sample's properties) in just a few minutes.

The Bottom Line

Think of this technique as a ghostly detective. Instead of shining a blinding flashlight on a fragile crime scene (the molecule), the detective sends in a pair of invisible, linked spies. One spy checks the scene, while the other stays at headquarters. Because they are linked, the detective knows exactly what happened at the scene without ever needing to turn on a bright light that would disturb the evidence.

This opens the door to studying delicate biological processes and new materials that were previously too fragile to examine with traditional lasers.

1. Problem Statement

Traditional optical spectroscopy relies heavily on measuring the amplitude (absorption) of light transmitted through a sample to determine its electronic structure. However, the phase shift imparted by the sample contains complementary information, particularly regarding dynamical processes and resonance linewidths.

Limitations of Classical Methods: Measuring phase usually requires interferometry (e.g., white-light or pump-probe), which often necessitates intense laser pulses. These high intensities can cause photodamage or irreversible changes in light-sensitive samples (e.g., organic fluorophores, quantum dots, single emitters).
Limitations of Existing Quantum Methods: Previous quantum spectroscopy techniques using entangled photon pairs (heralded absorption) successfully surpassed the shot-noise limit (SNL) for absorption measurements by utilizing intensity correlations. However, these methods were insensitive to phase shifts, measuring only absorption.
The Gap: There was a lack of a technique capable of simultaneously measuring both absorption and phase with ultra-low photon flux (to prevent sample damage) and high precision, without requiring complex active phase stabilization.

2. Methodology

The authors propose and demonstrate a scheme combining heralded absorption spectroscopy with spectrally resolved Hong-Ou-Mandel (HOM) interference.

Photon Source: They generate broadband, frequency-entangled photon pairs via Spontaneous Parametric Down-Conversion (SPDC) in a PPKTP crystal. One photon serves as the probe (interacting with the sample), and the other as the herald (reference).
Experimental Setup:
1. The probe beam passes through the sample, acquiring absorption ( $A$ ) and phase shift ( $\phi$ ).
2. The probe and herald beams are combined at a 50:50 beam splitter.
3. A variable delay ( $\tau$ ) is applied to the herald arm to scan the interference.
4. Output photons are detected by a time-tagging spectrometer (a camera with nanosecond timing resolution) capable of resolving the joint spectrum of photon pairs.
Dual-Parameter Extraction:
- Absorption ( $A$ ): Measured via the ratio of coincidence counts (paired photons) to single counts (unpaired photons). If the sample absorbs a probe photon, the herald photon is detected alone (single click). The strong intensity correlations between the twin beams allow for sub-shot-noise precision in determining transmission.
- Phase ( $\phi$ ): Measured via HOM interference fringes. When the probe and herald photons overlap in time, frequency, and polarization at the beam splitter, they exhibit quantum interference (bunching or antibunching). The position of these interference fringes in the joint spectrum depends on the relative phase difference between the two frequencies ( $\phi(\omega_1) - \phi(\omega_2)$ ). By varying the delay $\tau$ , the phase shift imparted by the sample is extracted from the fringe displacement.

3. Key Contributions

Simultaneous Measurement: This is the first demonstration of a single quantum probe measuring both absorption and phase spectra simultaneously.
Low-Intensity Operation: The technique operates with probe powers in the femtowatt range (few picojoules total energy), making it ideal for photosensitive samples where classical high-intensity lasers would cause damage.
Phase Stability: Unlike classical interferometers (Mach-Zehnder) that require active stabilization of path lengths, this HOM-based scheme relies on the phase difference between two frequencies. This allows for stable interference fringes even with wavelength separations $>100$ nm without active feedback.
Model-Free Characterization: The method provides a direct, model-free determination of the complete linear optical response (complex dielectric function) without relying on Kramers-Kronig relations to infer phase from absorption.

4. Results

The authors applied this technique to measure the infrared absorption and phase spectra of Silicon 2,3-naphthalocyanine dichloride (SiNC) dye molecules in a toluene solution.

Data Acquisition: Measurements were completed in approximately 5 minutes per sample with total exposure times of a few minutes.
Accuracy:
- The measured absorption spectrum matched the qualitative features and quantitative peak values of a conventional spectrometer (Horiba Duetta).
- The measured phase spectrum agreed with the phase calculated via Kramers-Kronig relations from the conventional absorption data.
Precision: The system demonstrated the ability to resolve resonance features in both amplitude and phase. The error bars (standard deviation from 10 repetitions) confirmed the statistical reliability of the measurements.
Systematic Errors: The authors identified that coupling light into single-mode fibers introduced systematic errors due to beam deflection by the sample cuvette (spatial-spectral correlations). They proposed calibration procedures and future engineering solutions (e.g., uncorrelated spatial-spectral sources) to mitigate this.

5. Significance

New Class of Quantum Spectroscopy: This work establishes a new paradigm where quantum correlations are used not just to beat the shot-noise limit, but to extract multiple physical quantities (amplitude and phase) from a single low-flux probe.
Biological and Chemical Applications: The technique is directly applicable to characterizing light-sensitive biological samples, organic molecules, and single emitters (like quantum dots) that cannot withstand the high intensities of traditional pump-probe or white-light interferometry.
Scalability: While the current system efficiency is limited by detector quantum efficiency and fiber coupling losses, the authors note that improvements in superconducting nanowire detectors and fiber-coupled sources could significantly enhance the signal-to-noise ratio and enable quantum-enhanced precision in broader applications.

In summary, this paper bridges the gap between high-precision quantum metrology and practical chemical spectroscopy, offering a robust, low-damage method to fully characterize the optical response of delicate materials.