50-km fiber interferometer for testing gravitational signatures in quantum interference

This paper reports the successful realization of a 50-km fiber Mach-Zehnder interferometer operating at the single-photon level that achieves sufficient phase sensitivity to detect modulated gravity-induced signals, thereby establishing a new milestone for testing quantum phenomena within general relativistic frameworks in a local laboratory setting.

The Gist

Imagine trying to hear a whisper in the middle of a roaring hurricane. That is essentially what physicists are doing when they try to measure how gravity affects a single particle of light.

This paper describes a groundbreaking experiment where scientists built a "super-sensitive ear" to listen to the universe's quietest whispers: the way gravity tugs on light. Here is the story of how they did it, broken down into simple concepts.

The Big Problem: Two Giants That Don't Talk

Physics has two "giant" rulebooks:

1. Quantum Mechanics: The rulebook for tiny things (like atoms and single photons).
2. General Relativity: Einstein's rulebook for huge things (like planets and gravity).

For over a century, these two books have lived in separate houses. They work perfectly on their own, but scientists have never been able to get them to have a conversation in a lab. We know gravity affects heavy things (like apples falling), and we know light behaves like a wave, but we haven't been able to prove how gravity changes the "dance" of a single photon of light in a way that requires both rulebooks to explain.

The Solution: A 50-Kilometer "Tightrope"

To hear that whisper, the scientists needed a very long path for the light to travel, but they couldn't build a telescope 50 kilometers long in their lab. Instead, they used fiber optic cables (the same kind that bring internet to your house) and coiled them up like a giant spool of yarn.

• The Setup: They created a "Mach-Zehnder interferometer." Imagine a race track split into two lanes.

  • Lane A: A 50-kilometer fiber optic cable.
  • Lane B: Another 50-kilometer fiber optic cable.
  • The Runner: A single photon (a particle of light) is sent into the system. It doesn't choose one lane; thanks to quantum magic, it runs down both lanes at the same time.

• The Goal: When the photon comes back together, the two "versions" of itself should meet perfectly in sync. If gravity pulls on one lane differently than the other, the photon gets slightly out of step (a "phase shift"). This tiny misalignment is the signal they are looking for.

The Challenge: The Hurricane of Noise

The problem is that the Earth is noisy.

• Thermal Noise: The fibers expand and contract as the temperature changes (even by a tiny fraction of a degree).
• Seismic Noise: Trucks driving by or people walking can shake the fibers.
• The Whisper: The signal from gravity is incredibly small. It's like trying to hear a pin drop while a jet engine is running next to you.

The Magic Trick: How They Solved It

The team (from the University of Vienna and MIT) used three clever tricks to silence the noise:

1. The "Twin" System: They didn't just measure the light; they sent a strong, steady laser beam (a "control laser") down the same path at the same time. This laser acts like a metronome. If the fiber expands or shakes, the control laser gets out of rhythm. The scientists use this to instantly fix the fiber's length, keeping the system perfectly stable.
2. The "Herald": They generated pairs of photons. One went into the 50km race, and the other was caught immediately by a detector. This "herald" photon told them, "Hey, a runner just started!" This allowed them to ignore all the random noise and only count the specific runners they were interested in.
3. The "Fake" Gravity: To prove their system worked, they didn't wait for a natural gravity shift (which is too slow). Instead, they simulated a gravity signal by slightly wiggling the control system. It's like shaking a ruler to see if a scale can detect the weight of a feather.

The Result: Hearing the Whisper

After running the experiment for 160 hours (almost a week straight), they succeeded.

• They measured a phase shift of roughly 0.00006 radians.
• To put that in perspective: If you had a clock hand that was 100 kilometers long, this shift would be moving the tip of the hand by less than the width of a human hair.
• They detected this tiny shift clearly above the background noise.

Why This Matters

This isn't just about measuring gravity; it's about opening a door.

• The Milestone: They proved that a "table-top" experiment (one that fits in a building, not a satellite) can be sensitive enough to test how gravity affects quantum particles.
• The Future: Now that they have this super-sensitive tool, they plan to build a version where the two fiber lanes are at different heights (one higher up than the other). This will allow them to measure the gravitational redshift (time running slower at the bottom than the top) on a single photon.

In a nutshell: They built a 50-kilometer-long, ultra-quiet listening device out of fiber optic cables. They taught it to ignore the noise of the Earth so it could finally hear the faint, quantum whisper of gravity. This is a massive step toward finally uniting the physics of the very small with the physics of the very large.

Technical Summary

1. Problem Statement

Modern physics rests on two pillars: Quantum Mechanics (QM) and General Relativity (GR). While both have been tested with high precision individually, experimental regimes where they must be applied simultaneously remain elusive.

• The Gap: Previous experiments testing gravity's effect on quantum systems (e.g., neutron interferometry) have been consistent with Newtonian gravity, not requiring a full GR explanation.
• The Challenge: Photons are massless, making them ideal for probing GR effects (like gravitational redshift) that Newtonian physics cannot describe. However, these effects are extremely small in Earth's weak gravitational field.
• Current Limitations: Laboratory-scale optical interferometers have historically lacked the sensitivity to detect these minute phase shifts. Space-based proposals exist but are technically demanding, costly, and weather-constrained. Existing fiber-based attempts have been limited by environmental noise and insufficient sensitivity.

2. Methodology

The authors constructed a large-scale, tabletop Mach-Zehnder fiber interferometer designed to operate at the single-photon level with extreme phase stability.

• Interferometer Architecture:
  • Scale: Two arms, each 50 km long, utilizing low-loss fiber spools.
  • Configuration: Both arms are maintained at the same height ($h=0$) in this initial demonstration to isolate system performance, though the theoretical framework ($\Delta\phi_g \propto h \cdot l$) allows for future vertical differential measurements.
  • Stabilization: The system uses active temperature control (stability at 0.1 mK) and acoustic isolation to minimize thermal and vibrational noise.
• Quantum Source & Detection:
  • Source: A Type-0 Spontaneous Parametric Down-Conversion (SPDC) source generates entangled photon pairs at 1550 nm.
  • Heralding: One photon serves as a "herald" (detected immediately), while the other traverses the 50-km interferometer.
  • Detectors: Superconducting Nanowire Single-Photon Detectors (SNSPDs) are used for high-efficiency detection.
  • Filtering: Dense Wavelength Division Multiplexers (DWDM) filter the photons to a 100 GHz bandwidth, achieving count rates $>40$ MHz.
• Phase Control & Locking:
  • A weak continuous-wave (CW) laser at 1542 nm co-propagates with the single photons to lock the interferometer phase.
  • Feedback Loop: A balanced homodyne detector measures the classical field's phase. Error signals drive an Acousto-Optic Modulator (AOM) for fast corrections and a fiber stretcher for slow drifts.
• Signal Injection:
  • To simulate a gravitational signal, weak sinusoidal modulations ($S_g$) are injected into the control signal.
  • The experiment targets a frequency range of 0.01 Hz to 5 Hz, where environmental noise is manageable.

3. Key Contributions

• Record Sensitivity: The team achieved a phase sensitivity of $4.42 \times 10^{-6}$ rad (RMS) within the 0.01–5 Hz frequency band. This represents a two-order-of-magnitude improvement over previous single-photon fiber interferometers.
• Signal Resolution: They successfully resolved a simulated signal with an RMS amplitude of $(6.18 \pm 0.44) \times 10^{-5}$ rad at 0.1 Hz. This magnitude is comparable to the gravitational phase shift expected from a tabletop apparatus with a vertical height difference.
• Noise Characterization: The study demonstrated that above 0.01 Hz, the system is limited by photon shot noise, confirming the quantum nature of the measurement. Below this frequency, classical noise (thermal, seismic) dominates.
• Scalability Proof: The successful operation of a 50-km fiber loop in a laboratory setting proves that long-baseline quantum sensing is feasible without satellite infrastructure.

4. Experimental Results

• Measurement Duration: Data was collected over two runs totaling 160 hours (68.8 h + 91.2 h), stitched together to form a "main measurement" dataset.
• Visibility: The interferometer maintained a fringe visibility of 98% when locked near $\phi_0 = \pi/2$.
• Signal Detection:
  • A reference tone at 0.25 Hz (amplitude $2.10 \times 10^{-3}$ rad) was used for calibration.
  • The target signal $S_g$ at 0.1 Hz (expected $6.48 \times 10^{-5}$ rad) was clearly resolved above the noise floor.
  • The measured value was $(6.18 \pm 0.44) \times 10^{-5}$ rad, consistent with the expected value within uncertainty.
• Stability: Allan Deviation (ADEV) analysis confirmed the signal is stationary and follows a $1/\sqrt{\tau}$ trend, characteristic of white noise processes, indicating high system stability over long integration times.
• Loss Budget: The total optical loss of the system was 14.99 dB (transmission efficiency ~3.17%), primarily due to fiber spools and components. This loss currently limits the count rate and thus the shot-noise floor.

5. Significance and Future Outlook

• Milestone in Quantum Sensing: This work establishes the first laboratory-based fiber interferometer capable of detecting gravitational signatures at the single-photon level. It bridges the gap between quantum optics and general relativity.
• Path to New Physics: The setup paves the way for testing Quantum Field Theory in Curved Spacetime (QFTCS). Future iterations will introduce a vertical height difference between the two arms to measure the differential phase shift between classical and quantum light.
  • The goal is to detect if entangled quantum fields experience gravitational redshift differently than classical fields, which could reveal deviations from current theoretical consensus.
• Technological Advancement: By replacing current fibers with ultra-low-loss fibers and improving vibration isolation, the authors project that the sensitivity can be further enhanced, potentially allowing for the detection of gravitational effects on entangled states in a local laboratory environment.

Conclusion:
This paper demonstrates a critical step toward unifying quantum mechanics and general relativity. By achieving unprecedented phase sensitivity in a 50-km fiber interferometer, the authors have created a viable platform to probe the intersection of gravity and quantum phenomena, moving beyond theoretical proposals to experimental reality.