Multi-loop and Multi-axis Atomtronic Sagnac Interferometry

This paper reports the experimental realization of a large-area, multi-loop, and multi-axis atomtronic Sagnac interferometer using Bose-Einstein condensates in an optical waveguide, achieving a record enclosed area of 8.7 mm² and demonstrating high-contrast rotation sensing capabilities across multiple arbitrary axes.

The Gist

Imagine you are trying to measure how much a spinning top is wobbling. To do this, you might send two tiny runners around a track in opposite directions. If the track is spinning, one runner will have to run slightly farther than the other to meet back up. By measuring that tiny difference, you can calculate exactly how fast the track is spinning.

This is the basic idea behind a Sagnac interferometer, a super-precise sensor used to detect rotation. Usually, scientists use light for this, but this paper describes a breakthrough using atoms (specifically, a cloud of ultra-cold rubidium atoms) instead.

Here is the story of what the scientists at Los Alamos National Laboratory achieved, explained simply:

1. The "Super-Cold" Cloud (The BEC)

First, the team created a Bose-Einstein Condensate (BEC). Think of this as taking thousands of atoms and cooling them down until they are so cold they stop acting like individual particles and start behaving like a single, giant "super-atom" wave. It's like a choir where every singer hits the exact same note perfectly in sync, creating a single, powerful sound wave.

2. The "Train Track" (The Waveguide)

Instead of letting these atoms fall through the air (which limits how long you can measure them), the scientists built an invisible "train track" made of laser light. This is called an optical waveguide.

• The Analogy: Imagine a marble rolling inside a long, curved glass tube. The tube keeps the marble from falling out and guides it exactly where you want it to go.
• The Benefit: Because the atoms are trapped in this "tube," the scientists can keep them around for a much longer time (about 0.4 seconds) compared to free-falling atoms. Longer time means a more sensitive measurement.

3. The "Multi-Loop" Trick (Running More Laps)

In a standard sensor, the atoms run one loop and meet back up. The scientists wanted to make the sensor more sensitive, so they made the atoms run multiple loops before meeting again.

• The Analogy: Imagine a runner on a track. If they run one lap, they cover a certain distance. If they run three laps, they cover three times the distance.
• The Result: By making the atoms run three loops, the scientists created a massive "enclosed area" (8.7 square millimeters). This is the largest area ever achieved in this type of guided setup. It's like turning a small garden path into a giant racetrack without making the track physically wider, just by making the runner go around more times.

4. The "Magic Lens" (Delta-Kick Collimation)

There was a problem: When you cool atoms, they still wiggle a little. If they wiggle too much, the "super-atom" wave gets blurry, and the measurement fails.

• The Solution: The team used a technique called "delta-kick collimation."
• The Analogy: Imagine a group of runners starting a race. Some are fast, some are slow, and they spread out. Just as they start to get messy, a "magic lens" (a quick pulse of force) hits them all at once, snapping them back into a tight, perfect line. This keeps the atoms organized for a long time, allowing them to run those multiple loops without losing their "team spirit."

5. The "360-Degree" Sensor (Multi-Axis)

Most rotation sensors can only tell you if something is spinning left or right (like a car turning). This new device can sense spinning in any direction (up, down, left, right) without needing to be rebuilt.

• The Analogy: Think of a standard compass that only points North. This new device is like a 3D gyroscope that can tell you if you are tilting forward, backward, or sideways, all using the same setup. They achieved this by simply rotating the "laser track" 90 degrees.

6. The "Vibration Problem" (The Accelerometer Fix)

The biggest enemy of these delicate experiments is vibration. If the table the equipment sits on shakes even a tiny bit, it looks like the atoms are moving, ruining the measurement.

• The Fix: The scientists attached a super-sensitive accelerometer (like the one in your phone that detects when you shake it) to the mirror that reflects the laser.
• The Result: The accelerometer measures the tiny shakes in real-time. The computer then uses this data to "subtract" the noise from the final result, like using noise-canceling headphones to remove the sound of a jet engine so you can hear a whisper. This doubled the clarity of their measurements.

Why Does This Matter?

This isn't just a cool science experiment; it's a step toward ultra-precise navigation.

• Current Tech: GPS is great, but it doesn't work underground, underwater, or in space where signals are blocked.
• The Future: This atom-based sensor is like a "quantum compass" that doesn't need satellites. It could guide submarines, spacecraft, or drones with incredible accuracy, even in places where GPS fails.

In a nutshell: The scientists built a tiny, ultra-cold "race track" for atoms, made them run extra laps to increase sensitivity, used a magic lens to keep them organized, and added a noise-canceling system to get a crystal-clear reading of rotation in any direction. It's a major leap toward making high-tech navigation devices small enough to fit in a backpack.

Technical Summary

1. Problem Statement

Atom interferometry is a powerful tool for measuring inertial forces, including rotation (Sagnac effect). However, traditional free-fall atom interferometers are limited by the time atoms spend in the air before hitting the ground, restricting interrogation times and the enclosed area (which dictates sensitivity). While guided atom interferometers (atomtronics) allow for longer interrogation times by trapping atoms in optical or magnetic waveguides, previous guided schemes faced challenges:

• Limited Enclosed Area: Achieving large Sagnac areas in guided systems is difficult due to geometric constraints and gravity-induced wavepacket separation.
• Multi-axis Sensing: Sensing rotation about multiple axes typically requires complex hardware reconfigurations or gravity compensation when tilting the loop plane away from horizontal.
• Contrast Degradation: Increasing the number of loops or interrogation time often leads to a loss of fringe contrast due to wavepacket overlap issues, mean-field interactions, and environmental noise.

The authors aim to realize a large-area, multi-loop, and multi-axis guided atom interferometer capable of high-sensitivity rotation sensing in a compact package, overcoming the limitations of free-fall and single-loop guided systems.

2. Methodology

The experiment utilizes a Bose-Einstein Condensate (BEC) of approximately 1,000 $^{87}$Rb atoms guided within a linear optical waveguide. The core methodology involves:

• Delta-Kick Collimation: The BEC is prepared in a large-size state with few thousand atoms to minimize mean-field interactions. A "delta-kick" lens (a time-averaged harmonic potential) is applied to collimate the wavepacket, achieving an effective temperature of 1.1 nK and an axial size of 120 µm. This allows for long interrogation times while maintaining high fringe contrast.
• Moving Waveguide Scheme: Instead of moving the atoms through a static guide, the optical guide itself is translated using an Acousto-Optic Deflector (AOD). The sequence involves:
  1. Beam Splitter (BS): Splits the BEC into two momentum states ($\pm 2\hbar k$) via Bragg diffraction.
  2. Guide Motion: The guide is moved outward and back using a "Shortcut to Adiabaticity" (STA) trajectory to minimize vibrations and maximize enclosed area.
  3. Mirror (M) Pulses: Reverses the momentum of the atoms to close the loop.
  4. Recombination: A final BS pulse recombines the wavepackets.
• Multi-Loop Operation: To increase the enclosed area, the system performs multiple Sagnac orbits. The last BS pulse is omitted, allowing wavepackets to pass through each other, followed by repeated guide motion and mirror pulses.
• Phase Correction: A critical component is the use of classical accelerometers (InnaLabs AI-Q-2110) mounted on the retro-reflection mirror and the optical table. These measure mirror vibrations and table motion, allowing for post-processing phase correction of each experimental run to remove noise.
• Multi-Axis Configuration: The system demonstrates rotation sensing in both vertical and horizontal planes by rotating the AOD by 90°, allowing the guide to move in orthogonal directions without changing the fundamental hardware.

3. Key Contributions

• Largest Guided Area: The authors report the largest enclosed Sagnac area achieved in a fully guided (one-dimensional) setup to date: 8.7 mm² using a three-loop interferometer.
• Multi-Loop Demonstration: Successful realization of a five-loop interferometer (enclosing 0.13 mm²) and a three-loop interferometer (enclosing 8.7 mm²) with a total interrogation time of ~0.4 s.
• Multi-Axis Capability: Demonstration that the interferometer maintains comparable contrast when sensing rotation in orthogonal planes (vertical vs. horizontal), proving the feasibility of multi-axis sensing without gravity compensation issues common in other guided schemes.
• Optimized Trajectory: Implementation of the STA protocol for guide motion, which increases the enclosed area by ~25% compared to constant-velocity motion by allowing wavepackets to travel further during the slow-start and slow-stop phases of the guide movement.

4. Key Results

• Interferometer Performance:
  • 3-Loop (Vertical): Total interrogation time $T \approx 371$ ms, enclosed area $8.7 \text{ mm}^2$, fringe contrast $C \approx 0.05$.
  • 2-Loop (Vertical): $T \approx 246$ ms, area $5.8 \text{ mm}^2$, contrast $C \approx 0.13$.
  • 1-Loop (Vertical): $T \approx 124$ ms, area $2.9 \text{ mm}^2$, contrast $C \approx 0.26$.
  • 5-Loop (Vertical): $T \approx 108$ ms, area $0.13 \text{ mm}^2$, contrast $C \approx 0.20$.
  • 1-Loop (Horizontal): $T \approx 160$ ms, area $3.2 \text{ mm}^2$, contrast $C \approx 0.12$.
• Contrast Improvement: The application of accelerometer-based phase correction improved the average fringe contrast by a factor of roughly 2 (e.g., from 0.23 to 0.6 in a static guide test).
• Sensitivity Metrics:
  • Scale Factor: $2.4 \times 10^4 \text{ rad/(rad/s)}$ for the 8.7 mm² loop.
  • Rotation Error: Estimated at 20 µrad/s.
  • Angle Random Walk (ARW): Estimated at 2.4 deg/$\sqrt{\text{hr}}$, comparable to state-of-the-art 2D waveguide interferometers.
• Limitations Observed: Contrast decreases with increasing loop numbers primarily due to technical issues (wavepacket overlap, table vibrations, thermal lensing from the AOD) rather than fundamental quantum limits. Phase diffusion due to atomic interactions is estimated to be negligible for the current timescales (~1 s).

5. Significance

This work represents a significant step toward realizing compact, high-performance atomic gyroscopes for inertial navigation.

• Scalability: By demonstrating that large areas can be achieved through multi-loop operations in a guided system, the authors show a path to scaling sensitivity without the massive physical footprint required by free-fall systems.
• Versatility: The ability to switch between vertical and horizontal sensing axes with the same setup addresses a major hurdle in developing practical, multi-axis inertial sensors.
• Robustness: The successful use of delta-kick collimation and accelerometer correction proves that high-contrast interference is achievable even with small atom numbers and long interrogation times, making the system more robust against environmental noise.
• Future Outlook: The paper suggests that further improvements in condensate production (sub-Hz machines), better beam steering (piezo mirrors), and higher momentum transfers could push the enclosed area to $1 \text{ cm}^2$ and improve bias stability to navigation-grade levels.