Evidence for Vortex Rings with Multiquantum Circulation in He II

Using particle tracking velocimetry with frozen deuterium tracers, this study presents evidence of anomalously long-lived vortex rings with multiquantum circulation in superfluid helium-4, challenging the standard paradigm that such vortices rapidly split into singly quantized filaments.

The Gist

Imagine you are watching a dance party inside a super-cold, frictionless liquid called Superfluid Helium. In this world, the liquid behaves like a quantum superhero, and the only way it can spin is by forming tiny, invisible tornadoes called vortex rings.

For decades, physicists believed they knew the rules of this dance perfectly:

1. The "One-Size-Fits-All" Rule: Every tornado must carry exactly one unit of spin (circulation). If a tornado tries to carry two or more units of spin, it's considered unstable. It's like trying to stack two spinning tops on top of each other; they immediately wobble, split apart, and become two separate, single spinning tops.
2. The "Shrinking Balloon" Rule: As these rings move, they lose a tiny bit of energy to the surrounding liquid (like a balloon losing air). This causes them to shrink. As they shrink, they spin faster and faster, accelerating until they vanish.

The Discovery: The "Impossible" Dancers

In this new study, a team of scientists at Florida State University decided to watch these dancers up close. They sprinkled tiny, frozen specks of deuterium (like microscopic snowflakes) into the liquid to act as "trackers." When a vortex ring passes by, it grabs a snowflake and drags it along, leaving a visible trail.

Usually, the snowflakes followed the expected rules: they moved slowly, or they sped up as the ring shrank, but everything matched the "single-spin" theory.

However, they found a few "ghosts" in the machine.

They spotted rare events where a snowflake was being dragged by a ring that was accelerating incredibly fast. When the scientists crunched the numbers, they realized something impossible:

• If this were a normal, single-spin ring, it would have to be microscopic in size to move that fast.
• But a ring that small would shrink and disappear in a fraction of a second.
• Yet, these rings kept going for much longer than physics said they should.

The Solution: The "Super-Tornado"

The only way to explain this was to break the "One-Size-Fits-All" rule. The scientists realized these rings weren't carrying just one unit of spin. They were carrying multiple units (between 3 and 20 times the normal amount).

Think of it like this:

• Normal Ring: A single bicycle wheel spinning. It's fast, but if you try to make it spin twice as fast, it breaks apart.
• The New Discovery: A massive, reinforced industrial turbine made of multiple wheels fused together. Because it's so big and heavy (in terms of spin), it can spin incredibly fast without breaking apart immediately.

Why is this a big deal?

1. The "Splitting" Myth: The old theory said, "If you have multiple spins, you must split immediately." These rings proved that sometimes, they can stay fused together for a surprisingly long time. It's like finding a snowflake that refuses to melt even though the sun is shining.
2. The "Sticky" Mystery: The scientists also noticed that the snowflakes were holding on tight even when the ring was moving at breakneck speeds.
   • Analogy: Imagine a fly stuck to a spinning fan blade. If the fan spins too fast, the fly gets flung off.
   • In a normal ring, the "fly" (snowflake) should have been flung off long ago.
   • But because this was a "Super-Tornado" (multiquantum), the "grip" on the fly was much stronger (scaling with the square of the spin). It was like the fan blade had super-strong glue, keeping the fly attached even at high speeds.

Could it be a trick?

The scientists asked: "Maybe it's not one big ring, but a bunch of tiny rings huddled together like a tight group of friends?"

• They ran computer simulations to test this.
• The result: If you put a bunch of single rings together, they act like a flock of birds that gets scattered by the wind almost instantly. They can't stay together long enough to explain what the scientists saw.
• This confirmed that these were likely true, fused multiquantum rings, not just a temporary crowd.

The Big Question

The paper ends with a fascinating mystery: How do they stay together?
In other quantum systems, scientists know how to stabilize these "super-spin" states (usually by filling the center with something else). But here, the only thing inside the ring is a single, tiny snowflake. It's like a tornado staying stable just because a single pebble is stuck in the middle.

In Summary:
The scientists found rare, long-lived "super-tornadoes" in liquid helium that carry multiple spins at once. They move fast, stay together against the odds, and hold onto their passengers tightly. This discovery challenges the old rulebook of quantum physics and suggests that nature has a few more tricks up its sleeve than we thought.

Technical Summary

Here is a detailed technical summary of the paper "Evidence for Vortex Rings with Multiquantum Circulation in He II."

1. Problem Statement

In superfluid $^4$He (He II), the dynamics of quantized vortices are generally considered well-understood within the framework of Landau's two-fluid model. The prevailing paradigm dictates that:

• Circulation is strictly quantized in units of $\kappa = h/m_4$.
• Vortices carrying more than one quantum of circulation ($n\kappa$, where $n > 1$) are energetically unfavorable. The energy of a single ring with $n$ quanta scales as $n^2$, whereas $n$ separate singly quantized rings scale as $n$. Consequently, multiquantum vortices are expected to rapidly split into singly quantized filaments.
• Vortex rings shrink and accelerate over time due to mutual friction (dissipation from thermal quasiparticle scattering).

The authors identify a discrepancy between this established theory and rare experimental observations: specific particle-tracking events show tracer particles accelerating in a manner consistent with shrinking vortex rings, but the kinematics cannot be explained by singly quantized rings ($n=1$).

2. Methodology

The study utilizes Particle Tracking Velocimetry (PTV) with frozen deuterium ($D_2$) tracers to visualize vortex dynamics in He II.

• Experimental Setup:
  • A mixture of $D_2$ and He gas is injected into an experimental cell connected to a He II bath.
  • The $D_2$ solidifies into ice particles with a mean radius $a_p \approx 1.1 \, \mu\text{m}$.
  • A chip-resistor heater is used to generate vortices via thermal pulses.
  • A thin laser sheet ($\sim 150 \, \mu\text{m}$) illuminates the particles, and a camera records motion at 200 Hz.
• Data Analysis:
  • Feature-point tracking algorithms extract particle coordinates.
  • Particle velocities ($v_p$) are analyzed to infer vortex ring kinematics (radius $R$ and propagation speed $v_{\parallel}$).
  • Theoretical models (Schwarz model) are used to predict the shrinkage and acceleration of vortex rings based on mutual friction coefficients ($\alpha$).
• Exclusion of Alternatives:
  • Electrostatic Drift: The authors ruled out electric field acceleration by testing various heater voltages and calculating the unrealistic charge ($Q \approx -800e$) required to explain the motion via electrostatics.
  • Bundle of Rings: They simulated bundles of closely spaced singly quantized rings using the Schwarz model to see if they could mimic a multiquantum ring.

3. Key Contributions and Results

A. Observation of Anomalous Kinematics

The researchers observed rare events where a single tracer particle moved at high speeds and accelerated rapidly, characteristic of a shrinking vortex ring.

• The Discrepancy: When fitting the observed initial speeds ($v_p(0)$) to the standard theory for a singly quantized ring ($n=1$), the inferred initial radius $R(0)$ was extremely small ($\approx 1.8 \, \mu\text{m}$). Such a small ring would dissipate and shrink too quickly to match the observed trajectory duration.
• The Multiquantum Fit: The data could only be reconciled with theory if the rings carried multiquantum circulation ($n\kappa$), with $n$ ranging from 3 to 20.
  • For $n > 1$, the effective core size increases, and the initial radius $R(0)$ becomes $n$ times larger than in the $n=1$ case.
  • This larger radius allows the ring to persist for the observed duration while accelerating, matching the experimental velocity curves ($v_p(t)$) perfectly.

B. Ruling Out Ring Bundles

The authors considered the possibility that the observed motion was actually a "bundle" of $n$ closely spaced singly quantized rings acting as a single entity.

• Simulation Results: Numerical simulations using the Schwarz model showed that such bundles disperse rapidly under mutual friction over distances far shorter than the observed particle trajectories.
• Conclusion: The persistence of the coherent motion rules out a simple bundle of singly quantized rings as the primary explanation.

C. Particle Trapping Stability

A critical puzzle was how the $D_2$ particles remained trapped on the vortex core despite reaching high speeds.

• Detrapping Threshold: For a singly quantized vortex, the maximum trapping force is limited. As the ring shrinks and speeds up, Stokes drag should pull the particle off the core once the speed exceeds a threshold ($v_{th} \approx \text{few mm/s}$).
• Multiquantum Resolution: In the multiquantum scenario, the trapping force scales with $n^2$. The authors calculated the ratio of observed final speeds to the detrapping threshold ($v_p/v_{th}$).
  • For $n=1$, the ratio was $>1$ (implying the particle should have detached).
  • For the inferred $n$ values (3–20), the ratio remained $<1$, confirming that the enhanced trapping potential of a multiquantum core is necessary to sustain the particle at the observed high speeds.

D. Universal Scaling

The data for various temperatures and heater voltages collapsed onto a universal scaling curve for the ring radius evolution:
$$R^2(t)/R^2(0) \simeq 1 - t/\tau$$
This confirms that the events are governed by vortex-ring dynamics, with the time scale $\tau$ dependent on the multiquantum circulation $n$.

4. Significance and Implications

• Challenge to Established Paradigm: The findings directly challenge the long-held belief that multiquantum vortices in He II are short-lived and instantly split into singly quantized filaments. The data suggests the existence of anomalously long-lived multiquantum rings.
• Stabilization Mechanism Unknown: The paper highlights a major theoretical gap: there is currently no framework explaining how these rings remain stable.
  • In other quantum fluids (e.g., two-component BECs), internal structure or mass loading stabilizes multiquantum vortices.
  • In this experiment, the only "internal structure" is the single trapped $D_2$ particle. The authors speculate that this particle might stabilize the core or a tightly packed bundle, but the physics of how a single micron-sized particle stabilizes a ring with a radius of $50\text{--}200 , \mu\text{m}$ remains unexplained.
• Future Research: The results call for dedicated scrutiny of core instability pathways and the potential role of particle loading in modifying vortex stability, suggesting that the "settled" physics of He II vortex dynamics may require revision.

Conclusion

The paper provides compelling experimental evidence for the existence of stable, long-lived vortex rings with multiquantum circulation ($n=3$ to $20$) in superfluid helium. By combining high-precision particle tracking, rigorous kinematic analysis, and numerical simulations, the authors demonstrate that standard singly quantized models fail to explain the observed acceleration and particle trapping, necessitating a re-evaluation of vortex stability mechanisms in quantum fluids.