[Paper Review] Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow

V. M. H. Ruutu, V. B. Eltsov+7 more|arXiv (Cornell University)|Dec 15, 1995

Quantum, superfluid, helium dynamics181 citations

TL;DR

This paper demonstrates that rapid quenching of superfluid 3He-B via neutron-induced heating nucleates a random network of quantized vortices, mimicking cosmological defect formation during symmetry-breaking phase transitions. The number of detectable vortices scales cubically with superflow velocity, and the critical velocity for vortex escape follows a universal scaling law consistent with Kibble-Zurek theory, validating laboratory analogues of early-universe topological defect formation.

ABSTRACT

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of the Magnus force and escape into the container volume where they are detected individually with nuclear magnetic resonance. The larger the superflow velocity the smaller the rings which can expand. Thus it is possible to obtain information about the morphology of the initial defect network. We suggest that the nucleation of vortices during the rapid cool-down into the superfluid phase is similar to the formation of defects during cosmological phase transitions in the early universe.

Motivation & Objective

• To investigate the nucleation of topological defects during a rapid, non-equilibrium phase transition in superfluid 3He-B, analogous to cosmological symmetry-breaking transitions in the early universe.
• To test the Kibble-Zurek mechanism for defect formation in a controlled laboratory environment using superfluid 3He-B as a model system.
• To measure the dependence of vortex nucleation on superflow velocity and temperature, and to extract the critical velocity threshold for vortex escape.
• To probe the initial morphology of the defect network by detecting individual vortices that expand under the Magnus force in a superflow.

Proposed method

• A thermal neutron from an Am-Be source is absorbed in superfluid 3He-B, depositing 0.76 MeV of energy in a localized, cigar-shaped region, heating it into the normal phase.
• The heated region cools rapidly via quasi-particle diffusion with a characteristic time τQ ~ 10⁻⁶ s, inducing a fast quench through the superfluid transition.
• The quench generates a random network of quantized vortices due to the Kibble mechanism, with vortex line density determined by the coherence length and quench rate.
• Superflow is created by rotating the container, inducing a relative velocity vs between the normal and superfluid components, which stabilizes and expands vortices beyond a critical size.
• Vortex rings that exceed the critical radius r₀(vs) expand and are pulled toward the container center, where they are detected individually via nuclear magnetic resonance (NMR).
• The number of detected vortices per neutron event is measured as a function of vs, and the data are fitted to a universal scaling law derived from the Kibble-Zurek theory.

Experimental results

Research questions

• RQ1 How does the number of nucleated vortices in superfluid 3He-B depend on the superflow velocity during a rapid quench?
• RQ2 Does the observed vortex nucleation rate and distribution match the predictions of the Kibble-Zurek mechanism for cosmological defect formation?
• RQ3 What is the critical superflow velocity vs,cn at which vortices begin to escape the heated region and become detectable?
• RQ4 Can the initial size distribution of vortex loops be probed by measuring the velocity dependence of vortex counts?
• RQ5 Is the vortex nucleation process in superfluid 3He-B a universal analog of topological defect formation in the early universe?

Key findings

• The number of vortices detected per neutron event increases cubically with superflow velocity, consistent with the theoretical prediction N(vs) ∝ (vs/vcn)³.
• The critical velocity vcn for vortex escape scales as vcn ∝ (1 − T₀/Tc)¹ᐟ³, matching the measured temperature dependence at different pressures.
• The vortex number distribution follows a scale-invariant power law n(D) ∝ D⁻⁴ for loop diameter D, with a lower cutoff Dmin ∝ ξ(t), the evolving coherence length.
• The experimental data collapse onto a universal curve N(vs/vcn) = (πC/9)[(vs/vcn)³ − 1], with C ≈ 0.3, confirming the universality of the Kibble-Zurek mechanism.
• The measured critical velocity vcn is smaller and exhibits a different temperature dependence than the critical velocity for vortex nucleation in the absence of neutron heating.
• The morphology of the initial defect network is probed by detecting vortices that form at earlier stages of the quench, with smaller loops detectable at higher superflow velocities.