When Dysprosium Atoms Sit in a Vacuum, Quantum Fluctuations Hold Them Together Like a Liquid

If you open a gas canister in a vacuum chamber, the atoms rush outward to fill every available cubic millimeter. A gas expands; a liquid holds its own volume.

In 2016, a research team led by Tilman Pfau at the University of Stuttgart crossed intersecting laser beams inside a ultra-high vacuum chamber, trapped a cloud of dysprosium atoms, cooled them to a few billionths of a kelvin above absolute zero, and then switched off the optical trap entirely.

The cloud did not expand. Instead, as published in Physical Review Letters and Nature, the dysprosium atoms formed a microscopic, self-bound liquid droplet floating in empty space. It held its shape without walls, containers, or external force fields.

Measured.

To understand why this breaks macroscopic intuition, consider how normal gases condense. Steam turns into liquid water because attractive van der Waals forces between molecules overcome thermal motion when the temperature drops. But ultracold atomic gases are ridiculously dilute—roughly eight orders of magnitude less dense than liquid helium. At those low densities, short-range atomic collisions usually supply a uniform, isotropic pressure. If the collisions are repulsive, the gas expands. If they are attractive, classical mean-field theory dictates that the cloud must implode, shrinking to a point until inelastic three-body collisions blast the atoms out of the trap.

Dysprosium changes the math because of its extreme electronic configuration. Atom 66 on the periodic table carries a massive magnetic dipole moment—nearly 10 Bohr magnetons. When dysprosium atoms chill into a Bose-Einstein condensate, they act like trillions of microscopic bar magnets aligned in parallel.

Two parallel magnetic dipoles repulse each other if they sit side-by-side, but attract each other if they align head-to-tail. This directional, long-range dipole-dipole force competes directly with the isotropic, short-range contact interaction between atoms.

By adjusting an external magnetic field, Pfau's team—including Igor Ferrier-Barbut, Matthias Schmitt, Matthias Wenzel, and Holger Kadau—tuned the short-range contact interaction so that it failed to counterbalance the magnetic dipole attraction. At the mean-field level, the net interatomic forces became purely attractive. Standard physics predicted an immediate mean-field collapse—a total implosion of the quantum gas.

The implosion never happened.

The collapse was arrested by a quantum mechanical effect first calculated in 1957 by Tsung-Dao Lee, Kerson Huang, and Chen-Ning Yang. In classical physics, a vacuum is empty space. In quantum mechanics, Heisenberg’s uncertainty principle guarantees that the zero-point energy of a field fluctuates continuously. When a dipolar quantum gas gets compressed into an ultra-dense state during an impending implosion, these zero-point quantum fluctuations generate a tiny, extra repulsive energy density.

Because this Lee-Huang-Yang correction grows faster with density than the attractive mean-field energy, it acts as an absolute quantum barrier. The attractive long-range dipoles pull the atoms together; the quantum fluctuations push back.

Where those two forces meet, a local minimum in the energy density forms. The result is a self-bound quantum droplet: a liquid state of matter held together by magnetic forces and stabilized against collapse by zero-point quantum uncertainty.

In their November 2016 report in Nature, the Stuttgart researchers demonstrated that these droplets exhibit a strict critical atom number. If a droplet contains several thousand dysprosium atoms, the attractive magnetic dipoles win out over the kinetic expansion, maintaining a stable liquid drop in a trap-free levitation field. But if evapouration reduces the droplet below a critical threshold, quantum pressure destabilizes the balance. The droplet abruptly undergoes an interaction-driven phase transition, evaporating back into a free gas.

The density of this liquid is a paradox in itself. It is a superfluid liquid—atoms flow without friction—yet its density is 100 million times lower than liquid water. It is a self-bound liquid made almost entirely of empty space, kept intact by the zero-point jitter of the vacuum.

Measured.

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