Breathing of Quantum Droplets: A Simple Formula for Precise Measurements ✛ ✦

Original: "Breathing mode of quantum droplets in dipolar quantum gases: A sum-rule analysis"
arXiv:2606.29370 · 2026-06-28 · CC BY 4.0 · 1 min
Simple formulas unveiled the pulsation rhythm of quantum droplets — ultra-dilute clumps of matter.

Quantum droplets are clumps of atoms cooled to near absolute zero. They form when magnetic atoms attract via dipole forces, but a constant microscopic jitter — quantum fluctuations — prevents them from collapsing. The droplet pulsates rhythmically, like a breathing ball. Its 'springiness' abruptly changes when transitioning from an ordinary Bose condensate (predicted by Einstein and Bose) to the droplet state. Chinese physicists developed a simple method to predict the frequency of this breathing: they used superposition — a mental blend of all motions — and derived concise formulas. Computer simulations and measurements of cloud expansion for dysprosium and erbium confirmed the calculations: the frequency jumped as if a foam ball turned into a rubber one. Thus, by measuring the droplet's pulse, one can precisely pinpoint the boundaries of the new phase and the strength of quantum jitter — just as Landau explained helium through collective waves. All of this became possible thanks to laser cooling to billionths of a degree. The method will pave the way to ultrasensitive sensors and the exploration of exotic states, such as supersolids.

Quantum droplets are the most dilute liquid in the Universe: the distance between atoms in them is comparable to the size of a virus.

\omega_{\mathrm{b}}^2 = \frac{m_1}{m_{-1}\hbar^2}
ω_b is the mode frequency, m_p are the energy-weighted moments of the dynamic structure factor
\omega_{\mathrm{b},z}^2 = -\sigma_{z0} \frac{\partial \omega_z^2}{\partial \sigma_{z0}}
σ_{z0} is the axial width of the ground state, ω_z is the trap frequency
Scientists
Albert EinsteinBarry BarishKip ThorneRichard FeynmanRussell HulseJohn Stewart Bell
Concepts
quantum gas Bose-Einstein condensate Gross–Pitaevskii equation exciton condensate Bose–Einstein statistics quantum droplet condensation ultracold atoms atomic cloud ideal gas law bubble collision quantum vacuum fluctuations