The Bose–Einstein condensate (BEC), an ultracold quantum gas often referred to as the fifth state of matter, has been extensively studied over the past decades. More recently, the realization of BECs composed of atoms with large magnetic dipole–dipole interactions (DDI) has opened a new avenue for exploring ferromagnetic superfluidity. A characteristic feature of BECs with strong dipolar interactions is their geometry-dependent stability. In particular, when such gases are elongated along the polarization direction of the dipoles, they are typically expected to become unstable and undergo collapse.

However, a key experimental study observed that the destabilization of BEC is not followed by a collapse, but rather by the formation of stable self-confined state called a droplet. This observation is surprising, as no obvious stabilization mechanism exists at the theoretical level. A few studies have put-forth possible theoretical explanations for this observation. BECs are generally studied using the simple mean field theory, involving the Gross–Pitaevskii (GP) equation. Yet numerical studies of the GP equation including DDI consistently predict collapse, failing to reproduce the experimentally observed droplets.

Two theoretical models have been proposed to address this issue. One model proposes stabilization via large conservative three-body forces, although there is currently no justification for why they should be present. The second involves quantum fluctuations, showing that extending the GP equation with a Lee–Huang–Yang (LHY) correction term, representing beyond–mean-field quantum fluctuation energy, can stabilize the droplets.

Building on this latter approach, the present study published in the Journal of the Physical Society of Japan investigated whether quantum fluctuations alone can stabilize droplets in dipolar BECs using the path-integral Monte Carlo (PIMC) method, which is exact aside from numerical errors and does not rely on mean-field or beyond-mean-field approximation. A system of ¹⁶⁴Dy atoms, closely resembling those used in the original experiments, was considered.

First, it is demonstrated that PIMC reproduces mean-field results in regimes where LHY corrections are negligible, with density profiles in good agreement with those obtained from the GP equation with DDI.

Next, PIMC simulations was conducted to examine the stable droplet state. The results showed that quantum fluctuations alone were sufficient to stabilize the droplet state, consistent with the GP equation with LHY correction. Importantly, this stabilization persists for finite-size, experimentally realistic systems, thereby clarifying the microscopic origin of droplet formation in dipolar BECs.

By resolving a long-standing debate on the stabilization mechanism of dipolar droplets, this work has provided a solid theoretical foundation for supersolid states observed in later experiments. Due to its lasting impact on ultracold atomic and quantum many-body physics, this study has been honoured with the Outstanding Paper Award of the Physical Society of Japan.

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