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arXiv:2409.16017 · Physical Review Letters

Dynamical Formation of Multiple Quantum Droplets in a Bose-Bose Mixture

Luca Cavicchioli, C. Fort, Francesco Ancilotto, Michele Modugno, F. Minardi, A. Burchianti

Published Mar 7, 2025• 29 citations
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Abstract

We report on the formation of multiple quantum droplets in a heteronuclear ^{41}K-^{87}Rb mixture released in an optical waveguide. By a sudden change of the interspecies interaction from the noninteracting to the strongly attractive regime, we initially form a single droplet in an excited compression-elongation mode. The latter axially expands up to a critical length and then splits into two or more smaller fragments, recognizable as quantum droplets. We find that the number of formed droplets increases with decreasing interspecies attraction and increasing atom number. We show, by combining theory and experiment, that this behavior is consistent with capillary instability, which causes the breakup of the stretching droplet due to the surface tension. Our results open new possibilities to explore the properties of quantum liquids and systems of multiple quantum droplets in two-component bosonic mixtures.

DOI
10.1103/physrevlett.134.093401

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We report on the formation of multiple quantum droplets in a heteronuclear ^{41}K-^{87}Rb mixture released in an optical waveguide. By a sudden change of the interspecies interaction from the noninteracting to the strongly attractive regime, we initially form a single droplet in an excited compression-elongation mode. The latter axially expands up to a critical length and then splits into two or more smaller fragments, recognizable as quantum droplets. We find that the number of formed droplets increases with decreasing interspecies attraction and increasing atom number. We show, by combining theory and experiment, that this behavior is consistent with capillary instability, which causes the breakup of the stretching droplet due to the surface tension. Our results open new possibilities to explore the properties of quantum liquids and systems of multiple quantum droplets in two-component bosonic mixtures.
We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitoniclike density profile evolves into a liquidlike droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signaled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, the numerical solution of a time-dependent generalized Gross-Pitaevskii equation shows either an evaporation of the cloud, the formation of a single self-bound droplet, or a fragmentation in multiple droplets. These results can be probed with lanthanide atoms and help in characterizing the effect of the dipolar interaction in a quasi-one-dimensional geometry.
Quantum Bose-Bose mixtures with large interspecies attraction can form self-bound, liquid-like droplets stabilized by quantum fluctuations. Despite equilibrium densities much lower than those of classical liquids, these droplets exhibit finite surface tension and liquid-like behaviors. Recent experiments have demonstrated Rayleigh-Plateau instability (a paradigmatic example of capillary instability) in elongated droplets confined in an optical waveguide. Here, we consider the case of an infinite filament and extend the theoretical description to include transverse harmonic confinement. By solving the Bogoliubov–de Gennes equations within a single-component framework, benchmarked against full Gross-Pitaevskii simulations, we show that increasing confinement progressively suppresses the instability, leading to complete stabilization beyond a critical trap frequency.
The ultracold and ultradilute bosonic heteronuclear mixture (41K - 87Rb) of Bose-Einstein condensates with tunable interspecies interaction at zero temperature is studied in the self-bound regime, using numerical simulations based on Density Functional Theory within the Local Density Approximation. In particular, the beyond mean-field effects embodied in the Lee-Huang-Yang energy contribution are explicitly included in the total energy functional. The thermodynamic properties of the homogeneous system are investigated to set the stability conditions of the self-bound droplet. The surface properties are discussed with (i) a variational approach, (ii) a numerical method and (iii) by solving the two coupled Gross-Pitaevskii equations associated to the two components of the mixture. The validity of the liquid-drop model is verified by computing the total ground state energy for systems with a different number of particles and, after the confinement in a quasi-1D configuration by means of an optical waveguide, we also discuss the transition between quantum droplets and bright solitons, two localized states of different nature.
We report on the production of a 41 K- 87 Rb dual-species Bose–Einstein condensate with tunable interspecies interaction and we study the mixture in the attractive regime; i.e., for negative values of the interspecies scattering length a 12 . The binary condensate is prepared in the ground state and confined in a pure optical trap. We exploit Feshbach resonances for tuning the value of a 12 . After compensating the gravitational sag between the two species with a magnetic field gradient, we drive the mixture into the attractive regime. We let the system evolve both in free space and in an optical waveguide. In both geometries, for strong attractive interactions, we observe the formation of self-bound states, recognizable as quantum droplets. Our findings prove that robust, long-lived droplet states can be realized in attractive two-species mixtures, despite the two atomic components possibly experiencing different potentials.
Significant efforts have been devoted to studying the properties of quantum droplets, an ultra low-temperature phase of bosonic quantum matter that emerges as a consequence of the Lee-Huang-Yang fluctuating correction. However, the temporal dynamics of droplet formation for heteronuclear bosonic mixtures is only partially understood. Here, we numerically analyze the droplet formation process for homonuclear and heteronuclear binary bosonic mixtures in one dimension, using a tight-binding model and real-time evolution with a novel, highly robust integration algorithm. We proceed with a systematic scan of interaction intensities, mass ratios, and initial conditions that allows us to characterize quantitative criteria for droplet formation and equilibrium prospects. Noticeably, most droplets readily form across the entire parameter space, although only a small fraction achieves a stable equilibrium configuration within the simulation horizon. We attribute this equilibrium deficiency to damping from a breathing mode, which we extract directly from the width oscillations at late times. The Lee-Huang-Yang contribution supplies essentially the entire binding energy, while, at late times, the density profile of the equilibrated subset is better described by a soliton-like shape rather than the flat-topped profiles characteristic of larger droplets. Referring to the energy of the free-atom band, the binding energy grows super-extensively with the number of atoms as Ebind∝N1.6E_{\text{bind}} \propto N^{1.6}Ebind​∝N1.6. Heteronuclear droplets bind more strongly as the mass ratio between their components increases and exhibit breathing oscillations that are greater than those of their homonuclear counterparts, which is consistent with the role of mass-imbalanced kinetic terms. Our analysis provides a methodological framework for interpreting real-time quantum droplet simulations.