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arXiv:2204.00817 · Physical Review Research

Quantum-fluctuation-driven dynamics of droplet splashing, recoiling, and deposition in ultracold binary Bose gases

Yinfeng Ma, Xiaoling Cui

Published Feb 13, 2023• 9 citations
arXivHTMLPDF

Abstract

Droplet impact on a surface is practically relevant to a variety of fields in nature and industry, while a complete control of its outcomes remains challenging due to various unmanageable factors. In this work, we propose the quantum simulation of droplet impact outcomes in the platform of ultracold atoms. Specifically, we study the quantum-fluctuation-driven dynamics (QFDD) of two-dimensional Bose-Bose mixtures from an initial Townes soliton towards the formation of a quantum droplet. By tuning the fluctuation energy of the initial Townes state through its size and number, the subsequent QFDD can produce various outcomes including splashing, recoiling, and deposition, similar to those in droplet impact dynamics. We have utilized the Weber number to identify the thresholds of splashing and recoiling, and further established a universal scaling law between the maximum spreading factor and the Weber number in the recoiling regime. In addition, we show that the residual QFDD in the deposition regime can be used to probe the collective breathing modes of a quantum droplet. Our results reveal a mechanism for the droplet impact outcomes, which can be directly tested in cold-atom experiments and can pave the way for exploring intriguing droplet dynamics in a clean and fully controlled quantum setting.

DOI
10.1103/physrevresearch.5.013100

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Droplet impact on a surface is practically relevant to a variety of fields in nature and industry, while a complete control of its outcomes remains challenging due to various unmanageable factors. In this work, we propose the quantum simulation of droplet impact outcomes in the platform of ultracold atoms. Specifically, we study the quantum-fluctuation-driven dynamics (QFDD) of two-dimensional Bose-Bose mixtures from an initial Townes soliton towards the formation of a quantum droplet. By tuning the fluctuation energy of the initial Townes state through its size and number, the subsequent QFDD can produce various outcomes including splashing, recoiling, and deposition, similar to those in droplet impact dynamics. We have utilized the Weber number to identify the thresholds of splashing and recoiling, and further established a universal scaling law between the maximum spreading factor and the Weber number in the recoiling regime. In addition, we show that the residual QFDD in the deposition regime can be used to probe the collective breathing modes of a quantum droplet. Our results reveal a mechanism for the droplet impact outcomes, which can be directly tested in cold-atom experiments and can pave the way for exploring intriguing droplet dynamics in a clean and fully controlled quantum setting.
A theoretical analysis of binary collisions of quantum droplets under feasible experimental conditions is reported. Droplets formed from degenerate dilute Bose gases made up from binary mixtures of ultracold atoms are considered. Reliable expressions for the surface tension of the droplets are introduced based on a study of low energy excitations of their ground state within the random phase approximation. Their relevance is evaluated considering an estimation of the expected excitation energy having in mind the Thouless variational theorem. The surface tension expressions allow calculating the Weber number of the droplets involved in the collisions. Several regimes on the outcomes of the binary frontal collisions that range from the coalescence of the quantum droplets to their disintegration into smaller droplets are identified. Atoms losses of the droplets derived from self-evaporation and three-body scattering are quantified for both homo- and hetero-nuclear mixtures. Their control is mandatory for the observation of some interesting effects arising from droplets collisions.
Quantum fluctuations play a pivotal role in determining the ground state properties and phase transitions of ultra-cold bosonic systems. This study presents a comprehensive theoretical investigation of fluctuation effects beyond mean-field theory in dilute Bose gases, examining their impact on the superfluid–Mott insulator transition, quantum droplet formation, and critical phenomena. Beginning with the Gross–Pitaevskii mean-field framework , we systematically incorporate quantum corrections through Bogoliubov theory, yielding the Lee–Huang–Yang (LHY) energy correction scaling as . The quantum depletion quantifies the fraction of atoms driven from the condensate by zero-point fluctuations. For the Bose–Hubbard model , quantum Monte Carlo simulations establish the superfluid–Mott insulator critical point at , shifted 15% from the mean-field prediction. Critical exponents and confirm 3D XY universality. Quantum droplets in binary mixtures are stabilized by the repulsive LHY correction against mean-field collapse, with equilibrium densities matching experimental observations in K mixtures. Finite-size scaling analysis and the Ginzburg criterion delineate regimes where fluctuation effects dominate. All theoretical predictions are validated against precision measurements in ultracold atomic gases.
Quantum droplets represent a striking manifestation of beyond-mean-field physics, with properties that depend sensitively on dimensionality. Although quantum droplets have been experimentally realized in one and three dimensions, their realization in two dimensions has remained elusive. Here, we observe the formation of a two-dimensional (2D) quantum droplet in a quasi-2D geometry by transferring the single-component Bose-Einstein condensates (BECs) into a spin mixture in the Lee-Huang-Yang (LHY) regime, where the LHY effect evidently deviates from its three-dimensional form. We find that, in our scheme, 2D quantum droplets are more stable and exhibit longer lifetimes than previously reported quantum droplets. By instead transferring the initial BECs into another single-spin state with a negative scattering length, we generate 2D Townes solitons. A comparison between the two types of self-bound states shows that, whereas 2D Townes solitons are stable only near a critical atom number determined by the scattering length, 2D quantum droplets remain well-defined and self-bound over a much broader parameter range. These realizations of quantum droplets and Townes solitons in two dimensions provide new insights into self-bound states and open new avenues for exploring nonlinear dynamics in quantum liquids.
The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large ``puddles'' with a broad flat-top plateau. Small droplets collide quasielastically, featuring the solitonlike behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e., merging and separation, depending on the velocity of the colliding pair. The critical velocity v_{c} that discriminates between the two cases displays a different dependence on the atom number N for small and large droplets. By comparing our experimental results with numerical simulations, we show that the nonmonotonic behavior of v_{c}(N) is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e., the droplet binding energy and the surface tension. These results also provide the first evidence of the liquidlike nature of quantum droplets in the large N limit, where their behavior closely resembles that of classical liquid droplets.
We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of mean-field collapse. As the droplet formation relies critically on the repulsive force provided by Lee–Huang–Yang quantum fluctuations, which can be easily compensated by thermal fluctuations, we find a significant temperature effect in the density distribution and collective excitation spectrum of the Bose droplet. A finite-temperature phase diagram as a function of the number of particles is determined. We show that the critical number of particles at the droplet-to-gas transition increases dramatically with increasing temperature. Towards the bulk threshold temperature for thermally destabilizing an infinitely large droplet, we find that the excitation-forbidden, self-evaporation region in the excitation spectrum, predicted earlier by Petrov using a zero-temperature theory, shrinks and eventually disappears. All the collective excitations, including both surface modes and compressional bulk modes, become softened at the droplet-to-gas transition. The predicted temperature effects of a self-bound Bose droplet in this work could be difficult to measure experimentally due to the lack of efficient thermometry at low temperatures. However, these effects may already present in the current cold-atom experiments.