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Physical Review Research

Harmonically trapped imbalanced quantum droplets

T. A. Flynn, N. A. Keepfer, Nicholas G. Parker, T. P. Billam

Published Feb 26, 2024• 21 citations
Publisher

Abstract

A two-component quantum droplet is an attractive mixture of ultracold bosons stabilized against collapse by quantum fluctuations. Commonly, two-component quantum droplets are studied within a balanced mixture. However, the mixture can be imbalanced resulting in a lower energy but less stably bound droplet, or even a droplet submerged in a gas. This work focuses on the experimentally relevant question: how are imbalanced droplets modified by harmonic trap potentials? Droplet ground states and breathing modes are analyzed across the two-dimensional parameter space of imbalance and trap strength. The robustness of the droplet imbalance is also studied by releasing the droplet from the trap, demonstrating that this can lead to the creation of free-space, imbalanced droplets. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013209

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A two-component quantum droplet is an attractive mixture of ultracold bosons stabilized against collapse by quantum fluctuations. Commonly, two-component quantum droplets are studied within a balanced mixture. However, the mixture can be imbalanced resulting in a lower energy but less stably bound droplet, or even a droplet submerged in a gas. This work focuses on the experimentally relevant question: how are imbalanced droplets modified by harmonic trap potentials? Droplet ground states and breathing modes are analyzed across the two-dimensional parameter space of imbalance and trap strength. The robustness of the droplet imbalance is also studied by releasing the droplet from the trap, demonstrating that this can lead to the creation of free-space, imbalanced droplets. Published by the American Physical Society 2024
A two-component quantum droplet is an attractive mixture of ultracold bosons stabilised against collapse by quantum fluctuations. Commonly, two-component quantum droplets are studied within a balanced mixture. However, the mixture can be imbalanced resulting in a lower energy but less stably bound droplet, or even a droplet submerged in a gas. This work focuses on the experimentally relevant question: how are imbalanced droplets modified by harmonic trap potentials? Droplet ground states and breathing modes are analysed across the two-dimensional parameter space of imbalance and trap strength. The robustness of the droplet imbalance is also studied by releasing the droplet from the trap, demonstrating that this can lead to the creation of free-space, imbalanced droplets.
Quantum droplets are a quantum analog to classical fluid droplets in that they are self-bound and display liquid-like properties---such as incompressibility and surface tension---though their stability is the result of quantum fluctuations. One of the major systems for observing quantum droplets is two-component Bose gases. Two-component droplets are typically considered to be balanced, having a fixed ratio between the densities of the two components. This work goes beyond the fixed density ratio by investigating spherical droplets in imbalanced mixtures. With increasing imbalance, the droplet is able to lower its energy up to a limit, at which point the droplet becomes saturated with the atoms of the majority component and any further atoms added to this component cannot bind to the droplet. Analyzing the breathing mode dynamics of imbalanced droplets indicates that the droplet can emit particles, as in balanced mixtures, but the imbalance leads to an intricate superposition of multiple simultaneously decaying collective oscillations.
We unravel the existence and stability properties of one-dimensional droplets arising in genuine two-component particle-imbalanced bosonic mixtures under the influence of a weak harmonic confinement. A plethora of miscible droplet phases is found with the majority component atoms in the vicinity of the minority ones assembling in a droplet configuration, while the remaining excess atoms are in the gas state. Our computations identify a transition from a bound to a trapped gas many-body state for increasing total atom number and fixed interactions, with the bound character being prolonged for stronger intercomponent attractions. The spectral stability of these two-component droplets is revealed by examining their underlying Bogoliubov--de Gennes excitation spectrum. Furthermore, the collective dynamics associated with the fundamental dipole and breathing modes of the system is monitored by suddenly shifting the trap's center or quenching the trap's frequency, respectively. There, a backaction of the significantly localized minority component is imprinted in the majority cloud. The present findings can be simulated in recent cold-atom experiments, thus setting the stage for probing the complex nonequilibrium dynamics of two-component droplets.
We explore the ground state properties and excitation spectra of one-dimensional three-component bosonic mixtures accommodating a droplet in two of the species and a third minority component. Relying on the suitable Lee-Huang-Yang framework, we reveal a plethora of distinct self-bound droplet phases and their phase transitions through variations of either the particle number of the majority components or the intercomponent coupling. The ensuing phases demonstrate that the minority component is being un-trapped, partially trapped, or fully trapped by the majority droplet species. These states are characterized by their binding energies captured by the chemical potentials and their low-amplitude excitation spectrum, including mode crossings at the particle-emission threshold. We further derive effective reduced models which are valid in the high-imbalance limit, and accurately reproduce the numerically computed ground states, while providing analytical insights into the role of quantum fluctuations. Our results map out the stability and structure of mixed droplet phases offering guidance into forthcoming experimental and theoretical studies of multicomponent quantum droplets.
We study the stationary and excitation properties of a one-dimensional quantum droplet in a two-component Bose mixture trapped in a harmonic potential. By constructing the energy functional for the inhomogeneous mixture, we elaborate the extended Gross-Pitaevskii equation applicable to both symmetric and asymmetric mixtures into a universal form, and the equations in two different dimensionless schemes are in a duality relation; that is, the unique parameters that are left are the inverse of each other. The Bogoliubov equations for the trapped droplet are obtained by linearizing the small density fluctuation around the ground state, and the low-lying excitation modes are calculated numerically. It is found that the confinement trap easily changes the flat-top structure for large droplets and intensively alters the mean-square radius and the chemical potential. The breathing mode of the confined droplet connects the self-bound and ideal-gas limits, with the excitation in the weakly interacting Bose condensate for large particle numbers lying in between. We explicitly show how the continuum spectrum of the excitation is split into discrete modes and finally taken over by the harmonic trap. Two critical particle numbers are identified by the minimum size of the trapped droplet and the maximum breathing-mode energy, both of which are found to decrease exponentially with the trapping parameter.
Self-bound quantum droplets are a newly discovered phase in the context of ultracold atoms. In this Letter, we report their experimental realization following the original proposal by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302], using an attractive bosonic mixture. In this system, spherical droplets form due to the balance of competing attractive and repulsive forces, provided by the mean-field energy close to the collapse threshold and the first-order correction due to quantum fluctuations. Thanks to an optical levitating potential with negligible residual confinement, we observe self-bound droplets in free space, and we characterize the conditions for their formation as well as their size and composition. This work sets the stage for future studies on quantum droplets, from the measurement of their peculiar excitation spectrum to the exploration of their superfluid nature.