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arXiv:2409.19852 · Physical Review A

Two-component droplet phases and their spectral stability in one dimension

E. G. Charalampidis, S. I. Mistakidis

Published Jan 30, 2025• 8 citations
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Abstract

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.

DOI
10.1103/physreva.111.013318

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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.
Abstract We explore the ground state phase diagram and nonequilibrium dynamics of genuine two-component particle-imbalanced droplets in both isotropic and anisotropic three-dimensional confinements. A gradual transition from mixed droplet-gas to gas configurations is revealed as the average intercomponent attraction decreases or the transverse confinement becomes tighter. Within the mixed structures, a specific majority fragment binds to the minority droplet, satisfying the density ratio locking condition, while the remaining atoms are in a gas state. Our extended Gross–Pitaevskii numerical results are corroborated by a suitable variational approximation capturing the shape and characteristics of droplet-gas fragments. The tunability of the relatively low gas fraction is showcased through parametric variations of the atom number, the intercomponent imbalance, the trap aspect ratio, or the radius of a box potential. To validate the existence and probe the properties of these exotic phases, we simulate the standard time-of-flight and radio frequency experimental techniques. These allow to dynamically identify the resilience of the droplet fragment and the expansion of the gas fraction. Our results, amenable to current experimental cold atom settings, are expected to guide forthcoming investigations aiming to reveal unseen out-of-equilibrium droplet dynamics.
We explore the formation of one-dimensional two-component quantum droplets with intercomponent particle imbalance using an ab initio many-body method. It is shown that for moderate particle imbalance each component maintains its droplet flat-top or Gaussian-type character depending on the intercomponent attraction. Importantly, large particle imbalance leads to a flat-top shape of the majority component with the minority exhibiting spatially localized configurations. The latter imprint modulations on the majority component which become more pronounced for increasing interspecies attraction. The same holds for larger mass or increasing repulsion of the minority species. Such structural transitions are also evident in the underlying two-body correlation functions. To interpret the origin and characteristics of these droplet states we derive an effective model based on the established Lee-Huang-Yang theory providing adequate qualitative analytical predictions even away from its expected parametric region of validity. In contrast, the droplet character is found to vanish in the presence of fermionic minority atoms. Our results pave the way for unveiling complex droplet phases of matter.
We address the existence and dynamics of one-dimensional harmonically confined quantum droplets appearing in two-component mixtures by deploying a nonperturbative approach. We find that, in symmetric homonuclear settings, beyond-Lee-Huang-Yang correlations result in flat-top droplet configurations for either decreasing intercomponent attraction or larger atom number. Asymmetric mixtures feature spatial mixing among the involved components with the more strongly interacting or heavier one exhibiting flat-top structures. Applying quenches on the harmonic trap we trigger the lowest-lying collective droplet excitations. The interaction-dependent breathing frequency, being slightly reduced in the presence of correlations, shows a decreasing trend for stronger attractions. Semianalytical predictions are also obtained within the Lee-Huang-Yang framework. For relatively large quench amplitudes the droplet progressively delocalizes and higher-lying motional excitations develop in its core. Simultaneously, enhanced intercomponent entanglement and long-range two-body intracomponent correlations arise. In sharp contrast, the dipole motion remains robust irrespective of the system parameters. Species-selective quenches lead to a correlation-induced dephasing of the droplet or to irregular dipole patterns due to intercomponent collisions.
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 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.