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arXiv:2607.14969

Collective dynamics of harmonically trapped 1D quantum droplets under linear gravitational-like confinement

Saurab Das, Jayanta Bera, Ajay Nath

Published Jul 16, 2026• 0 citations
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Abstract

We investigate the dynamics of harmonically confined quantum droplets in a binary Bose Einstein condensate within the one dimensional extended Gross Pitaevskii framework, including LHY corrections, under a constant linear (gravitational like) potential. By analyzing the COM and width dynamics, we show that the monopole (breathing) mode remains governed by the harmonic confinement, with a frequency asymptotically insensitive to the linear perturbation, demonstrating the robustness of internal collective excitations against uniform external forcing. In contrast, the COM exhibits interaction-dependent transport, with weak confinement producing large susceptibility and rapid displacement, whereas strong confinement suppresses transport even under large forcing. The COM response decreases monotonically with increasing trap frequency. We further characterize the evolving quantum state through the quantum Fisher information and Wigner quasi-probability distributions, showing that the linear potential enables controlled generation of states with enhanced metrological sensitivity over finite times, while stronger confinement shifts the onset of the high-sensitivity regime to larger forcing strengths. Numerical simulations based on the split-step Fourier method confirm the dynamical stability of the obtained solutions. These results illustrate the impact of linear gravitational like trap on the collective excitations, transport, and quantum metrological properties of 1D ultradilute quantum fluids.

DOI
10.48550/arxiv.2607.14969

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We investigate the dynamics of harmonically confined quantum droplets in a binary Bose Einstein condensate within the one dimensional extended Gross Pitaevskii framework, including LHY corrections, under a constant linear (gravitational like) potential. By analyzing the COM and width dynamics, we show that the monopole (breathing) mode remains governed by the harmonic confinement, with a frequency asymptotically insensitive to the linear perturbation, demonstrating the robustness of internal collective excitations against uniform external forcing. In contrast, the COM exhibits interaction-dependent transport, with weak confinement producing large susceptibility and rapid displacement, whereas strong confinement suppresses transport even under large forcing. The COM response decreases monotonically with increasing trap frequency. We further characterize the evolving quantum state through the quantum Fisher information and Wigner quasi-probability distributions, showing that the linear potential enables controlled generation of states with enhanced metrological sensitivity over finite times, while stronger confinement shifts the onset of the high-sensitivity regime to larger forcing strengths. Numerical simulations based on the split-step Fourier method confirm the dynamical stability of the obtained solutions. These results illustrate the impact of linear gravitational like trap on the collective excitations, transport, and quantum metrological properties of 1D ultradilute quantum fluids.
We investigate the influence of a constant and time-dependent linear gravitational-like potential on one-dimensional quantum droplets, governed by an extended Gross-Pitaevskii equation incorporating a repulsive cubic effective mean-field (EMF) term and an attractive quadratic beyond-mean-field (BMF) correction. By constructing a tailored external confinement, we derive an exact analytical family of droplet wave functions and explicitly characterize the effective interaction contributions. A key result is that the droplet's c.m. follows a strictly Newtonian equation of the form ${\stackrel{\ifmmode \ddot{}\else \"{}\fi{}}{X}}_{\mathrm{c}.\mathrm{m}.}(t)=\ensuremath{-}a(t)$, demonstrating that its falling trajectory depends solely on the applied linear potential. Notably, this motion is completely independent of atom number and of the EMF-BMF balance, providing a clean classical baseline for dynamics in linear-potential environments. Temporal modulation of the potential induces clear deviations from static trajectories and leaves measurable imprints on internal coherence, captured through the Shannon entropy and the Wigner phase-space distribution, with the modulation strength controlling phase-space localization, deformation, and coherence degradation. Numerical simulations substantiate the stability of the analytical solutions, demonstrating their robustness. These findings suggest promising implications for quantum sensing and metrological applications using ultradilute quantum fluids.
The collective excitation modes in quantum droplets trapped in a two-dimensional harmonic potential in the context of symmetric weakly interacting binary bosonic mixtures are studied. By utilizing the linearization technique, the time-dependent extended Gross--Pitaevskii equation, and a sum-rule approach with a variational approximation, the ground-state properties and collective excitations of such a two-dimensional quantum system are investigated for various system parameters. We present comprehensive analysis and calculations on the effect of the confinement strength and anisotropy of the trapping potential, the number of atoms in the droplet, and the collective excitation modes. The radius of the droplet, as well as the chemical potential, is nonmonotonically related to the number of atoms in the droplet, and the confinement tends to shift the minimum values towards the ideal-gas limit. The excitation frequency peaks, which are prominent in a self-bounded droplet, become less pronounced and smoother when subjected to a strong trapping potential. The sum-rule approach fails to reproduce the breathing mode frequency for a moderate number of atoms in a weak trapping potential, however, works perfectly well in a strong confinement. It was found that the anisotropy in the trap eliminates the degeneracy between the quadrupole and scissors modes that occurs in an isotropic trap, causing the frequencies of these two modes to immediately diverge from each other for any degree of anisotropy. These findings provide valuable insights into the unique characteristics and behavior of quantum droplets, offering potential implications for future research and applications in the dynamic behaviors of intriguing quantum droplets.
Abstract We explore the dynamical behavior of one-dimensional quantum droplets (QDs) governed by the extended Gross–Pitaevskii equation, under harmonic confinement supplemented by a static or time-dependent Gaussian spike (Gs) potential. Employing both variational analytical techniques and numerical simulations, we investigate the evolution of the root-mean-square (RMS) size, excitation spectrum, and phase-space dynamics of QDs. Our study reveals that while the harmonic trap sets the primary confinement, the Gs potential enables precise frequency tuning and control over droplet oscillations. A static Gs amplitude modifies the fundamental oscillation frequency depending on its sign, while a time-modulated Gs induces nonlinear dynamics, including higher harmonics and frequency mixing. Our analysis reveals that the resulting frequency spectrum is strongly influenced by inter- and intra-species interactions as well as by the parameters of the external trap. Notably, we establish a relationship between the frequency shift and the amplitude of the Gaussian spike. Wigner phase-space analysis further uncovers coherent rotational behavior, offering insights into hidden phase dynamics not apparent in real-space density profiles. These results highlight the role of time-dependent external potentials in tailoring the excitation landscape of quantum droplets, with implications for quantum simulation, precision control in atomtronics, and probing coherence in low-dimensional quantum fluids.
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.
We theoretically investigate the ground-state properties and breathing-mode collective excitations of three-dimensional dipolar Bose gases in anisotropic harmonic traps incorporating quantum fluctuations. Combining a Gaussian variational ansatz with a non-perturbative sum-rule analysis, we derive explicit analytical expressions for both axial and radial breathing-mode frequencies, which are validated by numerical solutions of the time-dependent extended Gross-Pitaevskii equation. Our theoretical predictions show excellent agreement with existing experimental data for 166^{166}166Er and 162^{162}162Dy gases. By constructing comprehensive phase diagrams across the parameter space of the sss-wave scattering length, atom number, and trap aspect ratio, we reveal both discontinuous first-order phase transitions and smooth crossovers between the dilute Bose-Einstein condensate and dense quantum droplet phases. We confirm that the enhanced incompressibility induced by quantum fluctuations significantly elevates the breathing-mode frequencies in the droplet phase compared to conventional weakly interacting Bose gases. Furthermore, the system undergoes a phase transition and a crossover over the scattering length under the quasi-two-dimensional and quasi-one-dimensional confinements, characterized by discontinuous jumps and continuous crossovers in peak density and atomic cloud sizes, respectively. Our work offers a rigorous and highly accurate framework to characterize collective excitations in dipolar quantum gases, providing quantitative insights for forthcoming ultracold atom experiments in lanthanide atoms and polar molecules.
We investigate interaction-mediated spectral transfer in a driven one-dimensional binary Bose–Einstein condensate beyond mean-field interactions. The system is modeled using the extended Gross–Pitaevskii equation incorporating beyond-mean-field fluctuations through the Lee–Huang–Yang correction and confined within a harmonic potential supplemented by a localized Gaussian spike with tunable interactions. Using a variational approach, we analyze the temporal evolution of droplet widths, their spectral response, and the associated phase-space dynamics when periodic perturbations are applied to only one condensate component. Temporal modulation of the trap strength, spike amplitude, and nonlinear interaction induces pronounced nonlinear dynamics characterized by higher harmonics and mixed-frequency spectra. Remarkably, these spectral signatures are simultaneously generated in the initially unperturbed component through intercomponent coupling, revealing a robust mechanism of interaction-mediated spectral transfer and nonlinear frequency mixing. Complementary analysis based on the Wigner phase-space distribution further uncovers coherent intercomponent dynamics and internal collective modes that do not trivially follow the real-space oscillations of the droplet widths. These results highlight the role of coupling-induced nonlinearities in driven multicomponent quantum fluids and establish binary quantum droplets as a controllable platform for nonlinear spectral engineering.