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arXiv:2609.14786

Fast dynamical control of quantum droplets via Feshbach resonances

Jing Li, Thomás Fogarty, Thomas Busch, A. Ruschhaupt

Published Sep 13, 2026• 0 citations
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Abstract

We propose a variational shortcut-to-adiabaticity scheme for the fast dynamical control of one-dimensional quantum droplets in ultracold Bose-Bose mixtures. The control is implemented through time-dependent mean-field (MF) and beyond-mean-field (BMF) nonlinearities, which can be adjusted by tuning intra- and interspecies scattering lengths near Feshbach resonances. Using a bright-droplet variational ansatz, together with inverse engineering, we derive time-dependent interaction protocols that connect prescribed initial and target self-bound states while suppressing residual excitations. We analyze three representative settings: simultaneous control of the MF and BMF terms, control with fixed BMF nonlinearity and time-dependent MF interaction, and control with fixed MF nonlinearity and time-dependent BMF interaction. For the constrained cases, additional variational degrees of freedom are introduced to optimize the protocols while respecting the imposed restrictions. Direct numerical simulations of the extended Gross-Pitaevskii equation confirm final fidelities exceeding $0.99$ on short time scales, and show that the optimised protocols are robust against finite calibration errors of the nonlinear control strength. Our results provide a route toward fast state-to-state manipulation of self-bound quantum fluids and may be useful for controlled matter-wave engineering in ultracold mixtures.

DOI
10.48550/arxiv.2609.14786

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We propose a variational shortcut-to-adiabaticity scheme for the fast dynamical control of one-dimensional quantum droplets in ultracold Bose-Bose mixtures. The control is implemented through time-dependent mean-field (MF) and beyond-mean-field (BMF) nonlinearities, which can be adjusted by tuning intra- and interspecies scattering lengths near Feshbach resonances. Using a bright-droplet variational ansatz, together with inverse engineering, we derive time-dependent interaction protocols that connect prescribed initial and target self-bound states while suppressing residual excitations. We analyze three representative settings: simultaneous control of the MF and BMF terms, control with fixed BMF nonlinearity and time-dependent MF interaction, and control with fixed MF nonlinearity and time-dependent BMF interaction. For the constrained cases, additional variational degrees of freedom are introduced to optimize the protocols while respecting the imposed restrictions. Direct numerical simulations of the extended Gross-Pitaevskii equation confirm final fidelities exceeding 0.990.990.99 on short time scales, and show that the optimised protocols are robust against finite calibration errors of the nonlinear control strength. Our results provide a route toward fast state-to-state manipulation of self-bound quantum fluids and may be useful for controlled matter-wave engineering in ultracold mixtures.
Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross-Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov-Kolokolov (VK) criterion and are found stable.
Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.
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 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.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultradilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation and study liquid Bose mixtures by using the variational hypernetted-chain Euler--Lagrange method, which accounts for correlations nonperturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio ${\ensuremath{\rho}}_{1}/{\ensuremath{\rho}}_{2}$ and near the total energy minimum. Deviations from a universal dependence on the sss-wave scattering lengths are significant despite the low density.