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Physica D Nonlinear Phenomena

Dynamics of 1D and 3D quantum droplets in parity-time-symmetric harmonic-Gaussian potentials with two competing nonlinearities

Jin Ming Song, Zhenya Yan

Published Sep 14, 2022• 10 citations
Publisher
DOI
10.1016/j.physd.2022.133527

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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.
The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.
The existence of quantum droplets in binary Bose-Einstein condensate mixtures rely on beyondmean field effects, competing with mean-field effects. Interestingly, the beyond-mean field effect is changing from repulsive in 3D to attractive in 1D leading to drastically different behaviors. We study in detail the crossover between these two regimes in a quasi-1D regime where the radial wavefunction is frozen. Quantum droplets exist for all values and sign of the mean-field interaction. We find that approaching the crossover is experimentally appealing as it reduces the relative importance of three-body losses and give realistic numbers for the realization of quantum droplet in the crossover, which would permit to test beyond-mean-field theories to an unprecedented precision.