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arXiv:2403.12209

The transition and coexistence of quantum droplets and solitons in quasi-1D dipolar Bose gas

Shi, Y. Y.

Published Mar 18, 2024• 0 citations
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Abstract

In our study, we investigated bright solitons, dark solitons, and quantum droplets in quasi-one-dimensional dipolar Bose gases, and further validated the crossover and coexistence of quantum droplets and solitons using the Lieb-Liniger energy within the framework of local density approximation. Increasing the particle number transforms the bright dipolar soliton state into a stable self-bound quantum droplet state, with further increases in leading to a broader quantum droplet that enables the presence of dark solitons within it.

DOI
10.48550/arxiv.2403.12209

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•Sep 1, 2020•0 citations
In our study, we investigated bright solitons, dark solitons, and quantum droplets in quasi-one-dimensional dipolar Bose gases, and further validated the crossover and coexistence of quantum droplets and solitons using the Lieb-Liniger energy within the framework of local density approximation. Increasing the particle number transforms the bright dipolar soliton state into a stable self-bound quantum droplet state, with further increases in leading to a broader quantum droplet that enables the presence of dark solitons within it.
We analyze a system of dipolar atoms confined in geometries of quasi low dimensionality. Due to the long-range and anisotropic nature of dipolar interactions, the system supports both stable solitons and quantum droplets. In quasi-one-dimensional geometries, the transition between these states is known to manifest either as a first-order phase transition, associated with bistability, or as a smooth crossover. We investigate this transition by calculating the structure factor and showing that the response of the breathing mode provides an experimentally accessible probe. In addition, we identify regions of both bistability and smooth crossover in quasi-two-dimensional geometries. Finally, we connect our findings to previous experimental results and delineate the conditions under which two-dimensional dipolar bright solitons can be realized.
We look into dark solitons in a quasi-1D dipolar Bose gas and in a quantum droplet. We derive the analytical solitonic solution of a Gross-Pitaevskii-like equation accounting for beyond mean-field effects. The results show there is a certain critical value of the dipolar interactions, for which the width of a motionless soliton diverges. Moreover, there is a peculiar solution of the motionless soliton with a nonzero density minimum. We also present the energy spectrum of these solitons with an additional excitation subbranch appearing. Finally, we perform a series of numerical experiments revealing the coexistence of a dark soliton inside a quantum droplet.
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multiatom Schrödinger equation, we discover that such systems can exhibit not only the well-known bright soliton solutions but also novel quantum droplets for a strongly coupled case. For larger systems, basing on microscopic properties of the found few-body solution, we propose a new equation for a density amplitude of atoms. It accounts for fermionization for strongly repelling bosons by incorporating the Lieb-Liniger energy in a local density approximation and approaches the standard Gross-Pitaevskii equation (GPE) in the weakly interacting limit. Not only does such a framework provide an alternative mechanism of the droplet stability, but it also introduces means to further analyze this previously unexplored quantum phase. In the limiting strong repulsion case, yet another simple multiatom model is proposed. We stress that the celebrated Lee-Huang-Yang term in the GPE is not applicable in this case.
Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states: bright solitons and quantum droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in an optical waveguide. We show theoretically that, depending on atom number and interaction strength, solitons and droplets can be smoothly connected or remain distinct states coexisting only in a bistable region. We measure their spin composition, extract their density for a broad range of parameters, and map out the boundary of the region separating solitons from droplets.
We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitoniclike density profile evolves into a liquidlike droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signaled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, the numerical solution of a time-dependent generalized Gross-Pitaevskii equation shows either an evaporation of the cloud, the formation of a single self-bound droplet, or a fragmentation in multiple droplets. These results can be probed with lanthanide atoms and help in characterizing the effect of the dipolar interaction in a quasi-one-dimensional geometry.
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.