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arXiv:2202.12071 · Physical review. B./Physical review. B

Formation and fragmentation of quantum droplets in a quasi-one-dimensional dipolar Bose gas

S. De Palo, E. Orignac, R. Citro

Published Jul 5, 2022• 14 citations
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Abstract

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.

DOI
10.1103/physrevb.106.014503

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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.
We investigate the breathing mode and the stability of a quantum droplet in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the droplet with a flat-top density profile is formed, the breathing-mode frequency scales as the inverse of the number of atoms in the cloud. This is straightforwardly derived within a phenomenological hydrodynamical approach and confirmed using both a variational method based on a generalized Gross-Pitaevskii action functional and the sum-rule approach. We extend our analysis also to the presence of axial confinement showing the effect of the trap on the density profile and therefore on the breathing-mode frequency scaling. Our analysis confirms the stability of the quantum droplet against the particle emission when the flat-top density profile is observed. Our results can be used as a guide to the experimental investigations of collective modes to detect the formation of quantum droplets in quasi-one-dimensional dipolar gases.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.
Abstract We consider quantum droplets in dipolar Bose–Einstein condensates embedded in optical lattices (OLs) within the framework of Gross–Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole–dipole interaction (DDI) provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the DDI increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of DDI. In presence of OLs, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.
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 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.