arXiv:2501.09903 · Physical review. E

Dynamically stable two- and four-droplet solitons in a very strongly dipolar NaCs condensate

Sadhan K. Adhikari

Published May 19, 2025• 1 citation

Abstract

A strongly dipolar Bose-Einstein condensate (BEC) of Dy atoms could sustain different types of states not possible in a nondipolar BECs. Motivated by the observation of a very strongly dipolar condensate of NaCs molecules [N. Bigagli et al., Nature (London) 631, 289 (2024)0028-083610.1038/s41586-024-07492-z], with dipolar interaction stronger by more than an order of magnitude compared with that of Dy atoms, we demonstrate that, in a very strongly dipolar NaCs BEC, it is possible to have a two- and a four-droplet metastable soliton, axially free along the polarization z direction. In this study, we employ imaginary-time propagation of an improved mean-field model, including the Lee-Huang-Yang interaction. The dipolar solitons are subject to an expulsive Gaussian potential at the center and a harmonic potential, both acting in the x-y plane. The phase-coherent solitons, possessing the isolated droplets, are free to move along the z-axis without any relative motion between the droplets. The dynamical stability and mobility of these solitons are demonstrated by real-time propagation employing the converged imaginary-time wave function as the initial state.

DOI: 10.1103/physreve.111.054212

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arXiv:2501.09903 · Physical review. E

Dynamically stable two- and four-droplet solitons in a very strongly dipolar NaCs condensate

Sadhan K. Adhikari

Published May 19, 2025• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.111.054212

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We investigate the quench dynamics of quasi-one- and two-dimensional dipolar Bose-Einstein condensates of

^{164}\mathrm{Dy}

atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays is probed with particle number and dipolar interaction. The dipolar strength is tuned by rotating the magnetic field with subsequent effects on phase boundaries. Following interaction quenches across the aforementioned phases, we monitor the dynamical formation of supersolid clusters or droplet lattices. We include losses due to three-body recombination over the crossover regime, where the three-body recombination rate coefficient scales with the fourth power of the scattering length

({a}_{s})

or the dipole length

({a}_{dd})

. For fixed values of the dimensionless parameter, ${\ensuremath{\epsilon}}_{dd}={a}_{dd}/{a}_{s}$, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.

{}^{164}

Dy droplet bound in a trapped nondipolar

{}^{87}

Rb BEC with a variable number of

{}^{164}

Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a

{}^{164}

Dy droplet by relaxing the trap on the

{}^{164}

Dy BEC in a trapped binary

{}^{87}

Rb-

{}^{164}

Dy mixture.