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arXiv:2507.22154 · Physical Review A

Spatially periodic states in a strongly dipolar Dy 164 − Dy 162 mixture

Sadhan K. Adhikari

Published Jul 29, 2025• 1 citation
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Abstract

We demonstrate the formation of a novel eigenstate in a strongly dipolar binary $^{164}\mathrm{Dy}\text{\ensuremath{-}}^{162}\mathrm{Dy}$ mixture, where the inter- and intraspecies dipolar lengths are larger than the corresponding scattering lengths. When this mixture is confined by a quasi-two-dimensional harmonic trap, the total density exhibits the formation of droplets on a spatially symmetric triangular or square lattice, where each droplet is formed of a single species of atoms; two types of atoms never exist on the same lattice site. The density of any of the species shows a partially filled incomplete lattice; only the total density exhibits a completely full lattice structure. In this theoretical investigation we employ the numerical solution of an improved mean-field model including a Lee-Huang-Yang-type interaction in the intraspecies components alone, meant to stop a collapse of the atoms at high atom density.

DOI
10.1103/lqds-zb7d

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We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164{}^{164}164Dy droplet bound in a trapped nondipolar 87{}^{87}87Rb BEC with a variable number of 164{}^{164}164Dy 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{}^{164}164Dy droplet by relaxing the trap on the 164{}^{164}164Dy BEC in a trapped binary 87{}^{87}87Rb-164{}^{164}164Dy mixture.
We study the statics and dynamics of a binary dipolar Bose–Einstein condensate soliton for repulsive inter and intraspecies contact interactions with the two components subject to different spatial symmetries—distinct quasi-one-dimensional and quasi-two-dimensional shapes—using numerical solution and variational approximation of a three-dimensional mean-field model. The results are illustrated with realistic values of parameters in the binary 164 Dy- 168 Er mixture. The possibility of forming robust dipolar solitons of a very large number of atoms make them of great experimental interest. The existence of the solitons is illustrated in terms of stability phase diagrams. Exotic shapes of these solitons are illustrated in isodensity plots. The variational results for statics (size and chemical potential) and dynamics (small oscillation) of the binary soliton compare well with the numerical results. A way of preparing and studying these solitons in the laboratory is suggested.
The recent experimental realization of the heteronuclear dipolar mixture of Dy and Er atoms opens fascinating prospects for creating intriguing novel phases in dipolar quantum gases. The experimentally measured value of intraspecies sss-wave scattering length of 166Er^{166}\mathrm{Er}166Er condensate in a $^{164}\mathrm{Dy}\text{\ensuremath{-}}^{166}\mathrm{Er}$ mixture is larger than its intraspecies dipolar length implies that the 166Er^{166}\mathrm{Er}166Er condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of 164Dy^{164}\mathrm{Dy}164Dy atoms with high magnetic moment induces droplet nucleation and supersolidity in the 166Er^{166}\mathrm{Er}166Er condensate via the long-range and anisotropic interspecies DDI. Remarkably, we find that the imbalance in the magnetic dipole moment combined with its strong anisotropic coupling leads to the emergence of unique ground-state phases. The emerging phases include doubly superfluid states, a mixture of insulating droplets and supersolid states, binary supersolids with uniform and alternating domains and a combination of supersolid-superfluid mixed states. We delineate the properties of all these ground-state phases and construct a phase diagram. We also explore the dynamical evolution across these phase boundaries via a linear quench of interspecies scattering length. Although we demonstrate the result for the $^{164}\mathrm{Dy}\text{\ensuremath{-}}^{166}\mathrm{Er}$ mixture, our results are generally valid for other dipolar bosonic mixtures of different Dy-Er isotope combinations and may become an important benchmark for future experimental scenarios.