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arXiv:2309.16799 · Physical Review A

Induced supersolidity in a Dy-Er mixture

Soumyadeep Halder, Subrata Das, Sonjoy Majumder

Published Jun 17, 2024• 6 citations
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Abstract

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 $s$-wave scattering length of $^{166}\mathrm{Er}$ condensate in a $^{164}\mathrm{Dy}\text{\ensuremath{-}}^{166}\mathrm{Er}$ mixture is larger than its intraspecies dipolar length implies that the $^{166}\mathrm{Er}$ condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of $^{164}\mathrm{Dy}$ atoms with high magnetic moment induces droplet nucleation and supersolidity in the $^{166}\mathrm{Er}$ 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.

DOI
10.1103/physreva.109.063321

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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 164Dy\ensuremath-166Er^{164}\mathrm{Dy}\text{\ensuremath{-}}^{166}\mathrm{Er}164Dy\ensuremath-166Er 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 164Dy\ensuremath-166Er^{164}\mathrm{Dy}\text{\ensuremath{-}}^{166}\mathrm{Er}164Dy\ensuremath-166Er 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.
The recent realization of a binary dipolar Bose-Einstein condensate [A. Trautmann et al., Phys. Rev. Lett. 121, 213601 (2018)] presents new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study the ground-state phases and dynamics of a Dy-Dy mixture. The dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the ground-state phase diagrams and characterize their different possible phases. The emergent phases include single-droplet (SD), multiple-droplets (MD), doubly supersolid (SS), and superfluid (SF) states in both miscible and immiscible phases. Intriguing mixed ground states are observed for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We also explore the dynamics across the phase boundaries by linear quenches of interspecies and intraspecies scattering lengths. During these dynamical processes, we observe an abrupt change in phase which initially results in some instability in the system and forms some metastable states in the intermediate timescale. However, the state produced in long-time evolution is similar to our predicted ground state. Although we demonstrate the possible results for a Dy-Dy mixture and for a specific parameter range of intraspecies and interspecies scattering lengths, our results are in general valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios.
We experimentally and theoretically investigate the influence of the dipole-dipole interactions (DDIs) on the total inter-species interaction in an erbium-dysprosium mixture. By rotating the dipole orientation we are able to tune the effect of the long-range and anisotropic DDI, and therefore the in-trap clouds displacement. We present a theoretical description for our binary system based on an extended Gross-Pitaevskii (eGP) theory, including the single-species beyond mean-field terms, and we predict a lower and an upper bound for the inter-species scattering length a12a_{12}a12​. Our work is a first step towards the investigation of the experimentally unexplored dipolar miscibility-immiscibility phase diagram and the realization of quantum droplets and supersolid states with heteronuclear dipolar mixtures.
We investigate the quench dynamics of quasi-one- and two-dimensional dipolar Bose-Einstein condensates of 164Dy^{164}\mathrm{Dy}164Dy 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 (as)({a}_{s})(as​) or the dipole length (add)({a}_{dd})(add​). 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.
Dipolar quantum gases, encompassing atoms and molecules with significant dipole moments, exhibit unique long-range and anisotropic dipole-dipole interactions (DDI), distinguishing them from systems dominated by short-range contact interactions. This review explores their behavior across dimensions, focusing on magnetic atoms in quasi-2D in comparison to 3D. In 3D, strong DDI leads to phenomena like anisotropic superfluidity, quantum droplets stabilized by Lee-Huang-Yang corrections, and supersolid states with density modulations. In 2D, we discuss a new scenario where DDI induces angle-dependent Berezinskii-Kosterlitz-Thouless transitions and potential supersolidity, as suggested by recent experimental realizations of strongly dipolar systems in quasi-2D geometries. We identify key challenges for future experimental and theoretical work on strongly dipolar 2D systems. The review concludes by highlighting how these unique 2D dipolar systems could advance fundamental research as well as simulate novel physical phenomena.
The recent experimental progress in realizing Bose-Fermi mixtures and dipolar quantum gases has created the exciting possibility of creating dipolar Bose-Fermi mixtures with intriguing and unique properties. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions may open up new possibilities for creating superfluids with unconventional pairings. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a three-dimensional setting in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We develop a procedure which allows us to determine the parameters such as densities and scattering lengths that are required to achieve optimal critical temperature before the system starts to phase separate. We perform a systematic investigation, finding that a superfluid with a critical temperature, that is orders of magnitude higher than achievable in nondipolar mixtures, can be realized in dipolar mixtures at experimentally accessible densities and scattering lengths before the system phase separates.