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arXiv:2205.05193 · Physical Review Research

Control of Dy 164 Bose-Einstein condensate phases and dynamics with dipolar anisotropy

Soumyadeep Halder, K. Mukherjee, S. I. Mistakidis, Subrata Das, P. G. Kevrekidis, Prasanta Kumar Panigrahi, Sonjoy Majumder, H. R. Sadeghpour

Published Nov 21, 2022• 25 citations
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Abstract

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.

DOI
10.1103/physrevresearch.4.043124

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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, \ensuremathϵdd=add/as{\ensuremath{\epsilon}}_{dd}={a}_{dd}/{a}_{s}\ensuremathϵdd​=add​/as​, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.
Toroidal Confinement and Beyond: Vorticity-Defined Morphologies of Dipolar 164^{164}164Dy Quantum Droplets
We investigate the formation, stability, and dynamics of 3D ring-shaped and multipole vortical quantum droplets (QDs) in non-rotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDI) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity SSS) are shaped as necklace-like modes, with the number of \textquotedblleft beads" (multipole's order) n=2Sn=2Sn=2S, up to S=6S=6S=6. The stability area of the multipoles shrinks with the increase of SSS. For higher values of SSS the centrifugal effect associated with the phase winding destabilizes the annular density and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy and peak density on the norm (number of particles) and SSS is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the non-rotating configurations.
We investigate the formation, stability, and dynamics of three-dimensional ring-shaped and multipole vortical quantum droplets (QDs) in nonrotating dipolar Bose-Einstein condensates held in a toroidal trapping potential. The QD dynamics are investigated in the framework of the extended Gross-Pitaevskii equation, which includes long-range dipole-dipole interactions (DDIs) and the beyond-mean-field Lee-Huang-Yang (LHY) term, revealing the emergence of self-bound states. Stable stationary solutions for multipole QDs with different values of the topological charge (vorticity S) are shaped as necklacelike modes, with the number of "beads" (multipole order) n=2S, up to S=6. The stability area of the multipoles shrinks with the increase of S. For higher values of S the centrifugal effect associated with the phase winding destabilizes the ring-shaped QDs and drives the formation of fragmented multipole droplet states. The dependence of the chemical potential, total energy, and peak density on the norm (number of particles) and S is produced. These findings uncover the stabilizing effect of the LHY correction and DDI anisotropy in maintaining complex QD states in the nonrotating configurations.
We investigate the vortex lattices of harmonically confined quasi-two-dimensional tilted rotational dipolar Bose-Einstein condensates. By employing an extended Gross-Pitaevskii equation for a rotating condensate, we reveal the structural transformation of vortices from square to triangular lattices as the tilt of dipolar bosons relative to the polarization axis approaches a critical angle. When the tilt of the magnetic dipoles surpasses the magic angle, the condensate elongates diagonally and becomes devoid of vortices. Moreover, we include the Lee-Huang-Yang correction, which enables the formation of vortices in the elongated condensate. Additionally, when dipoles are oriented perpendicular to the polarization axis, the Lee-Huang-Yang correction results in the fragmentation of condensates under strong rotation. The quench dynamics of the rotational frequency demonstrate the development of vortex lattices; however, with a strong rotational quench, the condensate remains free of vortices. Our numerical analysis highlights the beyond mean-field effects of the rotational properties of anisotropic dipolar bosons, which can be observed in current dipolar quantum gas experiments.
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.
The formation of quantized vortices above a certain critical trap rotation frequency serves as a hallmark signature of superfluidity. Based on the beyond mean-field framework, crucial for the formation of exotic supersolid and droplet states, we investigate dynamical protocols for vortex nucleation in the superfluid and supersolid states of a dipolar Bose-Einstein condensate (BEC) at a trap rotation frequency lower than the conventional critical rotation frequency. We find that the critical rotation frequency depends not only on the dipole-dipole interaction strength, but also on the polarization direction of the external magnetic field. Interestingly, in the superfluid state, the critical rotation frequency increases with the tilt angle of the magnetic field, whereas in the supersolid state, increasing the tilt angle lowers the critical threshold. Leveraging these characteristics of dipolar BECs, along with the robustness of vortices with respect to changes in the polarization direction and sss-wave scattering length, we demonstrate three dynamical protocols for vortex nucleation, even when rotating below the critical rotation frequency, viz., (i) varying the sss-wave scattering length, (ii) changing the polarizing angle, and (iii) successive modulation of both the scattering length and polarizing angle. These dynamical vortex seeding protocols could serve as important benchmarks for future experimental studies.
We investigate the dynamics of Bose-Einstein condensate droplets composed of 164^{164}164Dy atoms formed in a double-well potential following removal of the interwell barrier. By solving the dipolar Gross-Pitaevskii equation, we determine phase diagrams of ground-state configurations as functions of the atom number confined in the double-well potential. For an interwell separation 2d=3 μm2d=3\,μ\mathrm{m}2d=3μm, we consider the relative dipolar-to-contact interaction strengths εdd=1.4\varepsilon_{dd}=1.4εdd​=1.4, 1.451.451.45, and 1.51.51.5. Symmetry-broken lowest-energy configurations are found for εdd=1.5\varepsilon_{dd}=1.5εdd​=1.5 and, over a reduced range of atom numbers, for εdd=1.45\varepsilon_{dd}=1.45εdd​=1.45, whereas no symmetry-broken states are found for εdd=1.4\varepsilon_{dd}=1.4εdd​=1.4 up to N=5×104N=5\times10^4N=5×104. We analyze the subsequent time evolution after removal of the central barrier, revealing both droplet oscillations and merger events leading to the formation of larger droplets. The oscillations are driven by the external potential and by the repulsive tails of the in-plane component of the dipolar interaction. For the two-droplet states at εdd=1.5\varepsilon_{dd}=1.5εdd​=1.5 and 2d=3 μm2d=3\,μ\mathrm{m}2d=3μm, merging is found for N=8000N=8000N=8000 and 880088008800, whereas the droplets remain separated for the investigated cases with N≥9000N\geq9000N≥9000. Increasing the initial separation to 2d=5 μm2d=5\,μ\mathrm{m}2d=5μm shifts the approximate upper atom number for merging to N≃1.65×104N\simeq1.65\times10^4N≃1.65×104, demonstrating that the crossover is controlled by the competition between the post-quench excess energy and the repulsive inter-droplet barrier.