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arXiv:2210.00598 · Physical Review A

Two-dimensional miscible-immiscible supersolid and droplet crystal state in a homonuclear dipolar bosonic mixture

Soumyadeep Halder, Subrata Das, Sonjoy Majumder

Published Jun 8, 2023• 15 citations
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Abstract

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.

DOI
10.1103/physreva.107.063303

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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.
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We consider a binary magnetic gas and develop an extended Gross-Pitaevskii theory to study the system. We apply this theory to the regime where the two- body interactions are attractive for some arrangements of the atoms, and mean- field theory predicts mechanical collapse. In this regime quantum droplets of the binary magnetic gas can emerge, stabilised by quantum fluctuations. These quantum droplets can exist in miscible and immiscible regimes, and we characterise their properties over a broad parameter space. Simplified theories are developed to describe the droplets, and benchmarked against the full numerical calculations. The system dynamics are simulated for scenarios involving droplet formation and crossing the miscible-immiscible transition. Three-body loss is modelled in the dynamical simulations to account for the dominant loss process expected in experiments. We also study the supersolidity of a single-component dipolar gas in an infinite tube potential. An accurate computational algorithm is developed to calculate the ground state of the system in a unit cell. This algorithm is used to determine the phase diagram by characterising the crystalline order and superfluid fraction. Our results reveal that a system confined in a radially harmonic trap has a continuous transition for a range of density values, but is discontinuous for densities above and below this range. The theory is used to calculate the crystalline and supersolid states of a binary magnetic gas in a tube potential.
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We identify the quantum phases in a binary mixture of dipolar bosons in two-dimensional optical lattices. Our study is motivated by the recent experimental realization of binary dipolar condensate mixtures of Er-Dy [Phys. Rev. Lett. 121, 213601 (2018)]. We model the system by using the extended two-species Bose-Hubbard model and calculate the ground-state phase diagrams by using mean-field theory. For selected cases we also obtain analytical phase boundaries by using the site-decoupled mean-field theory. For comparison we also examine the phase diagram of two-species Bose-Hubbard model. Our results show that the quantum phases with the long-range intraspecies interaction phase separate with no phase ordering. The introduction of the long-range interspecies interaction modifies the quantum phases of the system. It leads to the emergence of phase-separated quantum phases with phase ordering. The transition from the phase-separated quantum phases without phase ordering to phase ordered ones breaks the inversion symmetry.
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 Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.