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arXiv:2007.00366 · Physical Review Letters

Quantum Droplet States of a Binary Magnetic Gas

Joseph C. Smith, D. Baillie, P. B. Blakie

Published Jan 13, 2021• 80 citations
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Abstract

Quantum droplets can emerge in bosonic binary magnetic gases (BMGs) from the interplay of short- and long-ranged interactions, and quantum fluctuations. We develop an extended mean field theory for this system and use it to predict equilibrium and dynamical properties of BMG droplets. We present a phase diagram and characterize miscible and immiscible droplet states. We also show that a single-component self-bound droplet can bind another magnetic component, which is not in the droplet regime, due to the interspecies dipole-dipole interactions. Our results should be realizable in experiments with mixtures of highly magnetic lanthanide atoms.

DOI
10.1103/physrevlett.126.025302

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Quantum droplets can emerge in bosonic binary magnetic gases (BMGs) from the interplay of short- and long-ranged interactions, and quantum fluctuations. We develop an extended mean field theory for this system and use it to predict equilibrium and dynamical properties of BMG droplets. We present a phase diagram and characterize miscible and immiscible droplet states. We also show that a single-component self-bound droplet can bind another magnetic component, which is not in the droplet regime, due to the interspecies dipole-dipole interactions. Our results should be realizable in experiments with mixtures of highly magnetic lanthanide atoms.
We develop two approximate theories to describe the miscible and immiscible droplets that can occur in a binary mixture of highly magnetic bosonic atoms. In addition to allowing simpler calculations, the approximate theories provide insight into the role of quantum fluctuations in the two regimes. Results are validated by comparison to those from the extended Gross-Pitaevskii equation. As an application, we solve for the ground-state droplets crossing the miscible-immiscible transition as a function of the short-ranged interspecies interaction parameter. We consider regimes where the transition occurs suddenly or as a smooth cross-over. Using dynamical calculations, we show that the character of the transition is revealed in the number of domains produced when ramping the droplet into the immiscible regime.
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.
We investigate droplet formation in three-component ultracold bosons. In particular, we identify the formation of a Borromean droplet, where only the ternary bosons can form a self-bound droplet while any binary subsystems cannot, as the first example of Borromean binding due to a collective many-body effect. Its formation is facilitated by an additional attractive force induced by the density fluctuation of a third component, which enlarges the mean-field collapse region in comparison to the binary case and renders the formation of a Borromean droplet after incorporating the repulsive force from quantum fluctuations. Outside the Borromean regime, we demonstrate an interesting phenomenon of droplet phase separation due to the competition between ternary and binary droplets. We further show that the transition between different droplets and gas phase can be conveniently tuned by boson numbers and interaction strengths. The study reveals the rich physics of a quantum droplet in three-component boson mixtures and sheds light on the more intriguing many-body bound state formed in multicomponent systems.
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.
Self-trapped droplets stabilized by quantum fluctuations have been experimentally realized in dipolar gases and binary boson mixtures. In this paper, we propose spinor Bose gases as another candidate for droplet formation. For spin-1 gas, we find that spin fluctuations give a dilute but self-trapped state for two different order parameters where the mean-field picture predicts collapse. A polar droplet phase can be stabilized by spin fluctuations for both antiferromagnetic and ferromagnetic spin-dependent coupling. An antiferromagnetic droplet phase can be stabilized similarly with a negative quadratic Zeeman shift. Furthermore, the beyond mean-field energy of the system depends on the quadratic Zeeman coupling, which provides a mechanism to tune the droplet formation and its density. We discuss the parameters necessary for the experimental realization of such spinor droplets.
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultradilute quantum liquids. While nondipolar self-bound (without external confinement) mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. Therefore, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible, and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual nonlocal intercomponent attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultradilute liquids, which should resemble to some extent that of ^{4}He-^{3}He droplets and impurity-doped helium droplets.