Quantum Droplet States of a Binary Magnetic Gas

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

Phys. Rev. Lett. 126, 025302 – Published 13 January 2021

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.

Received 6 July 2020
Accepted 3 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.025302

Physics Subject Headings (PhySH)

Cold atoms & matter waves Dipolar gases Mixtures of atomic and/or molecular quantum gases

Bose-Einstein condensates Quantum fluids & solids Ultracold gases

Mean field theory

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

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

Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin 9016, New Zealand

Quantum Droplets of Dipolar Mixtures

R. N. Bisset, L. A. Peña Ardila, and L. Santos

Phys. Rev. Lett. 126, 025301 (2021)

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Issue

Vol. 126, Iss. 2 — 15 January 2021

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Images

Figure 1
Free-space droplets and miscibility in a balanced BMG. (a) Phase diagram as a function of atom number and intraspecies interactions for various $a_{12}$ . BMG droplet binding predicted by variational theory (solid lines), EGPE (circles and thicker lines), and SSA EGPE (crosses). The immiscibility transition is at $a_{i i} = a_{12}$ (dotted horizontal lines) with shaded regions indicating where miscible self-bound droplets are predicted by variational theory. Self-binding for a single-component system is shown by green dashed lines and markers. Inset shows the variational results plotted as $1 / ε_{eff}^{dd}$ versus $N_{1} + N_{2}$ (the single-droplet results as $a_{i i} / a_{i i}^{dd}$ versus $N_{i}$ ). EGPE droplet solutions in the (b1) miscible and (b2) immiscible regimes shown with a density isosurface at $2.5 \times 10^{20} m^{- 3}$ for (b1) $n = n_{1} + n_{2}$ (grey surface) and (b2) $n_{1}$ (red surface) and $n_{2}$ (blue surface). (c) The maximum of $n_{1}$ (blue line) and $n$ (black line), and (d) the component overlap of the EGPE solution as $a_{i i}$ is varied. The parameters for (b1), (b2) and the results in (c),(d) are indicated in (a) by the diamonds and vertical line, respectively. Other parameters $a_{i i}^{dd} = 130.8 a_{0}$ , $m = 164 u$ , and in (b)–(d) $N_{i} = 5 \times 10^{3}$ .
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Figure 2
Immiscibility transition of a free-space BMG droplet comprised of $N_{1} = 5 \times 10^{3} Dy$ atoms and $N_{2} = 10^{4} Er$ atoms. (a1)–(a3) Chemical potentials, DDI energies, component overlap and peak densities as the interspecies scattering length is changed across the immiscibility transition. (b1),(b2) Density isosurfaces at $5 \times 10^{20} / m^{3}$ of the ground states at labeled $a_{12}$ values [component 2 is cut away in (b2) to reveal component 1]. Other parameters: ${a_{11}, a_{22}, a_{11}^{dd}, a_{22}^{dd}} = {75, 50, 130.8, 65.5} a_{0}$ , and $m = 165 u$ .
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Figure 3
Er condensate confined by a Dy droplet in free space. (a1),(b1) Dy (red) and Er (blue) density isosurfaces at $2 \times 10^{19} m^{- 3}$ , and (a2),(b2) the respective density on the $z$ axis. In (a) $a_{12} = 65 a_{0}$ and in (b) $a_{12} = 70 a_{0}$ . Other parameters: $N_{1} = 10^{4}$ , $N_{2} = 500$ , ${a_{11}, a_{22}, a_{11}^{dd}, a_{22}^{dd}} = {90, 80, 130.8, 65.5} a_{0}$ , and $m = 165 u$ .
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Figure 4
Preparation of BMG droplets from an initial miscible Dy-Dy condensate. (a1)–(a3) Results from a $τ_{r} = 10 ms$ ramp. (a1) $10^{20} / m^{3}$ density isosurfaces of component 1 (red) and 2 (blue) at $t = 100 ms$ . Evolution of (a2) peak total density $n_{peak}$ and (a3) pseudospin density $m_{z}$ . (b1)–(b3) Similar analysis for a $τ_{r} = 60 ms$ ramp. Initial and final values for the intraspecies scattering lengths are $a_{i i} = 110 a_{0}$ and $a_{i i}^{f} = 80 a_{0}$ , respectively. The initial harmonic confinement is $V = \frac{1}{2} m \sum_{ν} ω_{ν}^{2} x_{ν}^{2}$ , with $ω_{x, y} / 2 π = 250 Hz$ , and $ω_{z} / 2 π = 125 Hz$ . Other parameters: $N_{i} = 5 \times 10^{3}$ , $a_{i i}^{dd} = 130.8 a_{0}$ , $a_{12} = 90 a_{0}$ , and $m = 163.9 u$ .
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