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arXiv:2512.09715 · Europhysics Letters (EPL)

Time-dependent condensation of bosonic dysprosium

Max Regalado Kloos, Georg Wolschin

Published Dec 1, 2025• 0 citations
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Abstract

Abstract We investigate thermalization and time-dependent Bose-Einstein condensate formation in ultracold 164 Dy using a nonlinear boson diffusion equation. As compared to alkali atoms such as 39 K or 87 Rb, the strong magnetic dipole interaction modifies the scattering-length dependence of the transport coefficients that govern thermalization and condensate formation. A prediction for the time-dependent condensate fraction in 164 Dy is made.

DOI
10.1209/0295-5075/ae2ba0

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Abstract We investigate thermalization and time-dependent Bose-Einstein condensate formation in ultracold 164 Dy using a nonlinear boson diffusion equation. As compared to alkali atoms such as 39 K or 87 Rb, the strong magnetic dipole interaction modifies the scattering-length dependence of the transport coefficients that govern thermalization and condensate formation. A prediction for the time-dependent condensate fraction in 164 Dy is made.
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Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for 39K^{39}\mathrm{K}39K at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.
We report the Bose-Einstein condensation (BEC) of the most magnetic element, dysprosium. The Dy BEC is the first for an open f-shell lanthanide (rare-earth) element and is produced via forced evaporation in a crossed optical dipole trap loaded by an unusual, blue-detuned and spin-polarized narrowline magneto-optical trap. Nearly pure condensates of 1.5 × 10(4) (164)Dy atoms form below T = 30 nK. We observe that stable BEC formation depends on the relative angle of a small polarizing magnetic field to the axis of the oblate trap, a property of trapped condensates only expected in the strongly dipolar regime. This regime was heretofore only attainable in Cr BECs via a Feshbach resonance accessed at a high-magnetic field.
We report Bose–Einstein condensation of two isotopes of the highly magnetic element dysprosium: 162 Dy and Dy. For 162 Dy, condensates with 10 5 atoms form below T = 50 nK. We find the evaporation efficiency for the isotope 160 Dy to be poor; however, by utilizing a low-field Fano–Feshbach resonance to carefully change the scattering properties, it is possible to produce a Bose–Einstein condensate of 160 Dy with 10 3 atoms. The 162 Dy BEC reported is an order of magnitude larger in atom number than that of the previously reported 164 Dy BEC, and it may be produced within 18 s.
We report the measurement of the deca-heptuplet sss-partial-wave scattering length aaa of two bosonic isotopes of the highly magnetic element dysprosium: a=112(10)a0a=112(10){a}_{0}a=112(10)a0​ for 162Dy^{162}\mathrm{Dy}162Dy and a=92(8)a0a=92(8){a}_{0}a=92(8)a0​ for 164Dy^{164}\mathrm{Dy}164Dy, where a0{a}_{0}a0​ is the Bohr radius. The scattering lengths are determined by the cross-dimensional relaxation of ultracold gases of these Dy isotopes at temperatures above quantum degeneracy. In this temperature regime, the measured rethermalization dynamics can be compared to simulations of the Boltzmann equation using a direct-simulation Monte Carlo method employing the anisotropic differential scattering cross section of dipolar particles.
Atomic interactions play a crucial role in Bose-condensed alkali gases. The condensate self-energy, proportional to the two-body s-wave scattering length, strongly affects the stability and other properties of a condensate. Alkali atom scattering lengths have been determined only during the past few years by a combination of conventional molecular spectroscopy, photoassociation spectroscopy, and ultracold atomic collision studies. In this article, we present a brief review of alkali atom interactions and scattering length determinations.