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arXiv:2104.00724 · Physical Review A

Anisotropic thermalization of dilute dipolar gases

Reuben R. W. Wang, John L. Bohn

Published Jun 25, 2021• 18 citations
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Abstract

We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization [Monroe et al., Phys. Rev. Lett. 70, 414 (1993)], which, for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientation, scattering length, and thermalization geometry. These models compare favorably to Monte Carlo simulations and are shown to model well a recent experimental result on the rethermalization of polar molecular samples.

DOI
10.1103/physreva.103.063320

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We study collisional rethermalization in ultracold dipolar thermal gases, made intricate by their anisotropic differential cross sections. Theoretical methods are provided to derive the number of collisions per rethermalization [Monroe et al., Phys. Rev. Lett. 70, 414 (1993)], which, for dipolar gases, is highly dependent on the dipole alignment axis. These methods are formulated to be easily applied in experimental contexts, even reducing to analytic expressions if the route to thermal equilibrium is governed by short-time dynamics. In the analytic case, collisional rethermalization is fully characterized by the dipole magnitude and orientation, scattering length, and thermalization geometry. These models compare favorably to Monte Carlo simulations and are shown to model well a recent experimental result on the rethermalization of polar molecular samples.
Analytic expressions for the differential cross sections of ultracold atoms and molecules that scatter primarily due to dipolar interactions are derived within the first-order Born approximation and are shown to agree with the partial wave expansion. These cross sections are applied to the problem of cross-dimensional rethermalization. Strikingly, the rate of rethermalization can vary by as much as a factor of 2, depending on the orientation of the dipoles. Thus the anisotropic dipole-dipole interaction can have a significant effect even on the behavior of a nondegenerate ultracold gas.
We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic 167Er fermions, spin polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalization experiments, we observe a strong anisotropy of the scattering, which manifests itself in a large angular dependence of the thermal relaxation dynamics. Our result is in good agreement with recent theoretical predictions. Furthermore, we measure the rethermalization rate as a function of temperature for different angles and find that the suppression of collisions by Pauli blocking is not influenced by the dipole orientation.
We study the relaxation and damping dynamics of an ultracold, but not quantum degenerate, gas consisting of dipolar particles. These simulations are performed using a direct simulation Monte Carlo method and employing the highly anisotropic differential cross section of dipoles in the Wigner threshold regime. We find that both cross-dimensional relaxation and damping of breathing modes occur at rates that are strongly dependent on the orientation of the dipole moments relative to the trap axis. The relaxation simulations are in excellent agreement with recent experimental results in erbium. The results direct our interest toward a less explored regime in dipolar gases where interactions are dominated by collision processes rather than mean-field interactions.
We discuss the influence of collisions on the dynamics of an ultracold gas whose constituents interact via dipolar forces. This dynamics is governed by the elastic scattering cross section of the molecules, which is to some extent under the experimentalist's control. We compare side-by-side several different situations, highlighting their similarities and differences. These situations are collisions between: 1) point dipoles; 2) electric-field-shielded polar molecules; and 3) microwave-shielded polar molecules, including the effect of microwave ellipticity.
In this paper, we develop a direct simulation Monte Carlo method for simulating highly nonequilibrium dynamics of nondegenerate ultracold gases. We show that our method can simulate the high-energy collision of two thermal clouds in the regime observed in experiments [Thomas et al. Phys. Rev. Lett. 93, 173201 (2004)], which requires the inclusion of beyond sss-wave scattering. We also consider the long-time dynamics of this system, demonstrating that this would be a practical experimental scenario for testing the Boltzmann equation and studying rethermalization.
We report the measurement of collisions between two Bose–Einstein condensates with strong dipolar interactions. The collision velocity is significantly larger than the internal velocity distribution widths of the individual condensates, and thus, with the condensates being sufficiently dilute, a halo corresponding to the two-body differential scattering cross section is observed. The results demonstrate a novel regime of quantum scattering, relevant to dipolar interactions, in which a large number of angular momentum states become coupled during the collision. We perform Monte-Carlo simulations to provide a detailed comparison between theoretical two-body cross sections and the experimental observations.