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arXiv:1312.2893 · Physical Review A

Differential scattering and rethermalization in ultracold dipolar gases

John L. Bohn, Deborah Jin

Published Feb 5, 2014• 37 citations
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Abstract

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.

DOI
10.1103/physreva.89.022702

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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.
This paper deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent quantum formalism. It starts from the Schrödinger equation and introduces the experimental observables such as the differential or integral cross sections, and rate coefficients. Using a partial-wave expansion of the scattering wavefunction, the radial motion of the collision is described through a linear system of coupled equations, which is solved numerically. Using a matching procedure of the scattering wavefunction with its asymptotic form, the observables such as cross sections and rate coefficients are obtained from the extraction of the reactance, scattering and transition matrices. The example of the collision of two dipolar molecules in the presence of an electric field is presented, showing how dipolar interactions and collisions can be controlled.
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This chapter deals with the theory of collisions between two ultracold particles with a special focus on molecules. It describes the general features of the scattering theory of two particles with internal structure, using a time-independent quantum formalism. It starts from the Schrodinger equation and introduces experimental observables such as the differential or integral cross-sections, and rate coefficients. Using a partial-wave expansion of the scattering wave function, the radial motion of the collision is described through a linear system of coupled equations, which is solved numerically. Using a matching procedure of the scattering wavefunction with its asymptotic form, the observables such as cross sections and rate coefficients are obtained from the extraction of the reactance, scattering and transition matrices. The example of the collision of two dipolar molecules in the presence of an electric field is presented, showing how dipolar interactions and collisions can be controlled.
We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar bosonic gases. Such systems present both sss-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This paper presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established by Wang and Bohn [R. R. W. Wang and J. L. Bohn, Phys. Rev. A 106, 023319 (2022)], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy. An analysis of attenuation in linear waves illustrates the effect of this anisotropy in dipolar fluids, where we find a clear dependence on the dipole orientation relative to the direction of wave propagation.