Differential scattering and rethermalization in ultracold dipolar gases

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 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 two, depending on the orientation of polarization of the dipoles. Thus the anisotropic dipole-dipole interaction can have a profound effect even on the behavior of a nondegenerate ultracold gas.

Nonequilibrium dynamics of an ultracold dipolar gas

“…From this, w e conclude that the tw o-body scattering physics is strongly w ithin the quantum regim e, and the differential scattering cross sections are chosen accordingly [14].…”

“…O ther exam ples include the study o f collective m odes in finite-tem perature dynam ics [43][44][45], sym pathetic cooling o f m olecules [46], and degenerate Fermi gas dynam ics [47]. To our know ledge, our w ork is the first tim e that dipolar differential cross sections have been used [14]. This reduces the efficiency o f the DSM C by introducing a rejection-sam pling algorithm to sam ple the differential cross sections.…”

“…Intriguingly, cross sections which exhibit time-reversal sym metry, that is, ^(P rei,p 'rei) = ^( p 're,,Prei), yield irreversible dynamics in the Boltzmann equation as demonstrated by Boltzmann's famous H theorem [49], The relevant differential cross section for dipolar particles has been derived and discussed in detail in a recent article [14], and we briefly summarize the necessary results in Sec. Ill C. Analytic solutions to the Boltzmann equation are difficult to come by [49,50], An important exception are the well-known equilibrium solutions, the Maxwell-Boltzmann distribution, .…”

“…[14] using the Born approximation for the scattering amplitude between two dipolar particles, with dipole moments ad is the dipole length scale given by ad = mLL0n 2/(8 n h 2), fx0 is the vacuum permeability, fi is the atomic magnetic dipole moment (/u = 7 /rB in the case of erbium), and a is the swave scattering length. The subscripts F and B, respectively, correspond to fermionic and bosonic symmetry constraints ( l67Er, which was used in the experiment [15], is fermionic).…”

“…In such a situation the strength and anisotropy of the dipolar interactions can be made manifest through collisions, rather than through mean-field effects [14], A very recent experiment showed this explicitly, finding that collisional relaxation of a gas of erbium atoms at ~400 nK occurred on time scales that varied by a factor of 4, depending on the orientation of the atoms' magnetic dipole moments [15]. This landmark result illustrates the potential for anisotropic dipolar scattering to profoundly influence the kinetics of a cold, thermal gas, from rethermalization and relaxation to viscosity and the propagation of sound, to name but a few features.…”