Collisional relaxation in shielded dipolar molecular gases

TL;DR

This work analyzes how collisions govern relaxation in ultracold gases of dipolar molecules and how external fields can tune those collisions. It develops a Boltzmann-Enskog framework to connect relaxation rates to differential and integral cross sections, including anisotropic dipolar scattering and cross-dimensional rethermalization observables. It introduces effective shielded potentials for DC and microwave shielding, deriving their long-range forms $V_{\rm eff}$ with $r^{-3}$ and $r^{-6}$ tails and showing that shielded interactions act like adjusted point dipoles (with a sign change for microwave shielding). It also shows how microwave ellipticity can further tailor rethermalization by modifying cross sections, and it verifies with experiments on KRb and NaCs that the theory captures relaxation and lifetime improvements. The results provide practical guidelines for controlling collisional relaxation, enabling stable, tunable dipolar molecular gases for quantum simulation and information processing.

Abstract

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.

Figures (12)

• Figure 1: Cartoon of a cross-dimensional rethermalization experiment. Collisions that scatter primarily into the transverse directions promote thermalization, whereas forward scattering hinders it. Red indicates pre-collision colliders, while post-collision ones are blue. The right two panels illustrate that transverse collisions are "good" toward rethermalization, while forward scattering is "bad" as no cross-dimensional mixing occurs. This graphic is taken from Ref. Wang24_Boulder.
• Figure 2: The anisotropic differential cross sections (in arbitrary units) between point dipolar particles for various deflection angles $\eta = \cos^{-1}\hat{\boldsymbol{k}} \cdot \hat{\boldsymbol{{\cal E}}}$, comparing identical fermions (upper panel) and identical bosons (lower panel). This plot is reproduced with data from Ref. Bohn14_PRA.
• Figure 3: Numerically simulated pseudotemperature traces ${\cal T}_x(t)$ (solid green curves), ${\cal T}_y(t)$ (dashed blue curves) and ${\cal T}_z(t)$ (dotted red curves) for 3 values of $\Theta = 0^{\circ}, 45^{\circ}, 90^{\circ}$, in subplots (a), (b) and (c) respectively. The simulations assume a gas of 2000 $^{23}$Na$^{40}$K molecules with an effective dipole moment of $d_{\rm eff} = 0.75$ D, in a harmonic trap of mean trap frequency $\overline{\omega} = 2\pi \times 100$ Hz. This plot is reproduced with data from Ref. Wang23_PRA.
• Figure 4: The number of collisions per rethermalization for identical dipolar fermions ${\cal N}_{i j}$ (solid black curves) as a function of $\Theta$, for all nine excitation-rethermalization configurations from Eq. (\ref{['eq:NCPR_fermions']}). For comparison, we also plot ${\cal N}_p = 25/6$ for $p$-wave scattering (dashed gray lines). This plot is reproduced with data from Ref. Wang21_PRA.
• Figure 5: The (a) one and (b) two-molecule rigid rotor spectra as a function of d.c. electric field. The blue arrows in (a) indicate the resonant transitions in each molecule during Förster resonant shielding, while the blue star in (b) shows the combined molecular state crossing, that becomes avoided in the presence of dipole-dipole interactions. Not all states have been labeled to avoid clutter in the plot. The top left inset shows a schematic for the resonant energy exchange process between the two colliding molecules. See the main text for more details.