Probing open- and closed-channel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave resonances
D. J. M. Ahmed-Braun, Kenneth G. Jackson, Scott Smale, Colin J. Dale, Ben A. Olsen, S. J. J. M. F. Kokkelmans, Paul S. Julienne, Joseph H. Thywissen
Abstract
We study the near-threshold molecular and collisional physics of a strong $^{40}\mathrm{K}$ $p$-wave Feshbach resonance through a combination of measurements, numerical calculations, and modeling. Dimer spectroscopy employs both radio-frequency spin-flip association in the MHz band and resonant association in the kHz band. Systematic uncertainty in the measured binding energy is reduced by a model that includes both the Franck-Condon overlap amplitude and inhomogeneous broadening. Coupled-channels calculations based on mass-scaled $^{39}\mathrm{K}$ potentials compare well to the observed binding energies and also reveal a low-energy $p$-wave shape resonance in the open channel. Contrary to conventional expectation, we observe a nonlinear variation of the binding energy with magnetic field, and explain how this arises from the interplay of the closed-channel ramping state with the near-threshold shape resonance in the open channel. We develop an analytic two-channel model that includes both resonances as well as the dipole-dipole interactions which, we show, become important at low energy. Using this parametrization of the energy dependence of the scattering phase, we can classify the studied $^{40}\mathrm{K}$ resonance as broad. Throughout the paper, we compare to the well-understood $s$-wave case and discuss the significant role played by van der Waals physics. The resulting understanding of the dimer physics of $p$-wave resonances provides a solid foundation for future exploration of few- and many-body orbital physics.