Revising the Universality Hypothesis for Room-temperature Collisions

Abstract

Atoms constitute promising quantum sensors for a variety of scenarios including vacuum metrology. Key to this application is knowledge of the collision rate coefficient of the sensor atom with the particles being detected. Prior work demonstrated that, for room-temperature collisions, the total collision rate coefficient and the trap depth dependence of the sensor atom loss rate from shallow traps are both universal, independent of the interaction potential at short range. It was also shown that measurements of the energy transferred to the sensor atom by the collision can be used to estimate the total collision rate coefficient. However, discrepancies found when comparing the results of this and other methods of deducing the rate coefficient call into question its accuracy. Here the universality hypothesis is re-examined and an important correction is presented. We find that measurements of the post-collision recoil energy of sensor atoms held in shallow magnetic traps only provide information about the interaction potential at the very largest inter-atomic distances (e.g.~the value of $C_6$ for a leading order term of $C_6/r^6$). As other non-negligible terms exist at medium and long ranges, the total collision rate coefficient, even if universal, can differ from that computed solely from the value of $C_6$. By incorporating these other long-range terms into a simple semi-classical (SC) calculation, we find the SC prediction matches that of full, multi-channel, quantum mechanical scattering calculations using the complete potential. This work resolves the discrepancies, demonstrates the simplicity of estimating the rate coefficients for universal collision partners, and provides guidance for using atoms as a self-calibrating primary quantum pressure standard.