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arXiv:2409.12438 · Physical Review A

Universality and threshold laws for collision lifetimes at ultralow temperatures

Rebekah Hermsmeier, Timur V. Tscherbul

Published Dec 12, 2024• 0 citations
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Abstract

While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. Using multichannel quantum-defect theory, we derive a multichannel expression for the Smith lifetime $Q$ matrix that is valid far away from scattering resonances. For collisions mediated by short-range interaction potentials of the form $\ensuremath{-}{C}_{6}/{R}^{6}$, we obtain the average time delay in the incident $s$-wave collision channel in the limit of zero collision energy $E$ as ${Q}_{11}=A/\sqrt{E}+B$, where $A$ and $B$ are constants. We show that the time delay is dominated by elastic scattering and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the $S$ matrix and shortens with increasing the short-range loss parameter $y$.

DOI
10.1103/physreva.110.063313

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While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. Using multichannel quantum-defect theory, we derive a multichannel expression for the Smith lifetime QQQ matrix that is valid far away from scattering resonances. For collisions mediated by short-range interaction potentials of the form \ensuremath−C6/R6\ensuremath{-}{C}_{6}/{R}^{6}\ensuremath−C6​/R6, we obtain the average time delay in the incident sss-wave collision channel in the limit of zero collision energy EEE as Q11=A/E+B{Q}_{11}=A/\sqrt{E}+BQ11​=A/E​+B, where AAA and BBB are constants. We show that the time delay is dominated by elastic scattering and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the SSS matrix and shortens with increasing the short-range loss parameter yyy.
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A simple quantum-defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold 40K87Rb molecules, or an ultracold 40K atom with the 40K87Rb molecule [S. Ospelkaus et al., Science 327, 853 (2010).