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arXiv:1907.10653 · Physical Review Research

Time delays in ultracold atomic and molecular collisions

Matthew D. Frye, Jeremy M. Hutson

Published Oct 15, 2019• 7 citations
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Abstract

This paper investigates the time delay around Feshbach resonances in ultracold collisions. Far above threshold, the time delay shows a simple Lorentzian peak as a function of both energy and field, but close to threshold it is proportional to the scattering length and so has a pole-like oscillation as a function of field. For narrow resonances, the energy of the crossover between these behaviors is proportional to the square of the resonance strength ${s}_{\text{res}}$. For resonances that are wide or have large background scattering lengths, the behavior is more complicated.

DOI
10.1103/physrevresearch.1.033023

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This paper investigates the time delay around Feshbach resonances in ultracold collisions. Far above threshold, the time delay shows a simple Lorentzian peak as a function of both energy and field, but close to threshold it is proportional to the scattering length and so has a pole-like oscillation as a function of field. For narrow resonances, the energy of the crossover between these behaviors is proportional to the square of the resonance strength sres{s}_{\text{res}}sres​. For resonances that are wide or have large background scattering lengths, the behavior is more complicated.
In the absence of inelastic scattering, Feshbach resonances produce poles in scattering lengths and very large peaks in elastic cross-sections. However, inelastic scattering removes the poles. Whenever the resonant state is coupled comparably to the elastic and inelastic channels, the scattering length exhibits only a small oscillation and peaks in cross-sections are significantly suppressed. A resonant scattering length is defined to characterize the amplitude of the oscillation, and is shown to be small for many collisions of ultracold molecules. The results suggest that cross-sections for some ultracold collision processes will be much less sensitive to details of the potential than has been expected.
We describe procedures for converging on and characterizing zero-energy Feshbach resonances that appear in scattering lengths for ultracold atomic and molecular collisions as a function of an external field. The elastic procedure is appropriate for purely elastic scattering, where the scattering length is real and displays a true pole. The regularized scattering length procedure is appropriate when there is weak background inelasticity, so that the scattering length is complex and displays an oscillation rather than a pole, but the resonant scattering length ares{a}_{\mathrm{res}}ares​ is close to real. The fully complex procedure is appropriate when there is substantial background inelasticity and the real and imaginary parts of ares{a}_{\mathrm{res}}ares​ are required. We demonstrate these procedures for scattering of ultracold 85Rb^{85}\mathrm{Rb}85Rb in various initial states. All of them can converge on and provide full characterization of resonances, from initial guesses many thousands of widths away, using scattering calculations at only about ten values of the external field.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
We have carried out bound-state and low-energy quantum scattering calculations on He + NH (triplet Sigma) in magnetic fields, with the NH molecule in its n=1 rotationally excited states. We have explored the pattern of levels as a function of magnetic field and identified the nearly good quantum numbers in different regimes. We have used the bound-state calculations to locate low-energy Feshbach resonances. When the magnetic field is used to tune across such a resonance, the real and imaginary part of the scattering length show asymmetric oscillations and peaks with amplitude between 1 and 3 Angstroms. The scattering length does not pass through a pole at resonance. The resonant behavior is characterized by a complex resonant scattering length a_res. The corresponding inelastic cross sections show troughs as well as peaks near resonance. This may be important for efforts to achieve evaporative and sympathetic cooling for molecules, because it offers the hope that inelastic trap losses can be reduced by tuning close to a Feshbach resonance.
While Efimov physics in ultracold atoms is usually modeled with an isolated Feshbach resonance, many real world resonances appear in close vicinity to each other and are therefore overlapping. Here we derive a realistic model based on the mutual coupling of an open channel and two closed molecular channels while neglecting short-range physics as permitted by the narrow character of the considered resonances. The model is applied to three distinct scenarios with experimental relevance. We show that the effect of overlapping resonances is manifested most strikingly at a narrow resonance in whose vicinity there is a slightly narrower one. In this system the Efimov ground state extends not only over the scattering length zero crossing between the two resonances but also over the pole of the second resonance to finally meet the dissociation threshold below it. In the opposite scenario, when a narrow resonance is considered in the vicinity of a slightly broader one, we observe that the Efimov features are pushed to lower binding energies and smaller scattering lengths by a significant factor facilitating their experimental investigation. Both scenarios are compared with the case of two narrow resonances which are far enough away from each other to be effectively decoupled. In this case the two-channel model results are recovered. Finally, we analyze the rich excitation spectrum of the system and construct and explain its nodal pattern.