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Closed-channel parameters of Feshbach resonances
by Pascal Naidon
Submission summary
| Authors (as registered SciPost users): | Pascal Naidon |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2403.14962v2 (pdf) |
| Date submitted: | 2024-06-12 08:16 |
| Submitted by: | Naidon, Pascal |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
This work investigates how the closed channel of a Feshbach resonance is characterised by experimental observables. Surprisingly, it is found that the two-body observables associated with the Feshbach resonance can be insensitive to the properties of the closed channel. In particular, it is impossible in this situation to determine the energy of the bound state causing the resonance from the usual experimental data. This is the case for all magnetic Feshbach resonances in ultracold atoms, due to their deep two-body interaction potentials. This insensitivity highlights a major difference with Feshbach resonances that involve shallow interaction potentials, such as hadron resonances. It appears however that short-range two-body correlations and three-body observables are affected by a parameter of the closed channel called the "closed-channel scattering length". A photoassociation experiment is proposed to measure this parameter in ultracold atom systems.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
In this manuscript, the author uses a coupled-channel formalism to study the Feshbach resonance in a system with a single two-body bound state (called closed channel in the manuscript) coupled to a two-body continuum (called open channel in the manuscript). The main result is that if the potential in the open channel is deep enough at large distance, like the magnetic Feshbach resonances in the ultracold atoms, the quantum defect theory (QDT) can be applied and the two-body observable like the binding/resonance energy related to the Feshbach resonance is insensitive to the details of the bare bound state, i.e., insensitive to the parameters in the closed channel, which is different from the resonances involving shallow interaction potentials, such as hadron resonances. The author further points out that the three-body observables can be affected by the closed channel parameters such as the closed channel scattering length, which is suggested to be determined from the photoassociation experiments by the author. The manuscript renews our understanding and reveals some universality on the Feshbach resonance with deep open channel potential. Therefore, I recommend this manuscript for publication in SciPost Physics after the following questions have been addressed.
1) In Figs. 1 and 2, the author shows the dressed energy spectrum below the two-body threshold for a Feshbach bound state in a nonrelativistic model and in the QDT. How about the energy spectrum for a Feshbach resonance above the two-body threshold in these two models?
2) In Fig. 2, the dressed bound state energy of the Feshbach resonance has a big change near $B_0=202$ G. The author should explain the physical mechanism for such a large change.
3) The author claims that the two-body observables of resonances involving
shallow interaction potentials like hadron resonances can be sensitive to the closed channel parameters. Are the parameters physical? Is it possible to extract some information about the bare resonance in the closed channel for these resonances?
In particular, the author suggests extracting the closed channel scattering length from the photoassociation experiment. Is it possible to extract the closed channel parameters for near-threshold hadron resonances in similar experiments?
For example, for the $X(3872)$ resonance as a $D\bar{D}^{\ast}$ composite state with a $c\bar{c}$ core, how can the information about the core be obtained from experiments?
4) Some typos in the manuscript should be corrected.
In the seventh line in the caption of Fig. 2, Eq (7) -> Eq. (7).
In the third paragraph of Section 4.3, threhsold -> threshold.
Recommendation
Ask for minor revision