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Closed-channel parameters of Feshbach resonances
by Pascal Naidon
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Submission summary
| Authors (as registered SciPost users): | Pascal Naidon |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2403.14962v3 (pdf) |
| Date submitted: | 2024-10-22 06:30 |
| 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
List of changes
Following the referee's questions,
* Fig. 1 has been divided into three panels to show the scattering continuum in a similar way to Fig. 2. A white curve has been added in both Fig. 1 and 2 to show the location of the resonance in the continuum.
* A discussion has been added at the end of Section 4.3 to show how a model outside the QDT regime can assign a mass to the compact core responsible for a hadron resonance such as X(3872).
* Accordingly, sections have been added/expanded in the appendices to include a treatment of the effective range .
All changes can be seen in the file attached in the reply to the Referee.
Current status:
Reports on this Submission
Report
In the present work, the author shows that observations of a Feshbach resonance may not uniquely define the properties of the associated closed channel, especially in the case where the Feshbach resonance can be well-described by quantum defect theory (QDT). This paper builds upon the author's previous work on the properties of the closed channel associated with a Feshbach resonance, deriving the closed-channel scattering length in Ref. 21.
This result appears sound to me: the author cites several papers which successfully employ QDT to describe a Feshbach resonance while remaining deliberately ignorant of properties of the closed channel.
The author also demonstrates that the short-distance physics (which QDT hides) shows some dependency on the closed channel parameters, and that these may be studied with photoassociation spectroscopy.
Most of the evidence for the author's claims is relegated to the extensive appendices.
I thank the author for a well-written, stimulating manuscript, and recommend its publication after correcting the following typos:
- Immediately before Eq. 1, Appendix A and B -> Appendices A and B
- There are en dashes ("...grey - we come back..." on pg. 3 and "...negative value - (see Appendix..." on pg. 5) which should be em dashes
- Superfluous quotation mark in Fig 6 caption when referring to the orange curve
Recommendation
Ask for minor revision