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Quantum phase transition in $\Xi$-configuration Tavis-Cummings model driven by an electromagnetic field for a finite number of atoms
by Anahí Alvarado-Sánchez, Ramón López-Peña
Submission summary
| Authors (as registered SciPost users): | Anahí Alvarado-Sánchez |
| Submission information | |
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| Preprint Link: | scipost_202507_00024v1 (pdf) |
| Code repository: | https://drive.google.com/drive/folders/1C0thlbGyBxbRWqFN52ImmowWTbNkKHPN?usp=sharing |
| Data repository: | https://drive.google.com/drive/folders/1C0thlbGyBxbRWqFN52ImmowWTbNkKHPN?usp=sharing |
| Date submitted: | July 8, 2025, 5:49 p.m. |
| Submitted by: | Anahí Alvarado-Sánchez |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The quantum phase transitions of a three-level Tavis-Cummings model in the $\Xi$-configuration driven by one-mode electromagnetic field in a QED cavity are studied for $N_a=1,\,2$, and $4$ systems. Although the groundstate expectation value of usual observables, such as the number of photons and the population at the lowest and most excited levels, can be used to determine the quantum phase transitions of the system in the parameter space, it is shown that expectation values of quadratic Casimir invariants of the subsystems show more details, which are corroborated using the fidelity between neighbouring states. Additionally the entropy of entanglement is calculated to determine the correlations between matter and radiation. All the calculations show that increasing the intensity of the driving electromagnetic field shrinks the region in the parameter space where matter and radiation are decoupled until it dissapears.
Current status:
Reports on this Submission
Strengths
1- the work contains all mathematical details apt to reproduce the presented derivation. 2- the authors spend some time discussing the computational techniques, allowing to understand better how to reproduce their numerical results. 3- they characterize the system under study with different metrics (the expectation values of operators, entanglement, casimir invariants) providing a complete picture of the model in the parameter space.
Weaknesses
1- In some passages, the abundance of mathematical details is not balanced by as many physical considerations. This might confuse the reader. 2- There are too many plots and in most of them the information on the colorbar (as I infer by the graphs since it is not specified elsewhere) is the same of the one on the z-axis. This is a redundancy. 3- In general, most of Sec. 4 is spent describing the shape in plots without providing any deep physical consideration. 4- Eqs. (8-9) are not used in this work. 5- I think the paper fails to highlight the differences with respect to the case with no drive that was discussed in Ref. [34].
Report
While potentially interesting, I would ask the author to made the following changes in order for it to be considered for publication.
Requested changes
1- I would simplify Section 2: I would either say at the beginning that \gamma is arbitrary, or just set it to zero already in the beginning to simplify; I would explain better why the choice of that specific value of \alpha; I would omit Eqs. (8-9). 2- Maybe I would explain in a simpler way the procedure to get the ground state. In the end, since there is a drive the number of excitations is not a good quantum number and so one has to enlarge the Hilbert space to find the GS up to a certain precision. On other hand, in its current form this part seems unnecessarily complicated. 3- In commenting plots, I would comment a bit better the analogy with the two-level TC model. In particular, it seems to me that what is discussed on lines 150-154 is due to the resemblace of the system to a two-level system. 4- In general, I would omit most of the plot and just keep the relevant ones i.e., the ones in which a clear difference is noticed. For instance, I would keep Fig. 5 as it shows that this expectation value fails to capture the transition. 5-I would like to have a clarification on line 260. What this ratio is and how it is computed is not clear at all from the current text. 6-I would highlight better the differences and analogies with the no-drive case, already explored in Ref. [38].
Recommendation
Ask for major revision