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Bound impurities in a one-dimensional Bose lattice gas: low-energy properties and quench-induced dynamics
by Felipe Isaule, Abel Rojo-Francàs, Bruno Juliá-Díaz
Submission summary
| Authors (as registered SciPost users): | Felipe Isaule |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2402.03070v1 (pdf) |
| Data repository: | https://doi.org/10.5281/zenodo.10624576 |
| Date submitted: | 2024-02-06 16:30 |
| Submitted by: | Isaule, Felipe |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including the characterization of the critical strength for the formation of bound impurities. We also study the dynamics induced after an interaction-quench to examine the stability of the bound impurities. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.
Current status:
Reports on this Submission
Strengths
1. The authors study a concrete, experimentally relevant setup with exact diagonalization.
2. They look at a number of physical quantities to provide a picture for the nature of binding of the two impurities.
3. They predict collapse-and-revival dynamics of the dimer under an interaction quench, which may motivate experimental observations.
Weaknesses
1. The study is not particularly novel as the dimer formation and much of the ground-state properties are already known. In particular, there is significant overlap with a paper involving one of the authors (Ref.33).
2. The study is limited to small system sizes where it is difficult to characterize critical phenomena.
3. The authors have not discussed how their predictions may be detected experimentally.
Report
The authors study the binding of two spin impurities in a 1D Bose-Hubbard model at unit filling using exact diagonalization. In particular, as the bath-impurity repulsion U_{bI} is increased relative to the bath-bath repulsion U_{bb}, the impurities phase separate from the bath, forming a dimer. Although this binding in the ground state was already known from past work, particularly Ref. [33], the authors provide a more detailed characterization and also analyze low-energy excitations and dynamics following an interaction quench, which they show can lead to collapse and revival of the dimer.
The work is thorough and well written, despite being limited to small systems (9 sites), and constitutes a useful addition to the literature. However, it does not meet the acceptance criteria of SciPost Physics for groundbreaking results or novelty. It could be considered for SciPost Physics Core after addressing the following points.
1. The authors assume that the two impurity atoms do not interact with each other. Other than simplicity, is there any motivation to work at this limit? Have the authors considered the effect of nonzero interactions?
2. More generally, it will be useful to discuss in greater depth how realistic the setup is and whether one can observe the results, e.g. collapse and revival, in experiments.
3. I find the description of Fig. 2(b) in the last paragraph of Sec 3.1 somewhat confusing and lacking physical content. Firstly, the cutoff of 0.4 J_b for weak repulsion is quite arbitrary. (Also, “J_b” is missing in the text.) Secondly, it appears from the figure that the binding energy is quadratic for small for U_{bb} and linear for large U_{bb}, which results in the minima. Can the authors explain the physics behind the quadratic growth in the superfluid region?
4. On several occasions the authors use the term “critical” interaction strength for dimer formation. However, all of their plots at nonzero tunneling are (necessarily) smooth, becoming sharper in the Mott regime. Is there any reason to expect a phase transition as opposed to a crossover (in the thermodynamic limit)? If not, the authors should qualify their usage.
5. Can the authors explain why the energy gap in Fig. 6 falls sharply as the impurities become bound? What is the energy scale of dimer tunneling that sets the small gap?
6. In Fig 7(b) what are the almost equally spaced excitations at large U_{bI}? The gap is much smaller than U_{bb} which would be the cost of multiple doublons in the bath (as in Fig. 16).
7. In the quench dynamics do the authors expect the collapse and revival to persist for large systems? For instance, how does the corresponding spectral gaps scale with the number of sites M?
8. Can the authors explain how they get Eq. (9) for the average distance between two free bosons? Is there a similar expression for two free fermions?
Minor points:
1. In Eq. (7) the one of the occupations should have a subscript “\sigma^{\prime}” as opposed to “\sigma”
2. The last column in Table I should probably read “r_s^* / r_0” as opposed to “r_s^* / a” since Eq. (10 ) gives r_s^* > r_0.
3. Below Fig. 4 the authors state that the distance between the impurities vanishes for small U_{bb}. This is only valid if U_{bI} > U_{bb}/2, which would be useful to add here.
4. In Eq. (A.3) should the degeneracy be M choose 2 for small U_{bI}?
5. In labeling the curves in Figs. 2(b), 3(b), and 5(b) one should use “U_{bb}” [not “U_{BB}”] like everywhere else.
Requested changes
1. Discuss experimental realization(s).
2. Address questions in the report on phase transition and spectral gaps.
3. Incorporate the minor corrections listed in the report.