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Tachyonic and parametric instabilities in an extended bosonic Josephson junction
by Laura Batini, Sebastian Erne, Jörg Schmiedmayer, Jürgen Berges
Submission summary
| Authors (as registered SciPost users): | Laura Batini |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00054v1 (pdf) |
| Date submitted: | Nov. 27, 2024, 2:51 p.m. |
| Submitted by: | Batini, Laura |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We study the decay of phase coherence in an extended bosonic Josephson junction realized via two tunnel-coupled Bose-Einstein condensates. Specifically, we focus on the π-trapped state of large population and phase imbalance, which, similar to the breakdown of macroscopic quantum self-trapping, becomes dynamically unstable due to the amplification of quantum fluctuations. We analytically identify early tachyonic and parametric instabilities connected to the excitation of atom pairs from the condensate to higher momentum modes along the extended direction. Furthermore, we perform Truncated Wigner numerical simulations to observe the build-up of non-linearities at later times and explore realistic experimental parameters.
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Strengths
The work addresses a timely topic in quantum many-body dynamics and the analysis is well motivated, combining analytic and numerical approaches to gain insight into the dynamics beyond the mean-field regime.
Weaknesses
In particular the distinction between tachyonic and parametric resonance mechanisms, is valuable. 1.While the physics is rich, the manuscript would benefit from an introduction to the key physical concepts like “tachyonic” and “parametric” instabilities. 2. The manuscript would be strengthened by a more explicit comparison to prior theoretical and experimental studies of Josephson dynamics and self-trapping in BECs. For instance, how does this analysis extend or differ from earlier Truncated Wigner treatments of coupled condensates? E.g in Phys. Rev. B 106, 075426 the same type of Mathieu equations are discussed to describe the higher order resonances. As for the self-trapping part, how this study extends the Smerzi two mode model? 3. Regarding the quantum-fluctuation-induced instability of the π-mode it would be helpful to more clearly distinguish which features are inaccessible within mean-field theory. Is this instability somehow related to the Kapitza pendulum physics? 4. It’s not very clear why the primary instability is associated to the excitation of a pair of particles from the first condensate, to the second. Do they mean excitations made by bound particles? 5. The discussion of experimental parameters is a valuable aspect of the paper. However, it would be helpful to quantify more explicitly what detection signatures (e.g., momentum distributions, coherence fringes) would signal the presence of the described instabilities in a real experiment.
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condensates on the theoretical level and propose experimental realizations.
However, I think that some open questions need to be addressed:
The authors write: "After reviewing the stable mean-field dynamics,
we focus first on the effect of fluctuations on the linearized level,
destabilizing the state."
That sounds strange or even contradictory -- is the point here that a
spatially homogeneous mean-field solution is stable, while spatial
inhomogeneities can grow (similar to the origin of the CMB fluctuations)?
Then the authors use the phrase "tachyonic instability."
As far as I understand, this usually refers to the instability of a field
near the top of its effective potential.
As such, this instability should also occur at k=0 and may go away at
finite k (again similar to the origin of the CMB fluctuations).
However, what the authors find (if I understood correctly) is an
instability which is absent at k=0 but present at finite k?
Can the authors explain how this fits (if it does) to the top of an
effective potential?
It would also be nice to have a better (intuitive) understanding of
where the instability comes from (in the stationary case, the
parametric instability is more easy to grasp).
This would also help to justify publication in SciPost, I think.
Minor points: Eq.(1) is not normal ordered, i.e., singular.
In a footnote, the authors write: "We have indicated this regime with
the gray shaded area in Fig. 2." but I could not find it.
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