arxiv: 2604.27809 · v1 · submitted 2026-04-30 · ❄️ cond-mat.quant-gas

Recognition: unknown

Bosonic Josephson junction dynamics: interplay between quantum and thermal fluctuations

Andrea Bardin , Francesco Lorenzi , Luca Salasnich

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Pith reviewed 2026-05-07 06:23 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas

keywords bosonic Josephson junctionquantum fluctuationsthermal fluctuationsJosephson frequencymacroscopic quantum self-trappingspontaneous symmetry breakingtwo-site approximation

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The pith

Quantum fluctuations raise the Josephson frequency and lower the thresholds for self-trapping and symmetry breaking in bosonic junctions, while thermal fluctuations do the opposite.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to go beyond mean-field theory for bosonic Josephson junction dynamics by including both quantum and thermal fluctuations. Assuming negligible transport of non-condensed atoms, they use a homogeneous gas fluctuation formalism to correct the two-site equation of motion. This correction shows quantum and thermal fluctuations have opposite influences on the Josephson frequency, macroscopic quantum self-trapping strength, and spontaneous symmetry breaking threshold. Calculations based on experimental parameters indicate that quantum fluctuations are the dominant correction in recent realizations. This allows semianalytical prediction of fluctuation effects in different regimes.

Core claim

Within the two-site approximation and assuming negligible transport of the non-condensed component, fluctuations in a homogeneous gas yield a corrected equation of motion for the bosonic Josephson junction. Quantum fluctuations increase the Josephson frequency and decrease the critical strengths for macroscopic quantum self-trapping and spontaneous symmetry breaking, while thermal fluctuations produce the opposite shifts. Examination of parameters from recent experiments indicates that the quantum fluctuation regime is the relevant one for bosonic Josephson junctions.

What carries the argument

The fluctuation-corrected two-site equation of motion obtained from the homogeneous gas formalism with negligible non-condensed transport.

Load-bearing premise

The transport of the non-condensed component is negligible.

What would settle it

Measurement of the Josephson frequency in bosonic Josephson junctions at different temperatures to check for an increase at lower temperatures where quantum fluctuations prevail, as opposed to a decrease from thermal effects.

Figures

Figures reproduced from arXiv: 2604.27809 by Andrea Bardin, Francesco Lorenzi, Luca Salasnich.

**Figure 1.** Figure 1: FIG. 1. Schematic of a bosonic Josephson junction at finite view at source ↗

**Figure 2.** Figure 2: FIG. 2. Josephson frequency corrections. (a) Colormap view at source ↗

**Figure 3.** Figure 3: FIG. 3. Corrections to the spontaneous symmetry breaking view at source ↗

**Figure 4.** Figure 4: FIG. 4. Corrections to the macroscopic quantum self-trapping view at source ↗

**Figure 5.** Figure 5: FIG. 5. Colormap of the relative beyond-mean-field cor view at source ↗

**Figure 6.** Figure 6: FIG. 6. Colormap of the condensate fraction view at source ↗

read the original abstract

We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives concrete corrections showing quantum and thermal fluctuations push bosonic Josephson dynamics in opposite directions, but the key assumption on non-condensed transport lacks a quantitative check.

read the letter

The paper derives corrections to the two-site equation of motion for bosonic Josephson junctions that include both quantum and thermal fluctuations. It shows they act in opposite directions on the frequency, self-trapping strength, and symmetry-breaking threshold, and it maps the size of those corrections onto parameters from recent experiments to conclude that quantum fluctuations should dominate. What is new is the explicit combination inside the two-site model and the direct comparison of the two fluctuation types in accessible regimes. The work stays semianalytical, which keeps it practical for estimating when mean-field breaks down. The derivation relies on the assumption that the non-condensed component carries negligible transport, allowing the use of homogeneous-gas fluctuation formulas while keeping the two-site spatial structure. The paper states this assumption but does not provide a bound showing that the non-condensed transport timescale remains long compared to the Josephson period or self-trapping lifetime in the experimental parameters they use. Without that check or a comparison to full simulations, it is hard to know how large the error is when the assumption is only approximate. This is aimed at experimental groups working with ultracold bosonic Josephson junctions who want a quick way to gauge fluctuation effects without running heavy numerics. The calculation is honest about its approximations and engages the literature on the two-site model. I would send it for peer review. Referees can check the validity range of the non-condensed transport assumption and see whether the opposite trends survive more complete treatments.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates bosonic Josephson junction (BJJ) dynamics beyond mean-field theory by incorporating both quantum and thermal fluctuations. Starting from a fluctuation formalism for a homogeneous gas and invoking the assumption that non-condensed component transport is negligible, the authors derive a corrected two-site equation of motion. This yields modifications to the Josephson frequency (decreased by thermal fluctuations), the critical strength of macroscopic quantum self-trapping (MQST), and the threshold for spontaneous symmetry breaking (SSB). The work concludes that quantum fluctuations play opposite roles to thermal fluctuations and dominate in parameters extracted from recent BJJ experiments.

Significance. If the central assumption holds across the relevant timescales, the semianalytical corrections provide a practical route to estimate fluctuation effects on BJJ observables without requiring full numerical simulations of the inhomogeneous system. This could aid interpretation of ultracold-atom experiments on Josephson oscillations, MQST, and symmetry breaking, particularly in regimes where distinguishing quantum versus thermal contributions is experimentally challenging.

major comments (2)

[Abstract and derivation of the corrected EOM] The assumption that non-condensed transport is negligible (allowing the homogeneous-gas fluctuation formalism to be combined with a frozen two-site spatial structure) is stated in the abstract and used to obtain the corrected EOM, yet no quantitative bounds are supplied. Specifically, there is no comparison of the non-condensed transport timescale against the Josephson period, MQST lifetime, or SSB timescale for the experimental parameters extracted from recent BJJ realizations. This assumption is load-bearing: if it fails, the reported opposite roles of quantum and thermal fluctuations and the numerical corrections to frequency, MQST strength, and SSB threshold do not apply.
[Results section on corrections to dynamical quantities] The corrections to dynamical quantities are presented without direct validation against full numerical simulations of the inhomogeneous system or error estimates on the two-site plus homogeneous-fluctuation approximation. Consequently, the accuracy of the semianalytical predictions for the Josephson frequency shift, MQST critical strength, and SSB threshold remains unquantified in the regimes claimed to be experimentally accessible.

minor comments (2)

[Abstract] Abstract: 'strenght' should read 'strength'.
[Abstract] Abstract: 'self trapping' should be hyphenated as 'self-trapping' for consistency with standard terminology.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their detailed and constructive report. Their comments have prompted us to strengthen the justification of our central assumption and to provide additional estimates on the accuracy of our approach. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: [Abstract and derivation of the corrected EOM] The assumption that non-condensed transport is negligible (allowing the homogeneous-gas fluctuation formalism to be combined with a frozen two-site spatial structure) is stated in the abstract and used to obtain the corrected EOM, yet no quantitative bounds are supplied. Specifically, there is no comparison of the non-condensed transport timescale against the Josephson period, MQST lifetime, or SSB timescale for the experimental parameters extracted from recent BJJ realizations. This assumption is load-bearing: if it fails, the reported opposite roles of quantum and thermal fluctuations and the numerical corrections to frequency, MQST strength, and SSB threshold do not apply.

Authors: We appreciate the referee pointing out the need for quantitative support for the assumption of negligible non-condensed transport. This assumption allows us to combine the homogeneous fluctuation formalism with the two-site model. In the revised version of the manuscript, we have included a new appendix that provides estimates of the relevant timescales for the experimental parameters cited in the paper. Specifically, we estimate the non-condensed transport time using the thermal velocity and the barrier width, and compare it to the Josephson frequency period, the MQST lifetime, and the SSB dynamics timescale. For the parameters from recent experiments, our estimates indicate that the transport time is significantly longer than the relevant dynamical timescales, justifying the approximation in those regimes. We also discuss potential limitations when the temperature is higher or the barrier lower. This addition directly addresses the concern and provides the requested bounds. revision: yes
Referee: [Results section on corrections to dynamical quantities] The corrections to dynamical quantities are presented without direct validation against full numerical simulations of the inhomogeneous system or error estimates on the two-site plus homogeneous-fluctuation approximation. Consequently, the accuracy of the semianalytical predictions for the Josephson frequency shift, MQST critical strength, and SSB threshold remains unquantified in the regimes claimed to be experimentally accessible.

Authors: We acknowledge that the lack of direct comparison to full numerical simulations leaves the accuracy of the semianalytical corrections somewhat unquantified. Performing such simulations for the full inhomogeneous system with fluctuations is a substantial computational effort that lies outside the scope of the present semianalytical study, which aims to provide a practical tool for estimating fluctuation effects. In the revision, we have added a discussion in the results section on the expected range of validity and error estimates derived from the underlying fluctuation theory (e.g., the small parameter being the ratio of fluctuation density to total density). We compare our corrected EOM to the standard two-site model in limiting cases and show consistency with known results from literature on quantum fluctuations at T=0. Additionally, we have included a qualitative discussion of the expected accuracy of the predictions. While we cannot provide a direct benchmark against full simulations at this time, these enhancements allow readers to assess the reliability of the predictions in the experimentally relevant regimes. revision: partial

standing simulated objections not resolved

The request for direct validation against full numerical simulations of the inhomogeneous system, which would require extensive computational resources not available within the current scope of this semianalytical work.

Circularity Check

0 steps flagged

Derivation applies external homogeneous-gas fluctuation formalism plus stated assumption to obtain independent corrections

full rationale

The paper starts from a cited formalism for fluctuations in a homogeneous gas, invokes the explicit assumption that non-condensed transport is negligible, and derives a corrected two-site EOM. The resulting semianalytical expressions for Josephson frequency, MQST critical strength, and SSB threshold are then evaluated by inserting independently measured parameters from recent BJJ experiments. No equation reduces by construction to a fitted parameter defined from the same data, no central premise rests on a self-citation chain, and no ansatz is smuggled via prior work by the same authors. The derivation chain therefore remains self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the two-site approximation for the junction and the domain assumption that non-condensed atoms do not transport appreciably between wells; no new free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Transport of the non-condensed component is negligible
Explicitly stated as the assumption enabling the corrected two-site equation of motion.

pith-pipeline@v0.9.0 · 5487 in / 1311 out tokens · 62569 ms · 2026-05-07T06:23:50.516256+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Fron- tiere Quantistiche

LS acknowledges Iniziativa Specifica Quantum of Is- tituto Nazionale di Fisica Nucleare, the Project “Fron- tiere Quantistiche” within the 2023 funding programme ‘Dipartimenti di Eccellenza’ of the Italian Ministry for Universities and Research, and the PRIN 11 2022 Project “Quantum Atomic Mixtures: Droplets, Topolog- ical Structures, and Vortices”. Appen...

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High T emperature Limit In the limit ofα¯µ≪1, the integralI(α¯µ) can be expanded as the convergent series 10 8 10 6 10 4 γ 10 5 10 4 10 3 10 2 10 1 100 101 T ∗ (a) 10 5 0 5 10 (µ − µMF)/µMF % 10 8 10 6 10 4 γ 10 5 10 4 10 3 10 2 10 1 100 101 T ∗ (b) 10 5 0 5 10 (µ′ − µ′ MF)/µ′ MF % FIG. 5. Colormap of the relative beyond-mean-field cor- rection of the che...
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