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arxiv: 2510.11671 · v1 · submitted 2025-10-13 · ❄️ cond-mat.quant-gas

Finite-temperature phase diagram and collective modes of coherently coupled Bose mixtures

Sunilkumar V , Rajat , Sandeep Gautam , Arko Roy This is my paper

Pith reviewed 2026-05-18 08:05 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas
keywords coherently coupled Bose condensatesferromagnetic-paramagnetic transitionfinite temperaturecollective modesspin gapRabi couplingHartree-Fock-Bogoliubov
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0 comments X

The pith

The ferromagnetic-paramagnetic transition in Rabi-coupled Bose condensates is identified at finite temperature by the vanishing of the spin gap in uniform gases and the spin breathing mode in traps.

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

This paper studies the phase transition from ferromagnetic to paramagnetic order in Bose-Einstein condensates where the two components are coherently coupled by a Rabi field. The authors calculate the phase diagram at nonzero temperatures using a mean-field many-body approach and show how the transition point depends on both temperature and the strength of the coupling. They track the transition in a uniform gas by the closing of an energy gap in spin excitations and in a trapped gas by the frequency of a breathing oscillation going to zero. A reader should care because these results give concrete predictions for experiments that can tune temperature and coupling to explore quantum phase transitions in real ultracold atom systems.

Core claim

In the homogeneous three-dimensional case the critical line separating ferromagnetic and paramagnetic phases is located where the spin gap closes, and this line is plotted versus temperature and Rabi coupling strength. Magnetization drops continuously to zero along this line. In quasi-one-dimensional harmonic traps the same transition appears as the spin breathing mode frequency reaching zero, with the minimum of this frequency moving to smaller Rabi couplings as temperature is raised. All spin modes harden when temperature alone drives the system across the transition at fixed coupling, while hybridized density-spin modes become more density-like near the critical point.

What carries the argument

Softening of the spin gap in the homogeneous system and softening of the spin breathing mode in the trapped system, computed within the Hartree-Fock-Bogoliubov-Popov framework, as the diagnostic for the finite-temperature critical line.

If this is right

  • The critical Rabi coupling for the transition decreases with rising temperature.
  • Magnetization is progressively suppressed as temperature increases toward the critical line.
  • Spin modes harden monotonically when temperature drives the transition at fixed coupling.
  • Hybridized density modes acquire greater density character near the critical point.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar softening signatures may appear in other coherently coupled quantum systems such as polariton condensates.
  • Extending the calculation to include beyond-Popov corrections could test the robustness of the critical line near the transition.
  • Direct measurement of spin mode frequencies in trapped gases offers a practical way to locate the phase boundary experimentally.

Load-bearing premise

The Hartree-Fock-Bogoliubov theory with Popov approximation accurately describes the collective excitations all the way up to the finite-temperature critical line in both homogeneous and trapped geometries.

What would settle it

An experiment that measures the spin breathing mode frequency in a quasi-one-dimensional Rabi-coupled condensate and finds that the frequency remains finite at the temperature and coupling values where the theory predicts it reaches zero would falsify the predicted location of the transition.

Figures

Figures reproduced from arXiv: 2510.11671 by Arko Roy, Rajat, Sandeep Gautam, Sunilkumar V.

Figure 1
Figure 1. Figure 1: FIG. 1. Finite-temperature phase diagram of a homogeneous [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dispersion relations across the ferro–paramagnetic transition. (a)–(c): Excitation spectra at [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Total density profiles of a trapped coherently coupled [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Temperature dependence of the ferromagnetic spin [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Excitation spectrum of a trapped coherently cou [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Excitation spectrum of a trapped coherently coupled [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a1)–(a3)Total density profiles illustrating the trans [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Excitation spectrum of a trapped coherently cou [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
read the original abstract

We investigate the ferromagnetic-paramagnetic phase transition in coherently (Rabi) coupled Bose-Einstein condensates at zero and finite temperatures, exploring different routes to the transition by tuning the Rabi coupling or increasing the temperature at a fixed coupling. Using the Hartree-Fock-Bogoliubov theory within the Popov approximation, we map out the finite-temperature phase diagram of a three-dimensional homogeneous condensate and identify the critical line through the softening of the spin gap. Magnetization and the spin dispersion branch reveal the progressive suppression of the ferromagnetic order with increasing temperature. In quasi-one-dimensional harmonic traps, the transition, driven by Rabi coupling, is inferred through the softening of the spin breathing mode with its minimum shifting to lower coupling values with increasing temperature. Notably, the thermally driven transition causes monotonic hardening of all the spin modes. For both coupling and temperature-driven transition, the hybridized density modes in the ferromagnetic phase acquire more density character while approaching the critical point.

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.

Referee Report

2 major / 1 minor

Summary. The paper maps the finite-temperature ferromagnetic-paramagnetic transition in coherently coupled Bose mixtures. For the homogeneous 3D case it locates the critical line by spin-gap softening within Hartree-Fock-Bogoliubov theory in the Popov approximation; magnetization and spin dispersion are tracked as functions of temperature and Rabi coupling. In quasi-1D harmonic traps the transition is identified by softening of the spin breathing mode, whose minimum shifts with temperature, while hybridized density modes acquire more density character near the critical point.

Significance. If the Popov approximation remains quantitatively reliable up to the critical line, the work supplies a concrete phase diagram and mode spectra that can be compared directly with experiments on Rabi-coupled condensates. The self-consistent solution of the HFB equations and the distinction between coupling-driven and temperature-driven routes are technically sound contributions.

major comments (2)
  1. [§4] §4 (homogeneous system): the critical line is identified solely by closure of the spin gap within the Popov approximation, yet no comparison with quantum Monte Carlo or functional renormalization-group results is presented to quantify the shift of the transition temperature due to critical fluctuations.
  2. [§5] §5 (trapped geometry): the softening of the spin breathing mode is used to locate the transition, but the manuscript provides neither error estimates on the mode frequencies nor a convergence check with respect to the number of basis states or the cutoff in the Bogoliubov spectrum near the critical Rabi coupling.
minor comments (1)
  1. The abstract states that modes are computed within the Popov approximation but does not specify the numerical implementation details (e.g., discretization or self-consistency tolerance) that would allow independent reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each of the major comments below.

read point-by-point responses

  1. Referee: [§4] §4 (homogeneous system): the critical line is identified solely by closure of the spin gap within the Popov approximation, yet no comparison with quantum Monte Carlo or functional renormalization-group results is presented to quantify the shift of the transition temperature due to critical fluctuations.

    Authors: The Popov approximation within Hartree-Fock-Bogoliubov theory provides a self-consistent mean-field treatment that captures the essential physics of the ferromagnetic-paramagnetic transition driven by Rabi coupling and temperature. We recognize that critical fluctuations, which are not included in this approximation, would lead to a quantitative shift in the transition temperature. However, performing a full comparison with quantum Monte Carlo simulations or functional renormalization group methods would require a separate, computationally intensive study. We will revise the manuscript to explicitly state that the critical line is determined within the Popov approximation and to discuss qualitatively the expected effects of fluctuations. revision: partial

  2. Referee: [§5] §5 (trapped geometry): the softening of the spin breathing mode is used to locate the transition, but the manuscript provides neither error estimates on the mode frequencies nor a convergence check with respect to the number of basis states or the cutoff in the Bogoliubov spectrum near the critical Rabi coupling.

    Authors: We agree that providing numerical details on convergence and error estimates would strengthen the presentation. In our calculations, the basis set size and spectral cutoff were chosen to ensure convergence of the mode frequencies, particularly near the critical point. We will add a new subsection or appendix in the revised manuscript that includes convergence tests with respect to the number of basis states and the Bogoliubov cutoff, along with estimates of the numerical uncertainty in the mode frequencies. revision: yes

Circularity Check

0 steps flagged

No circularity: phase boundary obtained from self-consistent HFB-Popov solution

full rationale

The derivation solves the Hartree-Fock-Bogoliubov equations in the Popov approximation self-consistently for the homogeneous and trapped systems, then locates the ferromagnetic-paramagnetic boundary by the point at which the spin gap (or spin breathing mode frequency) reaches zero. This is a direct numerical consequence of the gap equation within the chosen mean-field framework rather than a redefinition, a fit to the target quantity, or a result imported via self-citation. No ansatz is smuggled in, no parameter is fitted to a subset of the same data and then called a prediction, and the central claim remains independent of the paper's own outputs. The approach is therefore self-contained against its stated approximations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the Popov approximation within HFB theory to finite-temperature coherently coupled condensates; no free parameters, new entities, or additional axioms are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Hartree-Fock-Bogoliubov theory in the Popov approximation is adequate for describing the finite-temperature phase boundary and collective modes
    Invoked to map the phase diagram and to compute spin and density modes near the critical line.

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