Pith. sign in

REVIEW 3 major objections 5 minor 61 references

Magnetic noise of a dark exciton Bose-Einstein condensate

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An optically invisible exciton condensate can be detected by the magnetic noise it emits; a soft spin mode brings that noise into an NV center's range.

desk verdict A clever new detection scheme for dark exciton condensates, but a missing μ0 in the NV dipole coupling inflates the predicted rates by orders of magnitude and undermines the central observability claim. read the letter →

arxiv 2608.11740 v1 pith:23GGGRGY submitted 2026-08-12 cond-mat.mes-hall cond-mat.quant-gas

Pieter M. Gunnink This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.quant-gas
keywords darkexcitonsBose-EinsteincondensateNVcentermagnetometrymagneticnoiseBeliaevdampingT1relaxometryspinorBECtransitionmetaldichalcogenides
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Dark $S_z = \pm 1$ triplet excitons—bound electron-hole pairs whose optical decay is spin-forbidden—can form long-lived Bose-Einstein condensates that emit no light and therefore evade standard optical detection. This paper argues that such a condensate should still produce a detectable magnetic fingerprint: an external magnetic field along the spin quantization axis tunes the condensate from antiferromagnetic to ferromagnetic spin ordering, and the softer of the two sound modes dips into the gigahertz frequency range as the field approaches the critical value $B_c = g'n/\gamma$ (about 2.3 T for parameters taken from recent TMD bilayer experiments). In that range, a nitrogen-vacancy (NV) center in diamond measures the stray magnetic-field noise through its spin relaxation rate $T_1^{-1}$. The paper derives the noise spectrum from the longitudinal spin susceptibility, including cubic corrections to the sound dispersion and Beliaev damping, and shows that the small-distance signal scales as $d \log d$ rather than a plain power law. If correct, NV relaxometry turns an optically invisible condensate into a measurable magnetic object and provides a way to certify its existence.

What carries the argument

The engine of the calculation is the retarded longitudinal magnetic susceptibility $\chi_{zz}(\omega,k)$, whose poles sit exactly at the Bogoliubov sound-mode energies; this is what turns a condensate's spin dynamics into measurable magnetic noise. It feeds into the NV relaxometry formula $1/T_1 = (\gamma_{\mathrm{NV}}^2/8) \coth(\omega/2T) \int d^2k/(2\pi)^2 e^{-2kd} k^2 \chi''_{zz}(\omega,k)$, in which the exponential factor filters the susceptibility at a wavelength set by the NV–sample distance $d$. Around the critical field, the lower sound velocity $c_-$ vanishes, making the $k^3$ term of the dispersion and the Beliaev damping $\Gamma_B k^3$ (decay of one sound quasiparticle into two) the dominant scales; their competition produces the logarithmic distance dependence. The parameters $g = 5\,\mu\mathrm{eV}\,\mu\mathrm{m}^2$, $g' = 0.2\,\mu\mathrm{eV}\,\mu\mathrm{m}^2$, $n = 2.0\times10^{11}\,\mathrm{cm}^{-2}$, and $m = m_e$ are taken from a recent two-component exciton-condensate experiment in a TMD bilayer, giving $B_c \approx 2.3$ T.

What would settle it

Scan an NV center over a TMD bilayer while sweeping the external field from about 1.8 T up to $B_c \approx 2.3$ T at a distance of 150 nm: the absence of a growing 1–10 GHz resonance as $B$ approaches $B_c$, or the failure of low-frequency small-distance data to follow $I_0 + I_1 d + I' d \log d$, would falsify the prediction.

Watch

Extended reading notes

Core claim

The central claim is that the longitudinal spin sound mode of the $S_z = \pm 1$ dark-exciton BEC softens as the external field approaches $B_c = g'n/\gamma$, and this softening brings it into the frequency window of NV $T_1$ relaxometry. In the antiferromagnetic phase the two Bogoliubov modes have sound velocities $c_\pm$ given by $c_\pm^2 = [n(g+g') \pm \sqrt{n^2(g-g')^2 + 4f_z^2 n^2 gg'}]/(2m)$; as $f_z \to 1$, $c_- \to 0$ and the $k^3$ correction to the dispersion becomes important. The retarded longitudinal magnetic susceptibility has poles at these sound energies, and the NV relaxation rate $1/T_1 = (\gamma_{\mathrm{NV}}^2/8) \coth(\omega/2T) \int d^2k/(2\pi)^2 e^{-2kd} k^2 \chi''_{zz}(\omega,k)$ acts as a momentum filter selecting $k \approx 1/d$. The paper further claims that Beliaev damping of the soft mode, $\Gamma_B k^3$ with $\Gamma_B \propto (1-f_z)^{-1/2}$, dominates the linewidth near the transition and, together with the cubic dispersion, yields a small-distance scaling proportional to $I_0 + I_1 d + I' d \log d$. This provides a route to detect exciton BECs through their spin component rather than their optical emission.

Load-bearing premise

The whole prediction assumes that a homogeneous, long-lived condensate of dark excitons actually forms with the interaction strengths, density, and mass taken from recent bilayer experiments, and that the diamond sensor's spin axis is aligned with the direction the exciton spins point; if any of those fail, the softened mode may sit outside the gigahertz window and the signal would not show up.

Editorial extensions

If this is right

  • At an NV–sample distance of 150 nm, fields as low as $0.99\,B_c$ pull the softened sound mode into the 1–10 GHz band, where the predicted $T_1^{-1}$ spectrum becomes observable.
  • At small separation ($d \lesssim 30$ nm), the low-frequency noise tail follows $I_0 + I_1 d + I' d \log d$, with coefficient $I' \propto \Gamma_B \alpha/(\alpha^2 + \Gamma_B^2)$, so fitting the tail extracts the ratio $\alpha/\Gamma_B$ as a function of the magnetic field.
  • Near the transition, Beliaev damping overtakes extrinsic damping at high momenta, making the condensate a setting in which to study two-dimensional many-body decay processes beyond ultracold atomic gases.
  • In the ferromagnetic phase the massive mode does not couple to the longitudinal susceptibility at zero temperature, and the remaining sound mode is too stiff to be detected by $T_1$ relaxometry, so the antiferromagnetic side of the transition carries the observable signature.
  • The scheme does not require optical emission from the excitons, so it can also certify condensates that may already exist in current bilayer experiments but have produced no optical signature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Inference: if the predicted $d \log d$ tail were observed at several probe frequencies, one could map the crossover momentum $k_* = c/\alpha$ as a function of field and thereby measure the cubic dispersion coefficient directly, a quantity the paper currently fixes by theory.
  • Inference: the same relaxometry could act as an equilibration probe, since a condensate that has not fully thermalized should produce a different frequency distribution of magnetic noise than the quasi-equilibrium spectrum computed here.
  • Inference: rotating the applied field away from the NV axis should suppress the signal, providing a control experiment that distinguishes exciton spin noise from other magnetic backgrounds.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper proposes detecting a two-dimensional Bose-Einstein condensate of optically dark S_z = ±1 triplet excitons through the magnetic field noise it emits, using the spin relaxation (T1) of a nearby NV center. For a two-component exciton gas with density interaction g and spin-anisotropy interaction g′, the authors derive the Bogoliubov spectrum of the antiferromagnetic (two-component) phase and show that the lower spin-sound mode softens as the Zeeman field approaches B_c = g′n/γ, entering the gigahertz band. They compute the retarded longitudinal spin susceptibility, include Beliaev damping that diverges as 1/√(1−f_z) near the critical point, insert both into the NV T1 formula, and predict both a measurable relaxation rate and, at small NV-sample distances d, a d log d scaling of the low-frequency rate arising from the cubic corrections to the dispersion and damping. Input parameters are taken from prior TMD experiments, with no fitting to the predicted noise; the claim is that NV relaxometry gives a viable, optically-blind detection channel for dark-exciton condensates.

Significance. The mechanism is well chosen and is the strongest part of the paper: the softening of the lower spin-sound branch at B_c derives from a standard two-component Bogoliubov treatment, the estimate B_c ≈ 2.3 T is concrete, and the Beliaev-damping divergence ∝ 1/√(1−f_z) is a physically interesting prediction. The derivation is transparent: the SM contains the full calculation, all inputs (g, g′, n, m, γ, Γ0) come from prior experiments or are stated as estimates, and no parameter is fitted to the predicted noise spectrum. The d log d small-distance scaling is a genuinely falsifiable fingerprint of the cubic corrections. However, the internal prefactor inconsistencies identified below affect precisely the quantities supporting the headline claims: the absolute rates in Fig. 1 and the coefficient quoted for the d log d term are not reliable, and the observability conclusion fails a direct SI-unit check. If the prefactor issues were corrected and the claims re-scoped, the theoretical content could be worth publishing; in the present form the central quantitative conclusion is not supported.

major comments (3)
  1. [SM §V, Eqs. (57)–(58); main text Eq. (13); Fig. 1] The stray-field coupling in the SM is missing the vacuum permeability. Equation (57) starts from B̂(r) = −(μ0/4π)[m̂/r³ − 3(r·m̂)r/r⁵], but Eq. (58) quotes f^η_k = (3d/4π)∫d²r e^{ik·r} r_η/r⁵ = (i/2)e^{−|k|d} k_η, i.e., the μ0 that is explicit in Eq. (57) drops out of the Fourier transform. The correct result is f^η_k = (iμ0/2)e^{−|k|d} k_η, so the prefactor in main-text Eq. (13) must be γ²_NV μ0²/8 and every absolute rate in Fig. 1 is overestimated by μ0² ≈ 1.6×10⁻¹². For the stated parameters the corrected peak rates are of order 10⁻¹⁴ s⁻¹, far below the sensitivity of NV T1 relaxometry; the headline claim that the softened mode 'can be measured' therefore has no quantitative support. This is an internal inconsistency between Eqs. (57) and (58) of the SM that is independent of whether the assumed dark-exciton BEC exists.
  2. [Main text Eq. (10); SM Eqs. (23) and (60)] The retarded susceptibility in Eq. (10) of the main text as typeset is ambiguous and needs to be reconciled with the SM. SM Eq. (23) gives the Matsubara correlator as 2γ² Q²_{η;k} ω_{ηk}/((iω_n)² + ω²_{ηk}), and the Lorentzian in SM Eq. (60) likewise has a numerator proportional to ω_q, so the retarded form should read 2γ² Σ_η Q²_{η;k} ω_{ηk}/((ω+i0⁺)² − ω²_{ηk}). If the intended form in Eq. (10) is Q²_{η;k}/(ω_{ηk}((ω+i0⁺)² − ω²_{ηk})), the spectral weight of the sound-mode resonance is off by 1/ω²_{ηk}, which changes all T1 integrals, including the low-frequency d log d analysis. Please correct Eq. (10) and confirm explicitly that Figs. 1–3 were computed with the Q²ω_{ηk} form.
  3. [SM §VI, Eqs. (63)–(65); main text Eq. (16)] The coefficient of the d log d term in Eq. (65) does not follow from Eq. (63). In the UV regime ω_q = αq³ and Γ_q = Γ_B q³, so the integrand of Eq. (63) is q⁵ · 4ω_qΓ_q/(ω_q² + Γ_q²)² = 4αΓ_B/[(α² + Γ_B²)² q]; carrying out the integral gives I′_UV = 8d · αΓ_B/(α² + Γ_B²)² · log(1/(dk*)). Equation (65) quotes 8d · αΓ_B/(α² + Γ_B²) · log(1/(dk*)), which is off by one power of (α² + Γ_B²). This factor then propagates to Eq. (16) of the main text, so the claimed extraction of α/Γ_B from the amplitude of the d log d term would be quantitatively wrong by the same factor.
minor comments (5)
  1. [Figs. 1 and 3; Eq. (13)] The temperature entering the reduced rate 1/T1 · sinh(ω/2T) in Figs. 1 and 3 is never stated; please specify T in the figure captions and state explicitly the units of T in Eq. (13), noting the ℏ = k_B = 1 convention.
  2. [Beliaev-damping section; Fig. 2] Γ0 is introduced as 'Γ0 = 100 ps the extrinsic damping lifetime'; as a rate this means Γ0 = 1/(100 ps) ≈ 10 GHz, which is comparable to the probe frequencies of Fig. 2. The value used in the numerics should be stated and labeled on the horizontal dotted line of Fig. 2.
  3. [Main text Eq. (16)] Equation (16) is written as a proportionality; once the coefficient of the d log d term is corrected, this should be given as an explicit equality, since the ratio α/Γ_B is the quantity claimed to be extractable.
  4. [Main text Eq. (10)] The quantity Q_{ηk} appearing in Eq. (10) is defined only in the SM; please define it in the main text.
  5. [Main text, Results and Conclusion] Calling the d log d behavior an 'unconventional UV scaling' overstates the case: a logarithmic short-distance correction of this type is the standard consequence of a 1/q high-momentum tail regulated at q ≈ 1/d; consider rephrasing.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted NV noise spectra and d log d scaling follow analytically from an externally parameterized model, with no fitted input renamed as a prediction.

full rationale

The derivation chain is self-contained and does not reduce to its own inputs. The action in Eq. (1) is a standard two-component spinor Bose gas with interaction parameters g and g' set from the experimental TMD bilayer work [23] and literature values for the exciton mass and gyromagnetic ratio [15,28,29]; the critical field B_c = g'n/gamma is then computed from these inputs rather than fitted. The Bogoliubov spectrum (7), the longitudinal susceptibility (10), and the NV relaxation formula (13) are derived from that action, and the Beliaev damping coefficient (15) is computed within the same model. The claimed d log d small-distance scaling is derived analytically in the Supplemental Material (Eq. (66)) from the cubic dispersion and Beliaev damping of the model, with the coefficient I' proportional to Gamma_B alpha / (alpha^2 + Gamma_B^2); the numerical fits in Fig. 3 are consistency checks of this derived functional form against the paper's own numerical evaluation of Eq. (13), not fits of any input parameter to an external or predicted data set. The only self-citation, Ref. [24], is the same-author Supplemental Material that contains the actual derivations used in the main text, so no load-bearing claim is justified solely by an unverified self-citation or by an imported uniqueness theorem. A separate quantitative concern about a possible missing mu_0 prefactor between Eqs. (57) and (58) affects the numerical magnitude of the predicted rates, but that is a correctness or error issue, not a circularity issue, because the missing factor is not an input that is later relabeled as an output. No step in the paper defines a prediction in terms of the quantity it is supposed to predict, and no parameter is fitted to the predicted T1 spectra; accordingly the circularity score is 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new entities. Its predictions rest on six empirical input parameters, the quasi-equilibrium BEC assumption, the NV relaxometry formula, and standard Bogoliubov plus Beliaev damping theory. The central detectability claim is sensitive mainly to g' and n via B_c and the sound velocity.

free parameters (6)
  • g (density interaction) = 5 μeV μm²
    Taken from Ref. [23] (TMD bilayer); determines sound velocities and B_c.
  • g' (spin anisotropy interaction) = 0.2 μeV μm²
    Taken from Ref. [23]; sets B_c = g'n/γ and the softening scale; a key parameter for detectability.
  • n (exciton density) = 2.0e11 cm^-2
    Set following Ref. [23]; controls B_c and T_c.
  • m (exciton mass) = m_e
    Assumed equal for both species; standard effective mass in TMDs.
  • γ (exciton gyromagnetic ratio) = 3.0 μ_B
    From Refs. [15,28,29]; sets the Zeeman coupling.
  • Γ0 (extrinsic damping rate) = 1/(100 ps)
    Chosen as the extrinsic linewidth; competes with Beliaev damping.
assumptions (6)
  • domain assumption The action Eq. (1) with local contact interactions g and g' describes the dark exciton gas.
    Assumes a dilute two-component exciton gas with contact interactions; no microscopic justification from exciton-exciton scattering is given.
  • domain assumption The system is in quasi-equilibrium with a well-defined condensate.
    The paper states 'we will assume (quasi-)equilibrium'; if the dark exciton gas is driven or has a finite lifetime, the Bogoliubov spectrum and noise correlator differ.
  • domain assumption The NV center is a point sensor with its axis parallel to the spin quantization axis, described by the Markovian T1 formula Eq. (13).
    Standard NV relaxometry result; assumes stationary noise and a specific alignment.
  • domain assumption The damped susceptibility has a Lorentzian form with the Beliaev-plus-extrinsic damping model.
    Standard damped harmonic oscillator response; the specific damping model is assumed to dominate at the relevant frequencies.
  • domain assumption Static and thermal bubble contributions to χ_zz are negligible.
    The paper disregards these terms, justified at low temperature, but they can contribute near the critical field.
  • domain assumption Beliaev damping only involves scattering within the critical branch.
    Scattering into the upper branch is kinematically suppressed due to the large sound velocity difference.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Magnetic noise of a dark exciton Bose-Einstein condensate." pith.science (2026). https://pith.science/paper/23GGGRGY

@misc{pith2026260811740,
  author       = {Pith},
  title        = {Pith review of: Magnetic noise of a dark exciton Bose-Einstein condensate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23GGGRGY}},
  note         = {Machine review of arXiv:2608.11740}
}
abstract

Excitons provide a promising platform for the realization of solid-state Bose-Einstein condensation (BEC), offering quantum coherence, strongly correlated electron-hole physics, and superfluidity. Yet, its unambiguous experimental identification remains challenging. In particular, $S_z= \pm 1$ triplet excitons are excellent candidates to realize an exciton BEC, because of their intrinsically limited recombination rate and thus long lifetimes. However, since their optical detection is inherently forbidden, experimental signatures remain elusive. In this work, we demonstrate that the magnetic nature of a $S_z= \pm 1$ triplet exciton BEC gives rise to stray magnetic field noise, that can be measured using nitrogen-vacancy (NV) center magnetometry. Using an external magnetic field to tune the system from an antiferromagnetic to a ferromagnetic ordering, the longitudinal spin sound mode of the BEC softens, bringing the mode into the characteristic gigahertz frequency range of the NV spin relaxation rate and thus allowing direct detection. Furthermore, we demonstrate an unconventional UV scaling at small distances $d$ from the sample, owing to the cubic corrections to the sound mode dispersion and damping rate in the form of Beliaev damping. Through this approach, we establish that the spin component of exciton BECs offers new approaches to detect exciton BECs.

Figures

Figures reproduced from arXiv: 2608.11740 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of magnetic noise of a Bose-Einstein conden [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The frequency ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The numerically obtained scaling of the low-frequency [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 1
Figure 1. Figure 1: FIG. 1. The forward self-energy, associated with Beliaev damping. [PITH_FULL_IMAGE:figures/full_fig_p011_1.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 51 canonical work pages

  1. [1]

    J. F. Allen and A. D. Misener, Flow of Liquid Helium II, Nature 141, 75 (1938)

    1938

  2. [2]

    Kapitza, Viscosity of Liquid Helium below the𝜆-Point, Nature 141, 74 (1938)

    P. Kapitza, Viscosity of Liquid Helium below the𝜆-Point, Nature 141, 74 (1938)

    work page 1938

  3. [3]

    M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor, Science269, 198 (1995)

    1995

  4. [4]

    K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. Van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein Con- densation in a Gas of Sodium Atoms, Physical Review Letters 75, 3969 (1995)

    work page 1995

  5. [6]

    D. M. Stamper-Kurn and M. Ueda, Spinor Bose gases: Symme- tries, magnetism, and quantum dynamics, Reviews of Modern Physics85, 1191 (2013)

    work page 2013

  6. [7]

    J. M. Blatt, K. W. B ¨oer, and W. Brandt, Bose-Einstein Conden- sation of Excitons, Physical Review126, 1691 (1962)

    work page 1962

  7. [8]

    Combescot, R

    M. Combescot, R. Combescot, and F. Dubin, Bose–Einstein condensation and indirect excitons: A review, Reports on Progress in Physics80, 066501 (2017)

    work page 2017

  8. [9]

    J ´erome, T

    D. J ´erome, T. M. Rice, and W. Kohn, Excitonic Insulator, Phys- ical Review158, 462 (1967)

    work page 1967

Show all 61 references
  1. [10]

    Kaneko and Y

    T. Kaneko and Y. Ohta, A New Era of Excitonic Insulators, Journal of the Physical Society of Japan94, 012001 (2025)

    2025

  2. [11]

    L. V. Butov, Exciton condensation in coupled quantum wells, Solid State Communications Quantum Phases at the Nanoscale, 127, 89 (2003)

    2003

  3. [12]

    M. M. Fogler, L. V. Butov, and K. S. Novoselov, High- temperature superfluidity with indirect excitons in van der Waals heterostructures, Nature Communications5, 4555 (2014)

    2014

  4. [13]

    F.-C. Wu, F. Xue, and A. H. MacDonald, Theory of two- dimensional spatially indirect equilibrium exciton condensates, Physical Review B92, 165121 (2015)

    2015

  5. [14]

    O. L. Berman and R. Y. Kezerashvili, High-temperature super- fluidity of the two-component Bose gas in a transition metal dichalcogenide bilayer, Physical Review B93, 245410 (2016)

    2016

  6. [15]

    Robert, T

    C. Robert, T. Amand, F. Cadiz, D. Lagarde, E. Courtade, M. Manca, T. Taniguchi, K. Watanabe, B. Urbaszek, and X. Marie, Fine structure and lifetime of dark excitons in tran- sition metal dichalcogenide monolayers, Physical Review B96, 155423 (2017)

    2017

  7. [16]

    Z. Wang, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Evidence of high-temperature exciton condensation in two-dimensional atomic double layers, Nature 574, 76 (2019)

    2019

  8. [17]

    G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomi- cally thin transition metal dichalcogenides, Reviews of Modern Physics90, 021001 (2018)

    2018

  9. [18]

    G. Wang, C. Robert, M. M. Glazov, F. Cadiz, E. Courtade, T. Amand, D. Lagarde, T. Taniguchi, K. Watanabe, B. Urbaszek, and X. Marie, In-Plane Propagation of Light in Transition Metal Dichalcogenide Monolayers: Optical Selection Rules, Physical Review Letters119, 047401 (2017)

    2017

  10. [19]

    Combescot, O

    M. Combescot, O. Betbeder-Matibet, and R. Combescot, Bose- Einstein Condensation in Semiconductors: The Key Role of Dark Excitons, Physical Review Letters99, 176403 (2007)

    2007

  11. [20]

    Alloing, M

    M. Alloing, M. Beian, M. Lewenstein, D. Fuster, Y. Gonz ´alez, L. Gonz´alez, R. Combescot, M. Combescot, and F. Dubin, Ev- idence for a Bose-Einstein condensate of excitons, Europhysics Letters107, 10012 (2014)

    2014

  12. [21]

    Anankine, M

    R. Anankine, M. Beian, S. Dang, M. Alloing, E. Cambril, K. Merghem, C. G. Carbonell, A. Lemaˆıtre, and F. Dubin, Quan- tized Vortices and Four-Component Superfluidity of Semicon- ductor Excitons, Physical Review Letters118, 127402 (2017)

    2017

  13. [22]

    J. Yu, G. Dai, S. Xing, W. Zhang, L. Dou, T. Shen, X. Zhang, X. Feng, and F. Gu, Direct observation of room-temperature exciton condensation (2025), arXiv:2511.09187 [physics]

    2025

  14. [23]

    R. Qi, Q. Li, J. Nie, R. Xia, H. Kim, H. Lim, J. Xie, T. Taniguchi, K. Watanabe, M. F. Crommie, A. H. MacDonald, and F. Wang, Two-component exciton condensates in an electron–hole bilayer, Nature654, 629 (2026)

    2026

  15. [24]

    See Supplemental Material at [URL inserted by publisher] for detailed calculation of the BEC, its excitations, Beliaev damp- ing, Landau damping, NV center magnetometry and the low- frequency scaling

  16. [25]

    H. Deng, H. Haug, and Y. Yamamoto, Exciton-polariton Bose- Einstein condensation, Reviews of Modern Physics82, 1489 (2010)

    2010

  17. [26]

    Kasprzak, M

    J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szyma´nska, R. Andr´e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, Bose–Einstein condensation of exciton polaritons, Nature 443, 409 (2006)

    2006

  18. [27]

    H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid,Ul- tracold Quantum Fields, Theoretical and Mathematical Physics (Springer, Dordrecht ; New York, 2009). 6

    2009

  19. [28]

    M. R. Molas, A. O. Slobodeniuk, T. Kazimierczuk, K. Noga- jewski, M. Bartos, P. Kapu ´sci´nski, K. Oreszczuk, K. Watan- abe, T. Taniguchi, C. Faugeras, P. Kossacki, D. M. Basko, and M. Potemski, Probing and Manipulating Valley Coherence of Dark Excitons in Monolayer WSe 2, Phy...

    2019

  20. [29]

    Robert, B

    C. Robert, B. Han, P. Kapuscinski, A. Delhomme, C. Faugeras, T. Amand, M. R. Molas, M. Bartos, K. Watanabe, T. Taniguchi, B. Urbaszek, M. Potemski, and X. Marie, Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers, Nature Communications11, 4037 (2020)

    2020

  21. [30]

    V. L. Berezinskii, Destruction of Long-range Order in One- dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems, Journal of Experimental and Theoretical Physics32, 493 (1971)

    1971

  22. [31]

    J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, Journal of Physics C: Solid State Physics6, 1181 (1973)

    1973

  23. [32]

    Prokof’ev, O

    N. Prokof’ev, O. Ruebenacker, and B. Svistunov, Critical Point of a Weakly Interacting Two-Dimensional Bose Gas, Physical Review Letters87, 270402 (2001)

    2001

  24. [33]

    Jarmola, V

    A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Bud- ker, Temperature- and Magnetic-Field-Dependent Longitudinal Spin Relaxation in Nitrogen-Vacancy Ensembles in Diamond, Physical Review Letters108, 197601 (2012)

    2012

  25. [34]

    Rondin, J.-P

    L. Rondin, J.-P. Tetienne, T. Hingant, J.-F. Roch, P. Maletinsky, and V. Jacques, Magnetometry with nitrogen-vacancy defects in diamond, Reports on Progress in Physics77, 056503 (2014)

    2014

  26. [35]

    Casola, T

    F. Casola, T. van der Sar, and A. Yacoby, Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond, Nature Reviews Materials3, 17088 (2018)

    2018

  27. [36]

    Rovny, Z

    J. Rovny, Z. Yuan, M. Fitzpatrick, A. I. Abdalla, L. Futamura, C. Fox, M. C. Cambria, S. Kolkowitz, and N. P. de Leon, Nanoscale covariance magnetometry with diamond quantum sensors, Science378, 1301 (2022)

    2022

  28. [37]

    Machado, E

    F. Machado, E. A. Demler, N. Y. Yao, and S. Chatterjee, Quan- tum Noise Spectroscopy of Dynamical Critical Phenomena, Physical Review Letters131, 070801 (2023)

    2023

  29. [38]

    Flebus and Y

    B. Flebus and Y. Tserkovnyak, Quantum-Impurity Relaxome- try of Magnetization Dynamics, Physical Review Letters121, 187204 (2018)

    2018

  30. [39]

    Stepanov, F

    V. Stepanov, F. H. Cho, C. Abeywardana, and S. Takahashi, High-frequency and high-field optically detected magnetic res- onance of nitrogen-vacancy centers in diamond, Applied Physics Letters106, 063111 (2015)

    2015

  31. [40]

    Moody, C

    G. Moody, C. Kavir Dass, K. Hao, C.-H. Chen, L.-J. Li, A. Singh, K. Tran, G. Clark, X. Xu, G. Bergh ¨auser, E. Malic, A. Knorr, and X. Li, Intrinsic homogeneous linewidth and broad- ening mechanisms of excitons in monolayer transition metal dichalcogenides, Nature Communicatio...

    2015

  32. [41]

    A. O. Slobodeniuk and D. M. Basko, Spin–flip processes and radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers, 2D Materials3, 035009 (2016)

    2016

  33. [42]

    W. He, J. Sears, F. Barantani, T. Kim, J. W. Villanova, T. Berlijn, M. Lajer, M. A. McGuire, J. Pelliciari, V. Bisogni, S. Johnston, E. Baldini, M. Mitrano, and M. P. M. Dean, Dispersive Dark Excitons in van der Waals Ferromagnet CrI3, Physical Review X15, 011042 (2025)

    2025

  34. [45]

    Hodby, O

    E. Hodby, O. M. Marag`o, G. Hechenblaikner, and C. J. Foot, Ex- perimental Observation of Beliaev Coupling in a Bose-Einstein Condensate, Physical Review Letters86, 2196 (2001)

    2001

  35. [46]

    N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, Beliaev Damping of Quasiparticles in a Bose-Einstein Condensate, Physical Review Letters89, 220401 (2002)

    2002

  36. [47]

    V. N. Popov, Hydrodynamic Hamiltonian for a nonideal Bose gas, Theoretical and Mathematical Physics11, 478 (1972)

    1972

  37. [48]

    L. P. Pitaevskii and S. Stringari, Landau damping in dilute Bose gases, Physics Letters A235, 398 (1997)

    1997

  38. [49]

    Vincent Liu, Theoretical Study of the Damping of Collec- tive Excitations in a Bose-Einstein Condensate, Physical Review Letters79, 4056 (1997)

    W. Vincent Liu, Theoretical Study of the Damping of Collec- tive Excitations in a Bose-Einstein Condensate, Physical Review Letters79, 4056 (1997)

    1997

  39. [51]

    C. Du, T. van der Sar, T. X. Zhou, P. Upadhyaya, F. Ca- sola, H. Zhang, M. C. Onbasli, C. A. Ross, R. L. Walsworth, Y. Tserkovnyak, and A. Yacoby, Control and local measurement of the spin chemical potential in a magnetic insulator, Science 357, 195 (2017)

    2017

  40. [52]

    H. Fang, S. Zhang, and Y. Tserkovnyak, Generalized model of magnon kinetics and subgap magnetic noise, Physical Review B105, 184406 (2022)

    2022

  41. [53]

    R. Xue, N. Maksimovic, P. E. Dolgirev, L.-Q. Xia, A. M¨ uller, R. Kitagawa, F. Machado, D. R. Klein, D. MacNeill, K. Watan- abe, T. Taniguchi, P. Jarillo-Herrero, M. D. Lukin, E. Demler, and A. Yacoby, Magnon hydrodynamics in an atomically-thin ferromagnet (2025), arXiv:2403.0...

    2025 arXiv

  42. [54]

    Zhang and Y

    S. Zhang and Y. Tserkovnyak, Flavors of magnetic noise in quantum materials, Physical Review B106, L081122 (2022)

    2022

  43. [55]

    S. P. Kelly and Y. Tserkovnyak, Superconductivity-enhanced magnetic field noise (2024), arXiv:2412.05465 [cond-mat]

    2024 arXiv

  44. [56]

    S. Li, S. P. Kelly, J. Zhou, H. Lu, Y. Tserkovnyak, H. Wang, and C. R. Du, Nanoscale observation and control of quasiparticle induced magnetic noise in a superconducting resonator, Physical Review Letters136, 076004 (2026), arXiv:2412.18896 [cond- mat.mes-hall]

    2026

  45. [57]

    Hammons, J

    B. Hammons, J. Kumar, S. Iqbal, P. B. Karki, K. Prasad, T. Li, A. Pirali, A. E. Aregbesola, R. Timalsina, X. Hong, J. Wang, K. Ambal, I. Fescenko, and A. Laraoui, Probing GHz Spin Dynamics across Magnetic Phase Transitions in CrCl 3 Nanoflakes Using Nitrogen-Vacancy Microscopy...

    2026

  46. [58]

    Source fields Expanding the source terms, we obtain the contribution to the action 𝑆𝐽 =− ∫ d𝑥 𝛾𝐵𝛼 𝐽(𝑥) ∑︁ 𝑚𝑚′ 𝜎𝛼 𝑚𝑚′ 𝜙0 𝑚 ¯𝜙′ 𝑚′(𝑥)+𝜙 ′ 𝑚′(𝑥) +𝜙′ 𝑚(𝑥) ¯𝜙′ 𝑚′(𝑥) ,(18) and we thus obtain parts of the action that are linear or quadratic in fluctuations. The terms quadratic in fl...

  47. [59]

    H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid,Ultracold Quantum Fields, Theoretical and Mathematical Physics (Springer, Dordrecht ; New York, 2009)

    2009

  48. [60]

    Kawaguchi and M

    Y. Kawaguchi and M. Ueda, Spinor Bose–Einstein condensates, Physics Reports Spinor Bose–Einstein Condensates,520, 253 (2012)

    2012

  49. [61]

    S. T. Beliaev, Application of the Methods of Quantum Field Theory to a System of Bosons, Soviet Phys. JETP7(1957)

    1957

  50. [62]

    S. T. Beliaev, Energy-Spectrum of a Non-ideal Bose Gas, Soviet Phys. JETP7(1957)

    1957

  51. [63]

    Giorgini, Damping in dilute Bose gases: A mean-field approach, Physical Review A57, 2949 (1998)

    S. Giorgini, Damping in dilute Bose gases: A mean-field approach, Physical Review A57, 2949 (1998)

    1998

  52. [64]

    Chung and A

    M.-C. Chung and A. B. Bhattacherjee, Damping in 2D and 3D dilute Bose gases, New Journal of Physics11, 123012 (2009)

    2009

  53. [65]

    Chung and A

    M.-C. Chung and A. B. Bhattacherjee, Dynamical Structure Factor and Spin-Density Separation for a Weakly Interacting Two-Component Bose Gas, Physical Review Letters101, 070402 (2008)

    2008

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.