Correlated Quantum Dephasometry: Symmetry-Resolved Noise Spectroscopy of Two-Dimensional Superconductors and Altermagnets

Abstract: Symmetry-resolved spectroscopies, such as angle-resolved photoemission spectroscopy and polarization-resolved Raman, are central for quantum material characterization, yet remain challenging at nanoscale dimensions and low frequencies. Here, we propose correlated quantum dephasometry, which enables symmetry resolved quantum noise spectroscopy of materials at nanoscale and low ($\sim$MHz) frequencies via correlated dephasing of two spin qubits near materials. Our approach leverages the finite-range spatial structures of nonlocal near-field noise correlations to isolate rotational symmetry of the material response in momentum space beyond single qubit capabilities. We apply our approach to two-dimensional (2D) superconductors, and predict clear fingerprints that discriminate s-, d-, and g-wave symmetry of the superconducting gap. To highlight the generality, we further show that the same framework resolves 2D s-wave antiferromagnets and d-wave altermagnets. Our results establish correlated quantum dephasometry as a nanoscale, low-frequency complement for symmetry-resolved spectroscopy applicable to a broad class of quantum materials.

• The paper demonstrates a novel CQD framework that leverages correlated dephasing in multiqubit sensors to achieve momentum-space tomography and symmetry resolution in noise spectroscopy.
• It employs rigorous theoretical and numerical analyses to extract angular harmonics, revealing superconducting gap functions and magnetic diffusion responses.
• The study details experimental protocols compatible with NV centers, emphasizing practical sensor configurations and low dephasing times in 2D quantum materials.

Correlated Quantum Dephasometry: Symmetry-Resolved Noise Spectroscopy of 2D Superconductors and Altermagnets

Introduction

The manuscript introduces and formalizes correlated quantum dephasometry (CQD) as a framework for symmetry-resolved noise spectroscopy of two-dimensional (2D) quantum materials, specifically superconductors and altermagnets (2604.22751). CQD leverages spatially correlated dephasing in multiqubit quantum sensors placed in the extreme near-field regime of surfaces, offering momentum-space tomography of material response functions with angular and frequency selectivity. The treatment connects advanced quantum sensor control, near-field electromagnetic theory, and condensed matter response functions, providing a comprehensive structure for extracting physical properties tied to pairing and magnetic symmetry.

Theoretical Framework for Correlated Dephasing

The authors develop a rigorous formalization of near-field correlated dephasing for an array of qubit sensors through spatially correlated magnetic noise fields originating from surface currents or magnetization fluctuations. The spin-field interaction is modeled as longitudinal coupling and the system dynamics are captured through a time-local master equation, separating single-qubit and pairwise correlated dephasing terms.

The spatially nonlocal noise correlation spectrum $J_c(\omega)$ is derived from the fluctuation-dissipation theorem and the electromagnetic Green's function, connecting the calculation directly to the underlying current or magnetization fluctuation spectra of the material. Notably, the pulse sequence filter function $F(\omega,t)$ provides frequency selectivity, while the sensor configuration (qubit orientation, spatial separation) yields angular and momentum selectivity.

Symmetry Channel Decomposition in CQD

CQD exploits the spatial configuration and orientation of qubit pairs to project the material response $\mathcal{O}(q,\theta_q,\omega)$ onto symmetry channels (harmonics) in momentum space. For materials with inversion symmetry, even-order channels are resolved via the angular Fourier decomposition of the correlated dephasing signal. The Jacobi-Anger expansion connects the qubit separation direction to the accessible harmonics, with generalized Bessel weighting determined by sensor geometry.

Analytic and numerical treatments demonstrate that arbitrary qubit orientations do not alter the accessible symmetry channels, only the weightings. Single-qubit dephasometry, by contrast, is fundamentally limited in resolving the full spectrum of rotational harmonics.

Momentum-Space Tomography

CQD enables angular and radial (momentum) tomography of material responses. The angular scan $\beta$ between sensor pairs interrogates the $\theta_q$ dependence, while variations in interqubit distance $D$ and sensor height $z$ provide access to radial momentum $q$ modes up to a cutoff set by $1/z$. Frequency selectivity is controlled via pulse sequence engineering. In practice, systematic scans reconstruct the relevant Fourier components $\mathcal{O}^{2n}(q,\omega)$ from experimental dephasing data.

Application to 2D Superconductors

The authors apply CQD to symmetry-resolved noise spectroscopy of 2D superconductors. In the regime $F(\omega,t)$0, the response reduces to $F(\omega,t)$1. The pairing symmetry of the superconducting gap (s-, d-, g-wave) determines the angular harmonics present.

Numerical calculations utilize a dimensionless BdG mean-field framework, evaluating $F(\omega,t)$2 for prototypical gap functions. The correlated dephasing kernel is shown to resolve angular harmonics characteristic of pairing symmetry. Strong numerical results confirm that CQD can distinguish between gap symmetries even at experimentally relevant sensor distances and temperatures, with typical dephasing timescales estimated in the microsecond regime for crystalline FeSe films.

Application to 2D Altermagnets and Antiferromagnets

CQD is also developed for probing 2D altermagnets and antiferromagnets via their spin diffusion susceptibilities $F(\omega,t)$3. The susceptibility structure, determined by magnon band anisotropy, contains both isotropic and anisotropic diffusion components. The derived Fresnel coefficients and susceptibility kernel connect directly to $F(\omega,t)$4 weighting and momentum-dependent diffusion.

Numerical estimates for materials such as $F(\omega,t)$5-Fe$F(\omega,t)$6O$F(\omega,t)$7 indicate that CQD can resolve the distinct symmetry channels, with shorter dephasing timescales (on the order of tens of microseconds) due to stronger magnetic interactions. The correlated signal decays with interqubit distance more rapidly than in superconductors, but remains robust for practical sensor geometries.

Complete Angular Tomography for Materials without Inversion Symmetry

An important extension is provided for materials lacking inversion symmetry. CQD is shown to resolve all angular harmonics in momentum space, including odd orders, by measuring not only correlated dephasing $F(\omega,t)$8 but also correlated phase rotations $F(\omega,t)$9. This phase rotation originates from the antisymmetric component in noise correlations and manifests as coherent dynamics in the sensor system. State tomography enables extraction of $\mathcal{O}(q,\theta_q,\omega)$0 harmonics, achieving complete angular characterization.

Experimental Feasibility and Implications

The manuscript discusses practical considerations for realizing CQD with solid-state qubit platforms, notably NV centers in diamond, including sensor placement, pulse control, and sample orientation. Diamond NV platforms with entanglement readout and covariance protocols are compatible with the correlated readouts necessary for CQD. Theoretical estimates indicate that dephasing timescales and signal strengths are compatible with existing quantum sensing capabilities for both superconducting and magnetic materials.

CQD provides a fundamentally new probe for momentum-space response functions, complementing conventional techniques such as ARPES and Raman with spatial resolution below the diffraction limit. It enables noninvasive tomography of pairing and magnetic symmetries and could be extended to study nonlocal correlations, topological responses, and dynamical critical phenomena in quantum materials.

Conclusion

Correlated quantum dephasometry is a mathematically rigorous and experimentally viable protocol for symmetry-resolved noise spectroscopy of 2D quantum materials. By leveraging multiqubit sensor arrays and careful control of their spatial and angular configurations, CQD enables tomography of pairing and magnetic symmetries in momentum space, including materials without inversion symmetry. The framework advances quantum sensor-based materials spectroscopy and is poised to foster developments in condensed matter physics and nanoscience. Future directions include integration with many-body quantum sensors for enhanced noise discrimination, application to non-Gaussian noise regimes, and extension to strongly correlated and topological phases.