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Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
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DOI：10.1063/5.0325267.png)
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Abstract
En 中文
Dirac exceptional points (EPs) represent a novel class of non-Hermitian singularities that, unlike conventional EPs, reside entirely within the parity-time unbroken phase and exhibit linear energy dispersion. Here, we theoretically investigate the quantum geometry of Dirac EPs realized in nitrogen-vacancy centers in diamond, utilizing fidelity susceptibility as a probe. We demonstrate that despite the absence of a symmetry-breaking phase transition, the Dirac EP induces a pronounced geometric singularity, confirming the validity of the fidelity in characterizing non-Hermitian EPs. Specifically, the real part of the fidelity susceptibility diverges to negative infinity, which serves as a signature of non-Hermitian criticality. Crucially, however, we reveal that this divergence exhibits a distinct anisotropy, diverging along the non-reciprocal coupling direction while remaining finite along the detuning axis. Furthermore, we establish that this anisotropy, characterized by at least one exact dark direction coexisting with divergent directions, is a generic consequence of the Dirac EP structure whenever the parameter derivatives collectively span the off-diagonal operator space at the Dirac EP. This behavior stands in stark contrast to the omnidirectional divergence observed in conventional EPs. Our findings provide a comprehensive picture of the fidelity probe near the Dirac EP, highlighting the critical role of parameter directionality in exploiting Dirac EPs for quantum control and sensing applications.
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