Theory of spin center sensing of diffusion and other surface electric dynamics

Surface electric dynamics influences the quantum coherence of near-surface spin centers (i.e., <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mn>1</a:mn></a:msub></a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>T</b:mi><b:mn>2</b:mn></b:msub></b:math> times) through spatial and temporal fluctuations of the surface charge density and the electrostatic potential at the crystal surface that are described by the spectral noise density <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>S</c:mi><c:mo>(</c:mo><c:mi>ω</c:mi><c:mo>)</c:mo></c:mrow></c:math>. We find that the electric noise's <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>S</d:mi><d:mo>(</d:mo><d:mi>ω</d:mi><d:mo>)</d:mo></d:mrow></d:math> dependence on the depth <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>d</e:mi></e:math> of a spin center below the surface follows a power law <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msup><f:mi>d</f:mi><f:mrow><f:mo>−</f:mo><f:mi>γ</f:mi></f:mrow></f:msup></f:math> not solely determined by whether the surface charges move as localized pointlike charges (monopoles) or dipoles. The exponent <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>γ</g:mi></g:math> instead reveals the structure of the surface charge and surface potential correlation functions. For surface dynamics originating from diffusion, the spin center's relaxation and decoherence times exhibit a temporal crossover near the correlation time of the fluctuators and thus provide a quantitative fingerprint of the diffusive behavior of charged particles at surfaces. Published by the American Physical Society 2024