Enhanced sensitivity in microscale high-field NMR via nuclear-spin locking with N- <i>V</i> centers

Solid-state defects such as nitrogen-vacancy ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mrow> <a:mi mathvariant="normal">N</a:mi> </a:mrow> </a:mrow> </a:math> - <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>V</d:mi> </d:math> ) centers in diamond have been utilized for NMR sensing at ambient temperatures for samples at the nanoscale and up to the microscale. Similar to standard NMR, <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mrow> <f:mi mathvariant="normal">N</f:mi> </f:mrow> </f:mrow> </f:math> - <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>V</i:mi> </i:math> -sensitivities can be increased using tesla-valued magnetic fields to boost nuclear thermal polarization, while structural parameters, such as chemical shifts, are also enhanced. However, with standard microwave- (MW) based sensing techniques, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mrow> <k:mi mathvariant="normal">N</k:mi> </k:mrow> </k:mrow> </k:math> - <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>V</n:mi> </n:math> centers struggle to track fast megahertz Larmor frequencies encountered in high-field scenarios. Previous protocols have addressed this by mapping target NMR parameters to the signal amplitude rather than the frequency, using a mediating radio-frequency field. Although successful, protocol sensitivities are limited by the coherence time ( <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msubsup> <p:mi>T</p:mi> <p:mn>2</p:mn> <p:mo>∗</p:mo> </p:msubsup> </p:math> ) of the NMR signal owing to the presence of stages where the sample magnetization freely evolves. In this work, we propose extending this coherence time, and consequently improving sensitivity, via amplitude encoding with weak nuclear-spin locking instead of free evolution, thereby taking advantage of the longer sample coherence times ( <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>T</r:mi> <r:mrow> <r:mn>1</r:mn> <r:mi>ρ</r:mi> </r:mrow> </r:msub> </r:math> ). We demonstrate that this can enhance protocol sensitivities by a factor of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mo>≳</t:mo> <t:mn>4</t:mn> </t:math> .