Micromotion-based DC sensing using continuously tracked trajectories of dipolar coupled nuclear spins

We report an experimental approach to excite, stabilize, and continuously track Bloch sphere trajectories of dipolar-coupled nuclear spins in a solid. We demonstrate these capabilities on a model system of hyperpolarized <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi mathvariant="normal">C</a:mi> <a:mprescripts/> <a:none/> <a:mn>13</a:mn> </a:mmultiscripts> </a:math> nuclear spins in diamond. We elucidate a method to drive, and preserve, the motion of spins in complex three-dimensional trajectories for over <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msubsup> <c:mi>T</c:mi> <c:mn>2</c:mn> <c:mo>′</c:mo> </c:msubsup> <c:mo>&gt;</c:mo> <c:mn>27</c:mn> <c:mspace width="0.16em"/> <c:mi mathvariant="normal">s</c:mi> </c:mrow> </c:math> even in the presence of interspin coupling. Indeed, without quantum control, interspin interactions lead to rapid spin decay in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msubsup> <f:mi>T</f:mi> <f:mn>2</f:mn> <f:mo>*</f:mo> </f:msubsup> <f:mo>≈</f:mo> <f:mn>1.5</f:mn> <f:mspace width="0.16em"/> <f:mi>ms</f:mi> </f:mrow> </f:math> . Furthermore, we show that the motion of the spins can be continuously tracked in three dimensions on the Bloch sphere for over <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>35</h:mn> <h:mspace width="0.16em"/> <h:mi mathvariant="normal">s</h:mi> </h:mrow> </h:math> . During this time the spins complete <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mo>&gt;</k:mo> <k:mn>68</k:mn> <k:mspace width="0.16em"/> <k:mn>000</k:mn> </k:mrow> </k:math> closed precession orbits, exhibiting high stability and robustness against error. Leveraging these long-lived, robust spin trajectories we devise a novel nonequilibrium quantum sensing scheme for DC magnetic fields, based on micromotion dynamics, and without a static counterpart. Sensing here proceeds for the entire <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msubsup> <m:mi>T</m:mi> <m:mn>2</m:mn> <m:mo>′</m:mo> </m:msubsup> </m:math> period, orders of magnitude longer than <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msubsup> <n:mi>T</n:mi> <n:mn>2</n:mn> <n:mo>*</n:mo> </n:msubsup> </n:math> , and operates in the dense sensor limit, yielding significant sensitivity improvements. Our results suggest new ways to stabilize and interrogate strongly coupled quantum systems through periodic driving and portend powerful applications of rigid spin orbits in quantum sensing.