Quantum sensing of time-dependent magnetic signals with molecular spins

Molecular spins offer a promising platform for quantum sensing, particularly in organic, supramolecular, and biological environments. Recognition of signals by these systems is of particular interest given their possible integration into more complex structures and their possible use as sensors in close proximity to analytes. In this work, we develop two quantum sensing protocols that enable discrimination between different time-dependent magnetic fields without requiring their periodicity to match the microwave manipulating sequence. These are based on the Hahn echo sequence and have been tested on VO(TPP) and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mrow> <a:mi>VOPt</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>SOCPh</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> <a:mn>4</a:mn> </a:msub> </a:math> molecular spins embedded in a superconducting yttrium barium copper oxide (YBCO) microwave planar resonator. We report a magnetic field sensitivity up to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>2.57</e:mn> <e:mo>×</e:mo> <e:msup> <e:mn>10</e:mn> <e:mrow> <e:mo>−</e:mo> <e:mn>7</e:mn> </e:mrow> </e:msup> </e:math> T <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>Hz</g:mi> <g:mrow> <g:mo>−</g:mo> <g:mstyle displaystyle="false" scriptlevel="0"> <g:mfrac> <g:mn>1</g:mn> <g:mn>2</g:mn> </g:mfrac> </g:mstyle> </g:mrow> </g:msup> </g:math> (with lower bounds approaching <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mn>2.87</k:mn> <k:mo>×</k:mo> <k:msup> <k:mn>10</k:mn> <k:mrow> <k:mo>−</k:mo> <k:mn>8</k:mn> </k:mrow> </k:msup> </k:math> T <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>Hz</m:mi> <m:mrow> <m:mo>−</m:mo> <m:mstyle displaystyle="false" scriptlevel="0"> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> </m:mstyle> </m:mrow> </m:msup> </m:math> ) for signals with a duration of a few microseconds. Under the given conditions, the minimum signal area that can be measured is in the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msup> <q:mn>10</q:mn> <q:mrow> <q:mo>−</q:mo> <q:mn>10</q:mn> </q:mrow> </q:msup> </q:math> T s range, suggesting a potential trade-off between the minimum measurable field, and the required signal duration and the memory time.