Prospects for relic neutrino detection using nuclear spin experiments

Direct detection of the cosmic neutrino background ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi mathvariant="normal">C</a:mi> <a:mi>ν</a:mi> <a:mi mathvariant="normal">B</a:mi> </a:mrow> </a:math> ) remains one of the most formidable experimental challenges in modern physics. In this work, we extend recent studies of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi mathvariant="normal">C</e:mi> <e:mi>ν</e:mi> <e:mi mathvariant="normal">B</e:mi> <e:mtext>−</e:mtext> <e:mi>induced</e:mi> </e:mrow> </e:math> coherent transitions in polarized nuclear spin ensembles. Adopting an open quantum system framework, we model coherent neutrino effects in large spin ensembles using a Lindblad master equation that also incorporates realistic experimental imperfections such as local dephasing and imperfect polarization. We solve the Lindblad equation numerically by way of a fast and computationally inexpensive method that can be extended to an arbitrarily large number of spins. Using our numerical solutions, we forecast the sensitivities of future experiments such as CASPEr to the local <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mi mathvariant="normal">C</i:mi> <i:mi>ν</i:mi> <i:mi mathvariant="normal">B</i:mi> </i:mrow> </i:math> overdensity parameter <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>δ</m:mi> <m:mi>ν</m:mi> </m:msub> </m:math> . Our findings indicate that a CASPEr-like experiment, though primarily aimed at axion dark matter search, could also constrain the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi mathvariant="normal">C</o:mi> <o:mi>ν</o:mi> <o:mi mathvariant="normal">B</o:mi> </o:mrow> </o:math> overdensity to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>δ</s:mi> <s:mi>ν</s:mi> </s:msub> <s:mo>∼</s:mo> <s:msup> <s:mn>10</s:mn> <s:mn>13</s:mn> </s:msup> </s:math> in configurations achievable by currently planned experimental efforts, and down to <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>δ</u:mi> <u:mi>ν</u:mi> </u:msub> <u:mo>∼</u:mo> <u:msup> <u:mn>10</u:mn> <u:mn>11</u:mn> </u:msup> </u:math> in the most optimized scenario. While <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mrow> <w:mi mathvariant="normal">C</w:mi> <w:mi>ν</w:mi> <w:mi mathvariant="normal">B</w:mi> </w:mrow> </w:math> detection remains out of reach in the foreseeable future, our results highlight the potential of using quantum sensing to probe fundamental physics.