Superradiant interactions of the cosmic neutrino background, axions, dark matter, and reactor neutrinos

In this paper, we do three things. First, we outline the conditions under which the interaction rate of processes that change the internal state of a system of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>N</a:mi></a:math> targets scales as <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>N</c:mi><c:mn>2</c:mn></c:msup></c:math>. This is an effect distinct from coherent scattering but with the same scaling. Second, we compute example rates for such processes for various weakly interacting particles. Finally, we point to potential quantum observables for these processes that go beyond traditional energy exchange. Maximal coherence in inelastic processes is achieved when the targets are placed in an equal superposition of the ground and excited states. These coherent inelastic processes are analogous to Dicke superradiance, where cooperative effects reinforce the emission of radiation from matter, and we thus refer to them as interactions. We compute the superradiant interaction rates for the cosmic neutrino background (<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:mrow></e:math>), dark matter scattering and absorption, and late-universe particles, such as reactor neutrinos, when the two-level system is realized by nuclear or electron spins in a magnetic field. The rates we find can be quite sizable on macroscopic yet small targets. For example, the <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> interacts with a rate of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="script">O</m:mi><m:mo stretchy="false">(</m:mo><m:mi>Hz</m:mi><m:mo stretchy="false">)</m:mo></m:math> when scattering off a 10 cm liquid or solid-state density spin-polarized sphere, a <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mi mathvariant="script">O</r:mi><r:mo stretchy="false">(</r:mo><r:msup><r:mrow><r:mn>10</r:mn></r:mrow><r:mrow><r:mn>21</r:mn></r:mrow></r:msup><r:mo stretchy="false">)</r:mo></r:mrow></r:math> enhancement compared to the incoherent inelastic contribution. For QCD axion dark matter, similar rates can be achieved with much smaller samples, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:mi>N</w:mi><w:mo>∼</w:mo><w:mi mathvariant="script">O</w:mi><w:mo stretchy="false">(</w:mo><w:msup><w:mrow><w:mn>10</w:mn></w:mrow><w:mrow><w:mn>15</w:mn></w:mrow></w:msup><w:mo stretchy="false">)</w:mo><w:msup><w:mrow><w:mo stretchy="false">(</w:mo><w:mfrac><w:mrow><w:mi>m</w:mi></w:mrow><w:mrow><w:mn>2</w:mn><w:mo stretchy="false">×</w:mo><w:msup><w:mrow><w:mn>10</w:mn></w:mrow><w:mrow><w:mo stretchy="false">−</w:mo><w:mn>8</w:mn></w:mrow></w:msup><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>eV</w:mi></w:mrow></w:mfrac><w:mo stretchy="false">)</w:mo></w:mrow><w:mrow><w:mo>−</w:mo><w:mn>1</w:mn><w:mo>/</w:mo><w:mn>2</w:mn></w:mrow></w:msup></w:mrow></w:math>, where <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi>m</fb:mi></fb:math> is the axion mass. Using the Lindblad formalism for open quantum systems, we show that these superradiant interactions can manifest as a source of noise on the system. This noise is tunable however and can serve as a signature of new physics, as the energy splitting controls the momentum transfer and hence, the amount of macroscopic coherence. These considerations point to new observables that go beyond traditional net energy exchange. These observables are sensitive to the of the excitation and deexcitation rates—instead of the net energy exchange rate which can be very suppressed—and can be viewed as introducing diffusion and decoherence to the system. While we postpone to upcoming work proposing a concrete protocol that extracts these effects from a macroscopic ensemble of atoms, the effects presented in this paper may point to a new class of ultra-low threshold detectors.