Detecting gravitational signatures of dark matter with atom gradiometers

We study the purely gravitational signatures of dark matter from the ultralight to the ultraheavy mass range in proposed long-baseline atom gradiometers, focusing on terrestrial designs, such as AION-km and MAGIS-km, as well as space-based concepts, such as MAGIS-space, AEDGE and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>AEDGE</a:mi><a:mo>+</a:mo></a:mrow></a:math>. Due to its exceptional acceleration sensitivity and depending on astrophysical backgrounds, a detector similar to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>AEDGE</c:mi><c:mo>+</c:mo></c:mrow></c:math> could detect a dark matter subcomponent which constitutes <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">O</e:mi><e:mo stretchy="false">(</e:mo><e:mn>10</e:mn><e:mo>%</e:mo><e:mo stretchy="false">)</e:mo></e:math> of the local dark matter energy density and is populated by compact clumps of mass between <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mn>10</j:mn><j:mn>6</j:mn></j:msup><j:mtext> </j:mtext><j:mtext> </j:mtext><j:mi>kg</j:mi></j:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mn>10</l:mn><l:mn>10</l:mn></l:msup><l:mtext> </l:mtext><l:mtext> </l:mtext><l:mi>kg</l:mi></l:math> (<n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mn>10</n:mn><n:mrow><n:mo>−</n:mo><n:mn>25</n:mn></n:mrow></n:msup><n:msub><n:mi>M</n:mi><n:mo stretchy="false">⊙</n:mo></n:msub><n:mo>≲</n:mo><n:mspace linebreak="goodbreak"/><n:mi>M</n:mi><n:mo>≲</n:mo><n:msup><n:mn>10</n:mn><n:mrow><n:mo>−</n:mo><n:mn>21</n:mn></n:mrow></n:msup><n:msub><n:mi>M</n:mi><n:mo stretchy="false">⊙</n:mo></n:msub></n:math>) in an otherwise unexplored region of dark matter model space. Furthermore, because the gravitational observable depends on the relative gravitational time delay measured by spatially separated atomic clouds, we find that atom gradiometers are parametrically more sensitive than laser interferometers, such as LIGO and LISA, to fast-oscillating spacetime perturbations sourced by energy density and pressure fluctuations of ultralight dark matter. Depending on astrophysical backgrounds, a detector akin to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi>AEDGE</s:mi><s:mo>+</s:mo></s:mrow></s:math> could probe a DM overdensity of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi mathvariant="script">O</u:mi><u:mo stretchy="false">(</u:mo><u:mn>10</u:mn><u:mo stretchy="false">)</u:mo></u:math> times the local dark matter energy density for masses <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>m</z:mi><z:mo>≲</z:mo><z:msup><z:mn>10</z:mn><z:mrow><z:mo>−</z:mo><z:mn>17</z:mn></z:mrow></z:msup><z:mtext> </z:mtext><z:mtext> </z:mtext><z:mi>eV</z:mi></z:math>.