Electron beam characterization via quantum coherent electric field imaging

We demonstrate an all-optical, minimally invasive electron beam <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mo>(</a:mo> <a:mi>e</a:mi> <a:mtext>−</a:mtext> <a:mtext>beam</a:mtext> <a:mo>)</a:mo> </a:math> characterization using Rydberg electrometry. An <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>e</b:mi> </b:math> -beam passes through a localized detector volume containing thermal Rb atoms that are optically excited in a quantum superposition of ground and Rydberg states. The <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>e</c:mi> </c:math> -beam's electric field perturbs atomic coherence and modifies resonance fluorescence in a narrow spectral region near the two-photon optical transition. Imaging Rb fluorescence provides a map of the electric field from the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>e</d:mi> </d:math> -beam via Rydberg state Stark shifts and allows us to reconstruct the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>e</e:mi> </e:math> -beam width, centroid position, and current. For an <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>e</f:mi> </f:math> -beam of 20 keV and electron currents of 20–40 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>µ</g:mi> <g:mi mathvariant="normal">A</g:mi> </g:mrow> </g:math> , we measured the centroid position with an accuracy of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mo>≤</i:mo> <i:mn>8</i:mn> <i:mspace width="3.33333pt"/> <i:mi>µ</i:mi> <i:mi mathvariant="normal">m</i:mi> </i:mrow> </i:math> and width to within 100 <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>µ</l:mi> <l:mi mathvariant="normal">m</l:mi> </l:mrow> </l:math> , limited by the experimental sensitivity of electric field reconstruction of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mo>∼</n:mo> <n:mn>0.02</n:mn> </n:mrow> </n:math> V/cm. This method is suitable for a wide range of electron energies and currents, and can be adopted for nuclear and high-energy experiments for minimally invasive real-time diagnostics and profiling of charged particle beams.