Large inverse Faraday effect for Rydberg states of free atoms and isolated donors in semiconductors

We report on the induction of magnetization in Rydberg systems by means of the inverse Faraday effect and propose the appearance of the effect in two such systems: Rydberg atoms proper and shallow dopants in semiconductors. Rydberg atoms are characterized by a large orbital radius. This large radius gives such excited states a large angular moment, which when driven with circularly polarized light translates to a large effective magnetic field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="script">B</a:mi><a:mtext>eff</a:mtext></a:msub></a:math>. We calculate this effect to generate effective magnetic fields of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>O</c:mi><c:mrow><c:mo>(</c:mo><c:mn>1</c:mn><c:mspace width="4pt"/><c:mrow><c:mi>µ</c:mi><c:mtext>T</c:mtext></c:mrow><c:mo>)</c:mo></c:mrow><c:mo>×</c:mo><c:msup><c:mrow><c:mo>(</c:mo><c:mfrac><c:mi>ω</c:mi><c:mrow><c:mn>1</c:mn><c:mspace width="4pt"/><c:mtext>THz</c:mtext></c:mrow></c:mfrac><c:mo>)</c:mo></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:msup><c:mrow><c:mo>(</c:mo><c:mfrac><c:mi mathvariant="script">I</c:mi><c:mrow><c:mn>10</c:mn><c:mspace width="4pt"/><c:mtext>W</c:mtext><c:mspace width="0.16em"/><c:msup><c:mtext>cm</c:mtext><c:mrow><c:mo>−</c:mo><c:mn>2</c:mn></c:mrow></c:msup></c:mrow></c:mfrac><c:mo>)</c:mo></c:mrow><c:msup><c:mi>n</c:mi><c:mn>4</c:mn></c:msup></c:mrow></c:math> in the Rydberg states of atoms such as Rb and Cs for off-resonant photon beams with frequency <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>ω</i:mi></i:math> and intensity <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi mathvariant="script">I</j:mi></j:math> expressed in units of the denominators and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>n</l:mi></l:math> the principal quantum number. Additionally, terahertz spectroscopy of phosphorus-doped silicon reveals a large cross section for excitation of shallow dopants to Rydberg-like states, which even for small <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi>n</m:mi></m:math> have the potential to be driven similarly with circularly polarized light to produce an even larger magnetization. Our theoretical calculations estimate <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msub><n:mi mathvariant="script">B</n:mi><n:mtext>eff</n:mtext></n:msub></n:math> as <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mrow><p:mi>O</p:mi><p:mo>(</p:mo><p:msup><p:mn>10</p:mn><p:mn>2</p:mn></p:msup><p:mspace width="0.28em"/><p:mtext>T</p:mtext><p:mo>)</p:mo></p:mrow></p:math> for Si:P with a beam intensity of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mrow><r:msup><r:mn>10</r:mn><r:mn>8</r:mn></r:msup><r:mspace width="0.28em"/><r:mtext>W</r:mtext><r:mspace width="0.16em"/><r:msup><r:mtext>cm</r:mtext><r:mrow><r:mo>−</r:mo><r:mn>2</r:mn></r:mrow></r:msup></r:mrow></r:math>.