Interfacing Rydberg atoms with a chip-based superconducting microwave resonator using an ac-Stark-shifted single-photon transition

Helium atoms in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>1</a:mn> <a:mi>s</a:mi> <a:mn>50</a:mn> <a:mi>s</a:mi> <a:mspace width="0.16em"/> <a:mmultiscripts> <a:mi>S</a:mi> <a:mn>1</a:mn> <a:none/> <a:mprescripts/> <a:none/> <a:mn>3</a:mn> </a:mmultiscripts> </a:mrow> </a:math> Rydberg level have been resonantly coupled to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>2</c:mn> <c:mi>π</c:mi> <c:mo>×</c:mo> <c:mn>11.722</c:mn> <c:mspace width="0.16em"/> <c:mi>GHz</c:mi> </c:mrow> </c:math> second harmonic mode of a chip-based superconducting coplanar wave-guide microwave resonator. To achieve this, the single-photon electric-dipole-allowed <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mn>1</e:mn> <e:mi>s</e:mi> <e:mn>50</e:mn> <e:mi>s</e:mi> <e:mspace width="0.16em"/> <e:mmultiscripts> <e:mi>S</e:mi> <e:mn>1</e:mn> <e:none/> <e:mprescripts/> <e:none/> <e:mn>3</e:mn> </e:mmultiscripts> </e:mrow> </e:math> <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mo>→</g:mo> </g:math> <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>1</h:mn> <h:mi>s</h:mi> <h:mn>50</h:mn> <h:mi>p</h:mi> <h:mspace width="0.16em"/> <h:mmultiscripts> <h:mi>P</h:mi> <h:mi>J</h:mi> <h:none/> <h:mprescripts/> <h:none/> <h:mn>3</h:mn> </h:mmultiscripts> </h:mrow> </h:math> transition was tuned into resonance with the resonator mode through the ac Stark shift induced by a second strong <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mn>2</j:mn> <j:mi>π</j:mi> <j:mo>×</j:mo> <j:mn>3.350</j:mn> <j:mspace width="0.16em"/> <j:mi>GHz</j:mi> </j:mrow> </j:math> microwave dressing field. The effects of this dressing field, and residual uncanceled dc electric fields at the location of the atoms close to the superconducting chip surface were interpreted with support from Floquet calculations of the energy level structure of the Rydberg states. To observe appreciable population transfer in the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mn>1</l:mn> <l:mspace width="0.16em"/> <l:mi>µ</l:mi> <l:mi mathvariant="normal">s</l:mi> </l:mrow> </l:math> atom-resonator interaction time using this transition, which had an electric dipole moment of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:mn>1500</o:mn> <o:mspace width="0.16em"/> <o:mi>e</o:mi> <o:mspace width="0.16em"/> <o:msub> <o:mi>a</o:mi> <o:mn>0</o:mn> </o:msub> </o:mrow> </o:math> , pulsed microwave fields were injected into the resonator. From the photon occupation number in the resonator mode under these conditions, the single-photon Rabi frequency associated with the coupling of the atoms to the resonator was estimated to be <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:mo>∼</r:mo> <r:mn>2</r:mn> <r:mi>π</r:mi> <r:mo>×</r:mo> <r:mn>100</r:mn> <r:mspace width="0.16em"/> <r:mi>Hz</r:mi> </r:mrow> </r:math> . These results represent an important step toward operation of this Rydberg-atom–superconducting-circuit interface in the single-photon strong-coupling regime.