Direct Microwave Spectroscopy of Andreev Bound States in Planar Ge Josephson Junctions

We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mi>Ge</a:mi></a:math> high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mi>Pt</d:mi></d:math><g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><g:mi>Si</g:mi></g:math><j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><j:mi>Ge</j:mi></j:math>). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><m:msup><m:mi mathvariant="normal">Δ</m:mi><m:mo>∗</m:mo></m:msup><m:mo>≈</m:mo><m:mn>48</m:mn><m:mspace width="0.2em"/><m:mtext fontfamily="times">μ</m:mtext><m:mi>eV</m:mi></m:math> and transmission <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><s:mi>τ</s:mi><s:mo>≈</s:mo><s:mn>0.94</s:mn></s:math>. The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><v:mn>1</v:mn><v:mspace width="0.2em"/><v:mtext fontfamily="times">μ</v:mtext><v:mrow><v:mi mathvariant="normal">m</v:mi></v:mrow></v:math> showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><bb:mi>Ge</bb:mi></bb:math>.