Direct Microwave Spectroscopy of Andreev Bound States in Planar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>Ge</mml:mi> </mml:math> Josephson Junctions

Abstract

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> . Published by the American Physical Society 2024

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