Revisiting Dissipation-Driven Phase Transition in a Josephson Junction

Despite extensive experimental and theoretical work over several decades, Schmid-Bulgadaev quantum phase transition remains a subject of debate. Here we revisit this problem by performing systematic experiments on low-frequency current-voltage characteristics of Josephson junctions over a wide range of parameters. The experiments are conducted in a true resistive environment formed by a metallic on-chip resistor located near the junction. Over the parameter range of the experiment, we find that the transition occurs when the resistance crosses the quantum value <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>h</a:mi> <a:mo>/</a:mo> <a:mo stretchy="false">(</a:mo> <a:mn>4</a:mn> <a:msup> <a:mrow> <a:mi>e</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msup> <a:mo stretchy="false">)</a:mo> <a:mo>≃</a:mo> <a:mn>6.5</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi mathvariant="normal">k</a:mi> <a:mi mathvariant="normal">Ω</a:mi> </a:mrow> </a:math> for Cooper pairs, as originally predicted. The temperature <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>T</g:mi> </g:math> of the experiment is naturally nonzero, but our basic theoretical modeling corroborates that the observations under these conditions can serve as the basis for the conclusions made, in particular, the crossover resistance from superconducting to insulating regime is the same as that at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>T</i:mi> <i:mo>=</i:mo> <i:mn>0</i:mn> </i:math> .