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A Josephson junction can make a collective quantum phase behave as a measurable dynamical coordinate. In current-biased Josephson phase dynamics, the Gauge-invariant Josephson phase $\varphi$ moves in a tilted Josephson washboard potential; the junction's capacitance supplies its effective inertia. A trapped phase gives zero mean electric potential difference, while sustained phase advance produces a nonzero mean electric potential difference. Quantized phase levels in a Josephson junction and quantum escape of a current-biased Josephson junction test quantum mechanics for this collective coordinate.

Begin with a stipulated parallel electrical circuit: an ideal sinusoidal Josephson junction, capacitance $C>0$, and effective electrical resistance $R>0$. The Kirchhoff node law and Josephson effect giveHere $I_b$ is the constant bias electric current, $I_{\mu }$ is a deliberately applied microwave electric current, and $I_N$ represents unwanted fluctuating electric current. Multiplication by $\hslash /(2e)$ puts the undriven equation into the mechanical formThe effective inertia is a coefficient for a dimensionless quantum phase, not a literal material mass moving through the insulating layer. The capacitor's energy, $C{V}^2/2=M_{\varphi }{\dot{\varphi }}^2/2$, provides a direct check of that identification. The effective $R$ includes loading by the external electrical circuit; a constant parallel $R$ is an approximation over the relevant frequency range.

The useful design freedom is that $I_b$ changes the confinement while $C$ changes its inertia. The same manufactured device can therefore connect a classical oscillation, discrete energy levels, and escape to an electrical readout. The Martinis-Devoret-Clarke circuit experiments separate these questions experimentally. John Clarke, Michel H. Devoret and John M. Martinis shared the 2025 Nobel Prize in Physics for circuit experiments establishing macroscopic quantum tunnelling and discrete energy levels.^[ref]