Superconducting Atomic Contacts under Microwave Irradiation

We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well-known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their nonsinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon-assisted multiple Andreev reflections. The results provide firm support for the full quantum theory of transport between two superconductors based on the concept of Andreev bound states.

Figure 1

Simplified schematics of the electromagnetic environment seen by the atomic contact (double-triangle symbol). Dashed grayed box shows the microfabricated on-chip environment. Dotted box shows components cooled down to base refrigerator temperature $T_0$. A low-frequency voltage source coupled through a large resistor provides a low-frequency current bias. Microwaves are injected through a small coupling capacitor.

Figure 2

Full lines: current-voltage characteristic of an Al atomic contact measured in type $B$ setup at refrigerator temperature $T_0=20\mathrm{mK}$. Grayed (green) line: best fit using zero temperature MAR theory, obtained for PIN $\{0.389,0.238,0.055\}$ and $\Delta =178.2\mu \mathrm{eV}$. Inset: zoom on the supercurrent peak. Grayed (cyan) line: best fit using environment temperature $T_e=133\mathrm{mK}$ in phase diffusion theory.

Figure 3

Full lines: $I(V)$s measured under microwave excitation for two different contacts, refrigerator temperature $T_0=20\mathrm{mK}$. Middle axis: voltage in Josephson voltage units ($V_J={\phi }_0\omega$). Upper and bottom axis: voltage in $\mu \mathrm{V}$. Upper panel: contact on a type $A$ sample, PIN $\{0.992,0.279,0.278\}$, $\Delta =177\mu \mathrm{eV}$, $\alpha =0.43$, $\omega /2\pi =9.3156\mathrm{GHz}$. Inset: zoom on the small Shapiro resonances at $V/V_J=1/3,1/2$. Grayed (magenta) lines, predictions of the mapping model with temperature $T_e=200\mathrm{mK}$. Lower curve: same sample as in Fig. 2, but different run and contact with PIN $\{0.573,0.233,0.037\}$, $\Delta =179.7\mu \mathrm{eV}$, $\alpha =0.86$, $\omega /2\pi =4.892\mathrm{GHz}$. Grayed (cyan) line: phase diffusion theory [18] with environment temperature $T_e=120\mathrm{mK}$.

Figure 4

Full lines: measured differential conductance of contact with PIN $\{0.696,0.270,0.076\}$ and $\Delta =177.6\mu \mathrm{eV}$. Upper curve (shifted upwards by $150\mu \mathrm{S}$): no microwaves. Lower curve: under microwave irradiation with $\alpha =0.70$, $\omega /2\pi =8.2935\mathrm{GHz}$. Grayed (green) lines: predictions of PAMAR theory, with no adjustable parameters. The theory includes neither the negative contribution of the Josephson peak at low voltages, nor the Shapiro resonances.