Observation of Transition from Escape Dynamics to Underdamped Phase Diffusion in a Josephson Junction

We have investigated the dynamics of underdamped Josephson junctions with a relatively small Josephson coupling $E_J$. In addition to the usual crossover between macroscopic quantum tunneling and thermally activated (TA) behavior we observe, for the first time, the transition from TA behavior to underdamped phase diffusion. Above the crossover temperature, the threshold for switching into the finite-voltage state becomes extremely sharp. We propose a ($T$, $E_J$) phase diagram with various regimes and show that for a proper description of it, dissipation and level quantization in a metastable well are crucial.

Figure 1

(a) The various operation regimes of a Josephson junction with low $E_J$. For details, see text. The UPD region corresponds to $R_s=500\Omega$, $C_J=100\mathrm{fF}$ ,and $\tau =100\mu \mathrm{s}$. (b) The dynamics in the upper well and schematic behavior upon escape. Inset: equivalent circuit of the junction with frequency dependent dissipation.

Figure 2

Cumulative histograms of the dc-SQUID at different temperatures and at different magnetic fields. Curves are shifted for clarity and the vertical spacing between ticks corresponds to unity escape probability. Solid lines are from simulations described in the text; dotted blue lines correspond to $P_{\Sigma }(I,T)$. Inset: scanning electron micrograph of the measured dc-SQUID and the experimental circuit.

Figure 3

(a) The positions ($I_{50\%}$) and (b) the widths ($\Delta I$) of the histograms. Black solid and dotted lines are results (with known junction parameters) of standard TA and MQT models, respectively, ignoring dissipation. Blue, red, and orange solid lines are the parameters of the simulated histograms based on the LO model discussed in the text.