Effect of a two-dimensional potential on the rate of thermally induced escape over the potential barrier

The thermally induced escape rate of a particle trapped in a two-dimensional (2D) potential well has been investigated through experiment and numerical simulations. The measurements were performed on a special type of superconducting quantum interference device (SQUID) which has 2 degrees of freedom. The energies associated with the motion perpendicular to (transverse) and along (longitudinal) the escape direction are quite different: the ratio between the transverse and longitudinal small oscillation frequencies is ${\mathrm{\omega }}_{\mathit{t}}$/${\mathrm{\omega }}_{\mathit{l}}$∼7. The SQUID’s parameters, which were used to determine the potential shape and energy scales were all independently determined. All data were obtained under conditions for which the 2D thermal activation (TA) model is expected to be valid. The results were found in good agreement with the theoretical prediction. The measured thermal activation energy is found to be the same as the barrier height calculated from the independently determined potential parameters. No evidence of apparent potential barrier enhancement recently reported in a similar system was found. In addition, the results of our numerical simulations suggest that the region in which the 2D thermal activation model is applicable may be extended to barriers as low as ΔU∼${\mathit{k}}_{\mathit{B}}$T.