Dissipative Quantum Tunneling of a Single Defect in a Submicron Bismuth Wire Below 1 K

The quantum mechanical problem of a particle tunneling in a double-well potential is of great theoretical and experimental interest. Interaction of the tunneling system with a dissipative environment can have a striking effect on the tunneling dynamics. A very interesting case is that of ohmic dissipation, which occurs when an atom tunnels in a metal in the presence of conduction electrons. We have studied the electrical resistance of submicron Bi wires at low temperature. Due to quantum interference of the conduction electrons, the resistance is highly sensitive to the motion of even a single scattering center. We observe discrete switching of the resistance due to the motion of bistable defects in the sample. We have measured the tunneling rates of a particular defect over the temperature range 0.1-2 K and magnetic field range 0-7 T. The energy asymmetry, varepsilon, of this defect varied over the range 40-420 mK depending on the value of the magnetic field. The temperature dependence of the tunneling rates is qualitatively different for the cases k_{B}T << varepsilon and k_{B}T gg varepsilon . We observe that for k_{B }T << varepsilon, the fast rate (transition rate from upper state to lower state) is roughly temperature independent and the slow rate (transition from lower state to upper state) decreases exponentially, as expected from a simple picture of spontaneous emission and stimulated absorption. When k_{B }T gg varepsilon, however, both rates increase as the temperature is lowered, as predicted by dissipative quantum tunneling theory. We fit our data to the theory and discuss the defect-electron bath coupling parameter alpha, and the renormalized tunneling matrix element Delta_{ rm r}. We have also studied the effect of Joule heating on the dynamics of the defect in the same sample. The ratio of the fast and slow transition rates of a defect depends on temperature through the detailed balance relation, gamma_{f}/ gamma_{s} e^ {varepsilon / k_{B}T}. We interpret this ratio as a local thermometer. When varepsilon / k_{B}T > 1, this ratio is sensitive to small changes in the temperature T seen by the defect. Since the defect is strongly coupled to the conduction electrons in the sample below 1 K, we interpret its sensitivity to drive current as an indication of electron heating. As the drive current increases, the defect temperature approaches a power law dependence with the drive current, independent of the nominal lattice temperature. The data are consistent with a simple model of heating, and strong thermal coupling between the defect and the electron bath. We also tried to measure the electron temperature directly, based on the temperature dependence of the amplitude of the resistance fluctuations, delta R. Since delta R depends only on the electron temperature, we expected delta R would serve as a good electron thermometer. The electron thermometer does not follow the simple heating model.