Effect of Dissipation on the Dynamics of Superconducting Single Electron Transistors

Abstract

In this thesis, I will present the experimental results of the dynamics of superconducting single electron transistors (sSETs), under the influence of tunable dissipation. The sSET, consisting of two dc SQUIDs in series and the third gate electrode, is deposited onto a GaAs/AlGaAs heterostructure which contains a two dimensional electron gas plane 100nm beneath the substrate surface. The Josephson coupling energy, charging energy and dissipation related Hamiltonian can all be tuned in situ, while keeping others unchanged. We measured the switching current statistics and the transport properties, as a function of the dissipation and gate charge at different temperatures.

If the sSET is in the classical regime where phase is a good quantum variable, we found that the switching current and corresponding Josephson energy decrease as dissipation increases. Our observation agrees qualitatively with the theoretical calculation of a single Josephson junction with dominant Josephson energy, in a frequency dependent dissipative environment where energy barrier decreases as dissipation increases in thermally activated escape regime. This dissipation dependence result can be understood as the consequence of a reduced quantum fluctuations in the charge numbers.

Whereas in the charging regime, the switching current shows a 1e periodicity with respect to gate charge, indicating a pronounced charging effect. At a specific gate charge number, quantum fluctuations of the phase variable are compressed as dissipation increases, resulting in an enhanced switching current and Josephson energy. This result matches the theory of a sSET capacitively coupled to a dissipative environment qualitatively. The temperature dependence of the switching current histogram indicates the existence of both quantum and classical thermal phase diffusion. Moreover, quantum charge fluctuations are minimized at the degeneracy point, causing a sharp dip on the width of the switching current histogram.

For a sSET with comparable Josephson energy and charging energy, quantum fluctuations of both phase and charge variables are significant. The influence of dissipation on the dynamics of the device is distinct in the classical and charging regimes. Dissipation compresses quantum phase fluctuations in the charging regime, whereas reduces the quantum charge fluctuations in the classical regime. The transition between these two regimes is found to be determined by the tunnel resistance of the SQUID. The competition between Josephson and charging energies, however, is not the intrinsic parameter of this transition. Our results imply that a detailed theoretical calculation of a sSET with comparable Josephson coupling energy and charging energy under the influence of dissipation is needed.