Transport phenomena and decoherence in short Josephson junction arrays
J. Jussi Toppari · Jyväskylä University Digital Archive (University of Jyväskylä) · 2003
In this thesis transport phenomena in the arrays consisting of two (SSET) or three (CPP) or more Josephson junctions are discussed. A quantitative theory of adiabatic Cooper pair transport in phase biased arrays is developed. The theory predicts that the quantum inaccuracy of the Cooper pair pumping in arrays with a small number of junctions is very large. The effects due to inhomogeneous arrays or nonideal gating sequences are also quantitatively treated. It is also shown explicitly how the pumped charge in the Cooper pair pump can be understood as a partial derivative of Berry’s phase with respect to the phase difference \(\varphi\) across the array. This makes possible to obtain information about Berry’s phase by measuring the pumped current in the CPP. Also the decoherence time \(\tau_{\varphi}\), which is one of the central quantities in quantum computing, is quantitatively estimated in a dissipative electromagnetic environment of the circuit. This method allows comparison of the suitability of a system as a quantum bit. Also a direct measurement of \(\tau_{\varphi}\) as a crossover between coherent and incoherent pumping in the single Cooper pair pump is suggested. In experiments with Cooper pair pump it is demonstrated in practise how the CPP can be used as a turnstile with help of dissipation. Also a regular pumping experiment is performed. To explain the twofold behavior of the CPP, sometimes yielding \(e\)-periodicity while sometimes \(2e\)-periodicity, the energy-minimisation model is developed. It is shown also experimentally that \(\text{Nb}\) based junctions with high critical temperature (\(T_c \approx 8.5\text{ K}\)) and Josephson coupling can be fabricated using the regular self-alignment technique. The measured \(\text{Al/Nb/Al}\) SSETs show a clear signature of resonant tunnelling of Cooper pairs combined with elastic cotunnelling of quasiparticles, \(q\text{-MQT}\), through the barrier of \(\Delta_{\text{Nb}}\).