The Hamiltonian operator for an unbiased array of Josephson junctions with gate voltages is constructed when only Cooper pair tunneling and charging effects are taken into account. The supercurrent through the system and the pumped current induced by changing the gate voltages periodically are discussed with an emphasis on the inaccuracies in the Cooper pair pumping. Renormalization of the Hamiltonian operator is used in order to reliably parametrize the effects due to inhomogeneity in the array and nonideal gating sequences. The relatively simple model yields an explicit, testable prediction based on three experimentally motivated and determinable parameters.
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
φ 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
τφ, 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
τφ 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
Nb based junctions with high critical temperature (
Tc≈8.5 K) and Josephson coupling can be fabricated using the regular self-alignment technique. The measured
Al/Nb/Al SSETs show a clear signature of resonant tunnelling of Cooper pairs combined with elastic cotunnelling of quasiparticles,
q-MQT, through the barrier of
ΔNb.
We present a detailed theoretical study of adiabatic Cooper-pair pumping in a one-dimensional array of Cooper-pair boxes and discuss its experimental feasibility. The Josephson tunneling and the gate voltage are two adiabatic couplings of our system. Using the concept of Berry phase and Abelian bosonization, we show that the evolution of the ground state follows a closed loop in the flux-voltage plane. Its adiabatic motion yields the Cooper-pair pumping in the system. We find the condition for blocking the Cooper-pair pumping even in the perfect pumping condition.
We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures ( T< or =0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e(2) approximately 26 kOmega. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.
We investigate Cooper-pair tunneling in a circuit consisting of two dc-superconducting quantum interference devices in series, with a gate capacitively coupled to the central island. Measurements cover a wide range of values of the ratio between Josephson coupling energy
EJ and charging energy
EC. The
ECEJ ratio dependence of the supercurrent is well described by the orthodox theory provided that strong fluctuations of the Josephson phase due to the electromagnetic environment are taken into account. Our data can be interpreted in terms of squeezing of the charge fluctuations with decreasing
ECEJ ratio.
The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.