We have developed a quantitative theory of Cooper pair pumping in gated one-dimensional arrays of Josephson junctions. The pumping accuracy is limited by quantum tunneling of Cooper pairs out of the propagating potential well and by direct supercurrent flow through the array. Both corrections decrease exponentially with the number N of junctions in the array, but give a serious limitation of accuracy for any practical array. The supercurrent at resonant gate voltages decreases with N only as $\mathrm{sin}(\ensuremath{\varphi}/N)/N,$ where $\ensuremath{\varphi}$ is the Josephson phase difference across the array.
We have experimentally demonstrated pumping of Cooper pairs in a single-island mesoscopic structure. The island was connected to leads through SQUID (superconducting quantum interference device) loops. Synchronized flux and voltage signals were applied whereby the Josephson energies of the SQUIDs and the gate charge were tuned adiabatically. From the current-voltage characteristics one can see that the pumped current increases in
1e steps which is due to quasiparticle poisoning on the measurement time scale, but we argue that the transport of charge is due to Cooper pairs.
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.
In this paper, we propose a novel kind of Josephson Energy Suppression Pump (JESP) controlled by a fully magnetic flux drive. The device presented here is composed of two superconducting loops interrupted at one side by superconducting nanowires which are joined together by a superconducting island. The phase difference developed at the edges of the nanowires by means of the magnetic flux threading the loops can collapse their Cooper condensates, leading to complete suppression of the Josephson energies. This mechanism allows to greatly reduce the leakage current when performing Cooper pair pumping by a pure magnetic pumping cycle without involving any gate modulation. The pumping capability of the JESP is studied through a master equation approach in the non-adiabatic case.
We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump---the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy pumping which results in a potential candidate for a metrological current standard. For measuring the pumped current, an additional Josephson junction is installed into the superconducting loop. We show in detail that the switching of this system from superconducting state into normal state as a consequence of an external current pulse through it may be employed to probe the pumped current. To our knowledge the experimental realization of our scheme would be the first observation of the Berry phase in superconducting circuits.