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Kluwer Academic Publishers eBooks

Decoherence Effects in the Josephson Current of a Cooper Pair Shuttle

Alessandro Romito, Rosario Fazio

Published Mar 9, 2006• 0 citations
Publisher

Abstract

The effect of decoherence on the Josephson current between two superconductors when Cooper pair transport is achieved through the shuttle mechanism can be of great relevance. In this paper we analyze the DC Josephson current in several experimentally relevant situations. We show that decoherence effect, due to gate voltage fluctuations, can either suppress or enhance the critical current and also change its sign. The current noise spectrum displays a peak at Josephson energy and it is phase sensitive. We finally propose a device that has the shuttle properties but requires no mechanically moving part.

DOI
10.1007/1-4020-2193-3_2

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The effect of decoherence on the Josephson current between two superconductors when Cooper pair transport is achieved through the shuttle mechanism can be of great relevance. In this paper we analyze the DC Josephson current in several experimentally relevant situations. We show that decoherence effect, due to gate voltage fluctuations, can either suppress or enhance the critical current and also change its sign. The current noise spectrum displays a peak at Josephson energy and it is phase sensitive. We finally propose a device that has the shuttle properties but requires no mechanically moving part.
We discuss coherent transport of Cooper pairs through a Cooper pair shuttle. We analyze both the dc and ac Josephson effects in the two limiting cases where the charging energy EC{E}_{C}EC​ is either much larger or much smaller than the Josephson coupling EJ{E}_{J}EJ​. In the limit EJ⪡EC{E}_{J}⪡{E}_{C}EJ​⪡EC​ we present the detailed behavior of the critical current as a function of the damping rates and the dynamical phases. The ac effect in this regime is very sensitive to all dynamical scales present in the problem. The effect of fluctuations of the external periodic driving is discussed as well. In the opposite regime the system can be mapped onto the quantum kicked rotator, a classically chaotic system. We investigate the transport properties also in this regime, showing that the underlying classical chaotic dynamics emerges as an incoherent transfer of Cooper pairs through the shuttle. For an appropriate choice of the parameters the Cooper pair shuttle can exhibit the phenomenon of dynamical localization. We discuss in detail the properties of the localized regime as a function of the phase difference between the superconducting electrodes and the decoherence due to gate voltage fluctuations. Finally we point out how dynamical localization is reflected in the noise properties of the shuttle.
Transportation of Cooper pairs by a movable single Cooper-pair box placed between two remote superconductors is shown to establish coherent coupling between them. This coupling is due to entanglement of the movable box with the leads and is manifested in the suppression of quantum fluctuations of the relative phase of the order parameters of the leads. It can be probed by attaching a high resistance Josephson junction between the leads and measuring the current through this junction. The current is suppressed with increasing temperature.
We analyze how decoherence appears in the $I\text{\ensuremath{-}}V$ characteristics of a voltage-biased single-Cooper-pair transistor. Especially the effect on resonant single or several Cooper-pair tunneling is studied. We consider both a symmetric and an asymmetric transistor. As a decoherence source we use a small resistive impedance $(\text{Re}[Z(\ensuremath{\omega})]⪡{R}_{Q}=h/4{e}^{2})$ in series with the transistor, which provides both thermal and quantum fluctuations of the voltage. Additional decoherence sources are quasiparticle tunneling across the Josephson junctions and quantum fff noise caused by spurious charge fluctuators nearby the island. The analysis is based on a real-time diagrammatic technique which includes Zeno-type effects in the charge transport, where the tunneling is slowed down due to strong decoherence. As compared to the Pauli-master-equation treatment of the problem, the present results are more consistent with experiments where many of the predicted sharp resonant structures are missing or weakened due to decoherence.
The transport properties of a small superconductor--normal-metal--superconducting tunnel junction can be controlled by a gate electrode coupled capacitively to the central island. We evaluate the critical Josephson current Ic{\mathit{I}}_{\mathit{c}}Ic​ through such a system as a function of the gate voltage Vg{\mathit{V}}_{\mathit{g}}Vg​ taking into account parity effects in the superconductors. The dependence Ic{\mathit{I}}_{\mathit{c}}Ic​(Vg{\mathit{V}}_{\mathit{g}}Vg​) shows resonant singularities and has a qualitatively different character for \ensuremath{\Delta}EC{\mathit{E}}_{\mathit{C}}EC​ and \ensuremath{\Delta}>EC{\mathit{E}}_{\mathit{C}}EC​, \ensuremath{\Delta} being the superconducting gap and EC{\mathit{E}}_{\mathit{C}}EC​=e2{\mathit{e}}^{2}e2/2C being the charging energy. Due to the sweeping of the gate voltage, the system can be driven to states which are metastable with respect to a change of the number of electrons on the central island. Since the lifetime of the metastable states can be macroscopically large, one can observe a remarkable bistability of the Josephson current. A weak magnetic field suppresses the interference of the electrons propagating through the central electrode, and, consequently, the magnitude of the critical current.
Motivated by recent experiments, we analyze transport of Cooper pairs through a double-island Josephson qubit. At low bias in a certain range of gate voltages, coherent superpositions of charge states play a crucial role. Analysis of the evolution of the density matrix allows us to cover a wide range of parameters, including situations with degenerate levels, when dissipation strongly affects the coherent eigenstates. At high noise levels, the so-called Zeno effect can be observed, which slows down the transport. Our analysis explains certain features of the I-V curves, in particular, the visibility and shape of resonant peaks and lines.