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arXiv:cond-mat/0609657 · Physical Review B

Transport properties of a periodically driven superconducting single-electron transistor

Alessandro Romito, Simone Montangero, Rosario Fazio

Published May 25, 2007• 0 citations
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Abstract

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 ${E}_{C}$ is either much larger or much smaller than the Josephson coupling ${E}_{J}$. In the limit ${E}_{J}⪡{E}_{C}$ 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.

DOI
10.1103/physrevb.75.184528

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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.
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 analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even-odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasiparticle tunneling rates are comparable to the coherent Cooper pair oscillation frequency. Furthermore, the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.
The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooperpair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a currentbiased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor.
We investigate a superconducting single-electron transistor capacitively coupled to a nanomechanical oscillator and focus on the double Josephson quasiparticle resonance. The existence of two coherent Cooper-pair tunneling events is shown to lead to pronounced back action effects. Measuring the current and the shot noise provides a direct way of gaining information on the state of the oscillator. In addition to an analytical discussion of the linear-response regime, we discuss and compare results of higher-order approximation schemes and a fully numerical solution. We find that cooling of the mechanical resonator is possible and that there are driven and bistable oscillator states at low couplings. Finally, we also discuss the frequency dependence of the charge noise and the current noise of the superconducting single electron transistor.