Control of the supercurrent in a mesoscopic four-terminal Josephson junction

We study the control of the supercurrent in a mesoscopic four-terminal superconductor–normal-metal–superconductor (SNS) junction, in which the N region is a quantum dot connected via tunneling barriers to two superconducting electrodes and two normal electrodes, respectively. By using the nonequilibrium Green’s function method, the current flowing into the quantum dot from each electrode is derived. We find that the supercurrent between two superconducting electrodes can be suppressed and even reversed by changing the dc voltage applied across the two normal terminals, similar to recent experiments of diffusive SNS junctions and previous theories for both the ballistic and diffusive SNS junctions. Then we investigate a three-terminal SNS junction, reduced from the four-terminal junction by decoupling the dot from one normal terminal. We find that even at zero bias of the normal terminal, the supercurrent still can be controlled by changing the coupling strength between the dot and the normal terminal. In addition, both the Andreev reflection current and Andreev quasibound states depend on the phase difference of two superconductors and the coupling strength between the dot and superconducting electrodes. Finally, the behavior of the supercurrent is discussed in the limit when the normal terminals are decoupled from the system.published_or_final_versio

Breaking of phase rigidity by a time-varying field for a two-terminal modified Aharonov-Bohm ring

For a two-terminal modified Aharonov-Bohm (AB) ring with a quantum dot inserted in one arm and threaded by a magnetic flux, the phase rigidity is observed experimentally in the linear response regime, and also established theoretically. We show that this phase rigidity can be broken, even in the linear response regime, by applying a time-varying field on the dot, together with the magnetic flux through the AB ring. This provides another way of observing the continuous variation of the transmission phase through a two-terminal mesoscopic system.published_or_final_versio

Lack of quenching for the resonant transmission through an inhomogeneously oscillating quantum well

The spectral weights of the wave-function sidebands for a quantum well in the presence of an inhomogeneous electromagnetic (EM) field are studied by introducing a wave function with the form of a Floquet state and then solving the time-dependent Schrödinger equation approximately. The two cases of radiation direction of the EM field parallel and perpendicular to the well axis are considered. We find that the inhomogeneity of the EM field may eliminate the sideband quenching. Based on the spectral weight, the transmission probability through the well is investigated. The energy-level splitting for a special case, the averaged vector potential equal to zero, is also studied.published_or_final_versio

Resonant Andreev reflection in a normal-metal–quantum-dot–superconductor system

We investigate the electron tunneling through a normal-metal–quantum-dot–superconductor (N-QD-S) system where multiple discrete levels of the QD are considered. By using the nonequilibrium-Green’s-function method, the current I and the probability of the Andreev reflection TA(ω) are derived and studied in detail. In addition to the resonant behavior of the Andreev tunneling as obtained in previous works, we find that the current I versus the gate voltage vg exhibits different kinds of peaks, depending on the bias voltage, the level spacing of the QD, and the energy gap of the superconducting electrode. Besides, in I-V characteristics extra peaks superimposed on the conventional current plateaus emerge, which stem from the resonant Andreev reflections. In the case with strongly asymmetric barriers, the BCS spectral density can be obtained directly from the I-V characteristics.published_or_final_versio

A scheme to aid construction of left-hand sides of axioms in algebraic specifications for object-oriented program testing

In order to ensure reliability and quality, software systems must be tested. Testing object-oriented software is harder than testing procedure-oriented software. It involves four levels, namely the algorithmic level, class level, cluster level, and system level. We proposed a methodology TACCLE for class-and cluster- level testing. It includes an important algorithm GFT for generating fundamental equivalent pairs as class-level test cases based on axioms in a given algebraic specification for a given class. This formal methodology has many benefits. However, system analysts often find it difficult to construct axioms for algebraic specifications. In this paper, we propose a scheme to aid the construction of the left-hand sides of axioms. The scheme alleviates the difficulties of the system analysts and also helps them check the completeness, consistency, and independence of the axiom system. © 2008 IEEE.published_or_final_versionUnion Grant of Guangdong Province and National Natural Science Foundation of China (#U0775001), Guangdong Province Science Foundation (#7010116), and by a grant of the Youth Science Foundation of Jinan University (#51208035)

Photon sidebands of the ground state and the excited state of a quantum dot: A nonequilibrium Green-function approach

The electron tunneling through an ultrasmall quantum dot in the presence of time-dependent microwave (MW) fields is studied. In the investigation, two single electronic states (the ground state and the excited state) and the intradot Coulomb interaction are considered. Assuming the tunneling through the system as a coherent process, the time-dependent current and the average current are derived using the nonequilibrium Green-function method. Then we consider two special cases with ħω>Δε and ħω<Δε, respectively, where ω is the frequency of MW fields and Δε is the energy difference between two electronic states. Both the sidebands of the photon-assisted tunneling originated from the ground state, and, in particular, from the excited state are obtained, which is in good agreement with the recent experiment by Oosterkamp et al. [Phys. Rev. Lett. 78, 1536 (1997)]. Moreover, the dependence of the integrated average current on the intensity of MW fields is also discussed, and attributed to the many-body effect of the quantum dot.published_or_final_versio

Theoretical study for a quantum-dot molecule irradiated by a microwave field

Motivated by the recent experiment by Oosterkamp et al. [Nature 395, 873 (1998)] we have developed a theory to describe electron tunneling through two coupled quantum dots irradiated by a microwave field. Our results for both the weak- and strong-coupling regimes are in excellent agreement with experiment. In addition, our theory suggests several unique features in the strong-coupling regime, including Rabi oscillations, which can be verified experimentally. The main resonance and the sideband resonance of the molecular level are also calculated for the entire range of the coupling strength, and show interesting crossover behavior.published_or_final_versio

Photon-assisted Andreev tunneling through a mesoscopic hybrid system

The electron tunneling through a mesoscopic hybrid system, a normal-metal–quantum-dot–superconductor (N-QD-S) system where the intradot Coulomb interaction is neglected, in the presence of the time-varying external fields, has been investigated. By using the nonequilibrium Green-function method, the time-dependent current jL(t) and the average current 〈j(t)〉 are derived. The photon-assisted Andreev tunneling (PAAT) and the normal photon-assisted tunneling (PAT) are studied in detail. In the case of ħωΔ, various PAT processes cause a rather complicated dependence of the current on the gate voltage. In addition, the current–bias-voltage characteristics become more complicated: each Andreev reflection peak is split into side-band peaks and each current plateau is split into substep plateaus.published_or_final_versio

Theory of excess noise of a quantum dot in the presence of a microwave field

The power spectrum of excess noise of a quantum dot coupled to two leads and irradiated by a microwave field of frequency Ω is derived exactly by directly solving the Heisenberg equation. We found that for Γ<ħΩ, where Γ is the linewidth of the intradot energy level, the power spectrum can be nonzero even if the averaged current is zero. This property originates from photon-assisted tunneling and is very different from the shot noise in steady state. For Γ≫ħΩ, our results are consistent with the recent experiment by Schoelkopf et al. and previous theory.published_or_final_versio

Electron transport through a mesoscopic hybrid multiterminal resonant-tunneling system

For a mesoscopic hybrid system which contains a normal central region coupled to multiple superconducting leads, a general expression of the current is derived by using nonequilibrium-Green-function method. This current formula can be used to describe the case with time-dependent external fields applied to any parts of the system, arbitrarily finite voltages, and any kinds of interactions in the central region. For a normal two-terminal interacting electron system, this expression reduces to the general time-dependent current formula previously obtained by Wingreen et al. [Phys. Rev. B 98, 8487 (1993)]. As an application, we use this current formula to study a special case of a noninteracting single-level central region coupled to two or three superconducting leads, respectively.published_or_final_versio