The tunneling rates for spin-up and -down electrons are investigated for a GaAs quantum dot in an in-plane magnetic field by using a real-time single-electron counting scheme with a nearby charge detector. An extremely small spin-polarized current on the order of attoamperes is analyzed with the spin and energy dependences of the tunneling rates. Fully spin-polarized current is obtained when only a spin-up Zeeman sublevel is located in the transport window. When both Zeeman sublevels are allowed to contribute to the transport, we find that the tunneling rate for spin-up electrons is considerably higher than that for spin-down electrons. This partially spin-polarized current can be explained by the exchange-enhanced spin splitting in low-density regions near the tunneling barriers.

Single-electron counting is widely used to probe single electron dynamics and correlated electron transport through quantum dots. However, finite frequency bandwidth in amplifying and analyzing the detector current removes fast counting events and alters the statistics. We have developed a correction scheme to obtain the actual tunneling rates through a quantum dot, when the detector has a low pass filter with a cutoff frequency comparable to the rates. The accuracy of our scheme is confirmed by simulating the filtering effect on Poisson random switching events and by applying it to experimental data for self-checking.

The detailed characteristics of classical states in a radio-frequency superconducting quantum interference device (rf-SQUID) with well-designed energy-potential shape are investigated at 4.2 K. Using Nb/AlO x standard process which enables precise circuit-parameter implementation, the rf-SQUID is designed in its energy potential. Directions of persistent current can be distinguished in the rf-SQUID we have fabricated. Analyses in circuit simulations indicate the device design based on enough high critical current provides available parameters to construct the device for 10 mK measurement by circuit-parameter scaling. This knowledge may contribute to the precise design of the rf-SQUID for superconducting qubit through device process with lower critical current density.

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