Associate Professor Quantum-Phase Electronic Centre, The University of Tokyo

The phase of a wave function is the most fundamental concept of quantum mechanics. Among a variety of interference phenomena that can reveal this quantum phase, a two-path interference is the simplest. Consequently, the Aharonot-Bohm (AB) interferometer, which is usually considered as a towpath interferometer, has been the most popular playground for physicists. In the AB interferometer, the relative transmission phase between the two paths can be controlled by external magnetic field B. This phase difference causes an oscillation of the current as a function of B. It turned out, however, that the two-terminal linear conductance through an AB ring suffers from the so-called phase rigidity.

Onsager’s law for linear conductance, G(B)=G(-B), implies that the phase of the AB oscillation can only take the values 0 or π at B = 0. To satisfy this boundary condition, contribution from paths of an electron encircling the AB ring multiple times needs to be added. What is usually observed in an AB experiment is therefore not an ideal two-path interference. Using multi-terminal as well as multi-channel AB interferometers, numerous attempts have been made to measure and control the phase shift of an electron wave, however, no reliable phase measurement had been realized.

In this work, we showed that a pure two-path interference is realized by combining the AB ring with parallel tunnel-coupled quantum wires that allow tunnelling of an electron between the two paths.

Adjusting the tunnel coupling energy, we can monitor and suppress the contribution of encircling paths while keeping the large AB oscillation amplitude. This solid-state analogue of the double-slit experiment allows for measurement and control of the true transmission phase shift of an electron.

We applied this phase measurement technique to investigate the scattering of an electron wave by an artificial atom. We embedded a quantum dot into one of the two paths of the interferometer to measure the scattering phase through an artificial atom. In addition to the Friedel sum rule, which connects the number of electrons in the quantum dot to the scattering phase, we have revealed influences of the parity of orbital wave function and the interaction between a local spin confined in the quantum dot and conducting electrons in the reservoirs, i.e., the Kondo effect. In particular, we observed π/2 phase shift in the Kondo regime as the hallmark of the Kondo effect, interpreted as the fingerprint of local moment screening.

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