Spin-Orbit Splitting of Andreev States Revealed by Microwave Spectroscopy

Atomic spectra contain fine structure—split spectral lines that arise from the coupling of the spin of the electron with its orbital motion around the nucleus. Here, we show analogous fine structure in the quantized excitation spectrum of a superconducting electrical circuit that includes a semiconducting nanowire with strong spin-orbit coupling. Remarkably, the spin state of a single electron in the nanowire has a measurable impact on the electrical properties of the circuit, which contains over a trillion electrons.

The circuit consists of a submicron indium arsenide (InAs) nanowire enclosed by a superconducting aluminum loop. Discrete localized states, known as “Andreev bound states,” form in the nanowire as a result of coupling to the superconductor. When absorption of a photon induces a transition between two of these states, the loop inductance changes. We measure the absorption spectrum of the circuit by monitoring the resulting frequency shift of a microwave resonator inductively coupled to the loop. The spectrum shows a fine structure of spin-split Andreev states, well accounted for by a simple model with spin-orbit coupling as the key ingredient.

In the longer term, the challenge will be to manipulate an individual spin in a superconductor—the spin of a single quasiparticle that is physically located at the same place as the many electrons forming the superconducting ground state. Here, we have done the first step: showing that there are spin-resolved states.

L. Tosi, C. Metzger, M. F. Goffman, C. Urbina, H. Pothier, Sunghun Park, A. Levy Yeyati, J. Nygård, and P. Krogstrup
Phys. Rev. X 9, 011010 (2019) (arxiv here)

Some other recent works from this team:
– Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy.
S. Probst, V. Ranjan, Q. Ansel, R. Heeres, B. Albanese, E. Albertinale, D. Vion, D. Esteve, S. J. Glaser, D. Sugny, and P. Bertet.
Journal of Magnetic Resonance 303, p. 42-47 (2019), (arxiv here)
– Ultrahigh-quality-factor superconducting microwave resonator on diamond for quantum information processing.
M. Lee.
Jpn. J. Appl. Phys. 58 100914 (2019),

Effect of an in-plane magnetic field on the ABS excitation spectrum around δ=0. The Andreev states correspond to the same gate voltage as in Fig. 5. Field is applied parallel [(a),(c)] or perpendicular [(b),(d)] to the wire. Green lines are the result from the theory using g=12 and g=8 (see text).