Report
Teaser, summary, work performed and final results
Periodic Reporting for period 1 - MASSS (Manipulation of a Single Spin in a Superconductor)
Teaser
Controlling and manipulating the quantum state of individual quantum systems is presently an extremely active and fertile field in atomic and condensed matter physics, with a profound impact on our understanding of the laws of quantum physics and with applications in many...
Summary
Controlling and manipulating the quantum state of individual quantum systems is presently an extremely active and fertile field in atomic and condensed matter physics, with a profound impact on our understanding of the laws of quantum physics and with applications in many fields ranging from metrology to quantum information. The MASSS project’s goal was to achieve the coherent manipulation of a single electronic spin within a superconducting device.
I based my strategy on the combination of two basic condensed matter physics phenomena. On the one hand, the trapping of an electron in one of the discrete localized states -called Andreev states- that form at a weak-link between two superconductors. On the other hand, the coupling of the electron spin degree of freedom to its trajectory in space- called spin-orbit coupling-, which is particularly strong in some semiconducting materials. This combination was therefore expected to lead, even in absence of a magnetic field, to spin-split Andreev states for an electron trapped in a semiconducting weak link, the fundamental required ingredient for the spin manipulation.
The project was successful on all its aspects. The original results of the experiments that I carried out were recently published in Phys. Rev. X 9 011010 (2019), and constitute an important step in the field of superconducting spintronics. Moreover, this Marie Skłodowska-Curie fellowship allowed me to build strong collaborations with several groups in Europe and to interact with many of the field leading scientists during international conferences and visits. Finally, it has provided me with the necessary tools to start a career as an independent researcher.
Work performed
I started my project by the fabrication of weak-links tailored in semiconducting InAs nanowires with strong spin-orbit coupling. Thanks to a collaboration we established with P. Krogstrup of the University of Copenhagen, we benefited from high-quality nanowires covered by a thin layer of Al that induces superconductivity in the semiconductor. As shown in the upper-right panel of the Figure, the weak link (green in the figure) is fabricated by removing the Al shell (grey) over a submicron segment of the wire. We developed a robust process for the reproducible fabrication of samples, which also include a metallic lateral gate electrode used to tune electrostatically the electron density at the weak link.
We then designed an experiment to perform the spectroscopy of the Andreev states and the quantum manipulation of single spins trapped in them. As shown in the left panel of the Figure, the submicron indium arsenide (InAs) weakling is included in a superconducting aluminum loop. The magnetic flux threading the loop allows to tune the energy of the Andreev states. The gate is also used as an antenna to inject a microwave excitation that induces transitions between the Andreev states if the energy of the photons match the energy difference between them. The key point is that such a single spin transition results in a measurable change of the loop inductance. We obtained the absorption spectrum of the circuit (see lower-right panel) by monitoring the resulting frequency shift of a microwave resonator inductively coupled to the loop.
The measured absorption spectrum of Andreev states is very rich. In collaboration with the theory group of A. Levy Yeyati in Madrid, we developed a model that explains well the main features of the spectrum. The model allows to calculate the spectrum of Andreev states as a function of the flux through the loop, taking into account the geometrical characteristics of the device and the spin-orbit coupling in the semiconductor. An example with two spin-split Andreev states in the weak link is shown in the bottom part of the left panel. There are four possible transitions between them (only one is sketched in the Figure). They correspond to the peculiar bundle of four lines observed in the experiment (highlighted in green in lower-right panel).
Caption of Figure: (upper-right panel) Electron microscope image of a 400nm weak link (green) tailored in an InAs-Al (core-full shell) nanowire. A metallic gate electrode (in yellow) is used to control the electronic density of the nanowire. (left panel) The weak-link is enclosed in a superconducting loop (in grey) and microwave photons (in red) are injected through the gate to drive transitions between Andreev states. The bottom part shows the calculated energy of two discrete Andreev states as a function of the magnetic flux threading the loop. Each of the Andreev states is spin-split due to the strong spin-orbit coupling in the semiconducting material. (lower-right panel) Measured microwave absorption spectrum as a function of the flux and the frequency of the excitation. The grey-scale corresponds to the measured shift of the resonant frequency of a microwave resonator coupled to the loop (not shown). The bundle of four lines highlighted in green corresponds to the four possible transitions between the spin-split Andreev states shown in the left panel.
Final results
The bundle of four lines observed in the experiment is the equivalent of the fine structure observed in the spectral lines of atoms, a fundamental quantum phenomenon resulting from the coupling of the spin of the electron with its orbital motion around the nucleus. This is the first time that such a fine structure is observed in a quantum circuit. It demonstrates that the spin of a single electron can rule the macroscopic behavior of a circuit. We also performed some preliminary experiments on the coherent manipulation of these spin dependent two-level systems, but the coherence times turned out to be too short to draw robust conclusions. Work in this direction is underway.
In conclusion, even if some work is still necessary to fully reach all the goals of the project, the demonstration of spin-split Andreev states is a proof of the validity of the chosen strategy and of the success of my MSCA project. This discovery was published in Phys. Rev. X 9 011010 (2019), and was highlighted by the editors of the American Physical Society with a synopsis in Physics.