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Josephson Junction Spectroscopy of Mesoscopic Systems

Periodic Reporting for period 4 - JSPEC (Josephson Junction Spectroscopy of Mesoscopic Systems)

Reporting period: 2019-10-01 to 2020-03-31

Mesoscopic physics offers an opportunity to study quantum mechanics in a controlled setting. At the atomic scale, systems cannot be easily engineered, whereas mesoscopic systems--such as graphene devices, single-molecule magnets, nanowire or carbon nanotube quantum dots, and superconducting weak links--can be fabricated to have well-defined quantum states upon cooling to sub-Kelvin temperatures. Despite a wide range of relevant transition energies in mesoscopic systems, the experimentalist is often restricted to probing them at frequencies below 20 GHz. At higher frequencies, it becomes exceedingly difficult and costly to propagate and detect microwaves in a cryostat. From the far infrared down to the sub-THz range, free space coupling is difficult because of the mismatch between photon wavelength and the size of single nano- or micro-structures. An alternative strategy is needed to characterize the high-frequency electronic properties of such structures.

This project will develop an on-chip Josephson-junction (JJ) based spectrometer which allows investigation of the electronic properties of mesoscopic systems between 2 GHz and 2 THz. Not only does the technique provide access to a frequency range outside the reach of conventional microwave and optical methods, but the spectrometer is expected to have a narrow emission linewidth comparable to that of the best sources, a high sensitivity comparable to that of the best detectors, and the ability to couple on-chip to mesoscopic systems uniformly over the entire bandwidth. The large bandwidth and on-chip coupling allows following transitions tuned by an external parameter, such as the electric field in graphene or the magnetic flux in superconducting circuits.

This spectrometer will address several outstanding questions on the nature of elementary excitations in different mesoscopic systems. The experiments proposed are a direct measurement of the hybridization of Andreev states in closely spaced superconducting weak links; spectroscopy of diabolic points in topologically non-trivial superconducting circuits; and spectroscopy of zero-crossing Andreev states (Weyl nodes) in multijunction weak links. These experiments will further our understanding of mesoscopic superconductivity, elucidating the link between physical parameters of a superconducting circuit and topological features in its energy spectrum.

Such advances in understanding could lead to device applications in electronics, specifically metrology (quantized current sources, improvements in Josephson junction based voltage standards) and quantum computing (topological quantum bits and gates). These advances are important for a society in which technology plays a more and more important role. Progress in metrology will lead to better detectors, clocks, digitizers, sources, and diverse other components which will find applications in equipment from phones to satellites. Progress in quantum information will lead to computers which can solve certain problems, such as predicting protein-folding or simulating chemical reactions, which are not tractable for classical computers.
"We have succeeded in designing, developing, fabricating, measuring, testing, and utilizing the Josephson spectrometer. We implemented a novel circuit using a SQUID operated at half-flux bias and increased sensitivity by careful engineering the electromagnetic environment and using a current amplifier based measurement scheme. We evaluated the detection sensitivity by measuring background current signal. We succesfully coupled to a test RF-SQUID on-chip as well as off-chip with a ""flip-chip"" technique. We also developed a novel, low-noise voltage biasing scheme to reduce the Josephson oscillation linewidth.

We proposed the Andreev molecule as an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction’s ""atomic"" orbitals, Andreev Bound States. We showed that non-local quantum effects arise due to this hybridization, including the appearance of gaps in the energy spectrum. The Andreev molecule is a prime candidate system to measure with the Josephson spectrometer. We have published two theoretical papers, one in Nano Letters which already has five citations and another in SciPost Physics Core. Several researchers have already published follow-up papers.

On the experiment side, we have designed a circuit to validate our theory of the Andreev molecule and fabricated three-terminal superconductor/semiconductor nanowire Andreev molecules. We have developed a novel highly sensitive switching current measurement scheme using cryogenic HEMT amplifiers and measured devices showing promising signatures of Andreev state hybridization. Future directions are an experimental validation of the Andreev molecule with Josephson spectroscopy, the development of novel devices such as magnetometers, and simulating many-body Hamiltonians with Andreev polymers.

Concerning topological systems, we have developed a novel understanding of the role of topology in systems with multiple Josephson tunnel junctions. It is now clear to us how physical parameters in the Hamiltonian describing such multi-junction circuits can give rise to topological invariants. Topologically non-trivial Josephson junction circuits give rise to quantization of charge, flux, and resistance. We have shown how to complete the metrological triangle with only Josephson junctions and numerically validated our proposed circuit.

We have identified a circuit based on epitaxial semiconductor/superconductor InAs/Al nanowires which should harbor Majorana zero modes with the right combination of electric field, magnetic field, and spin-orbit coupling."
Various applications of the superconducting circuits developed for the spectrometer include a Josephson vector network analyzer, a cryogenic mixer, a THz camera, a detector for radioastronomy, and a scanning microwave impedance microscope. In itself the proposed Josephson junction spectrometer is a general purpose tool that will benefit researchers studying mesoscopic systems. Ultimately, Josephson junction spectroscopy should not only be useful to detect existing elementary excitations but also to discover new ones.

Beyond high-frequency spectroscopy of mesoscopic systems, there are numerous potential applications of these Josephson junction circuits:
* Cryogenic mixers or other components to facilitate the scaling and integration of superconducting circuit based quantum computers.
* Sources and detectors for the terahertz range, useful for communication, science, manufacturing, and medicine.
* Combining an array of terahertz detectors a highly-sensitive camera could be developed, with applications for security imaging and sensing.
* Coherent detectors of radiation from outer space, a tool for studies of the cosmic microwave background, the composition of the early universe, or other cosmological phenomenon.
* Scanning microwave impedance microscopy
* Topologically protected superconducting quantum bits.
* Improvements to Josephson voltage standards for metrology.
* Improvements to current standards for metrology.
Spectrometer data 2
Spectrometer data 1
Josephson spectrometer coupled to SQUID, optical image
Josephson Spectrometer, optical image
Josephson spectrometer, small loop, optical image