In an extended superconductor-topological insulator-superconductor (S-TI-S) Josephson junction in a magnetic field, localized Majorana bound states (MBS) are predicted to exist at the cores of Josephson vortices where the local phase difference across the junction is an odd-multiple of $\pi$. These states contribute a supercurrent with a $4\pi$-periodic current-phase relation (CPR) that adds to the conventional $2\pi$-periodic sinusoidal CPR. In this work, we present a comprehensive experimental study of the critical current vs. applied magnetic field diffraction patterns of lateral Nb-Bi$_2$Se$_3$-Nb Josephson junctions. We compare our observations to a model of the Josephson dynamics in the S-TI-S junction system to explore what feature of MBS are, or are not, exhibited in these junctions. Consistent with the model, we find several distinct deviations from a Fraunhofer diffraction pattern that is expected for a uniform sin$({\phi})$ CPR. In particular, we observe abrupt changes in the diffraction pattern at applied magnetic fields in which the current-carrying localized MBS are expected to enter the junction, and a lifting of the odd-numbered nodes consistent with a $4\pi$-periodic sin$(\phi/2)$-component in the CPR. We also see that although the even-numbered nodes often remain fully-formed, we sometimes see deviations that are consistent with quasiparticle-induced fluctuations in the parity of the MBS pairs that encodes quantum information.

We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral $p$-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-de Gennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In particular, we predict a change in the critical current diffraction pattern in which the odd integer-flux nodes are lifted in a fermion parity-dependent fashion. We model the competing stochastic effects of thermal noise and macroscopic quantum tunneling within the RCSJ framework and show the emergence of a bimodal critical current distribution. We demonstrate that increasing the parity transition rate suppresses the bimodal nature of the distribution, thus strongly emphasizing the non-trivial parity dependent nature of the many-body ground state. Finally, we consider a trijunction geometry with three islands and discuss possible schemes to braid Majorana bound states by moving the Josephson vortices to which they are bound.

As part of the intense effort toward identifying platforms in which Majorana bound states can be realized and manipulated to perform qubit operations, we propose a topological Josephson junction architecture that achieves these capabilities and which can be experimentally implemented. The platform uses conventional superconducting electrodes deposited on a topological insulator film to form networks of proximity-coupled lateral Josephson junctions. Magnetic fields threading the network of junction barriers create Josephson vortices that host Majorana bound states localized in the junction where the local phase difference is an odd multiple of , i.e. attached to the cores of the Josephson vortices. This enables us to manipulate the Majorana states by moving the Josephson vortices, achieving functionality exclusive to these systems in contrast to others, such as those composed of topological superconductor nanowires. We describe protocols for: (1) braiding localized Majorana states by exchange, (2) controlling the separation and hence the coupling of adjacent localized Majorana states to effect non-Abelian rotations via hybridization of the Majorana modes, and (3) reading out changes in the non-local parity correlations induced by such operations. These schemes utilize current pulses and local magnetic field pulses to control the location of vortices, and measurements of the Josephson current-phase relation to reveal the presence of the Majorana bound states. Finally, we present brief discussions of readout schemes and viable experimental settings for realizing the platform. (c) 2020 Elsevier Inc. All rights reserved.

The multilevel system 55 Mn 2+ is used to generate two pseudoharmonic level systems, as representations of the same electronic sextuplet at different nuclear spin projections. The systems are coupled using a forbidden nuclear transition induced by the crystalline anisotropy. We demonstrate Rabi oscillations between the two representations in conditions similar to two coupled pseudoharmonic quantum oscillators. Rabi oscillations are performed at a detuned pumping frequency which matches the energy difference between electronuclear states of different oscillators. We measure a coupling stronger than the decoherence rate to indicate the possibility of fast information exchange between the systems.

Precise detection of spin resonance is of paramount importance to achieve coherent spin control in quantum computing. We present a novel setup for spin resonance measurements, which uses a dc-SQUID flux detector coupled to an antenna from a coplanar waveguide. The SQUID and the waveguide are fabricated from 20 nm Nb thin film, allowing high magnetic field operation with the field applied parallel to the chip. We observe a resonance signal between the first and third excited states of Gd spins S=7/2 in a CaWO_4 crystal, relevant for state control in multi-level systems.

Ion's behavior plays an important role in plasma etching processes and is determined by the local electric potential in the etched trenches. In this study, with the trench powered by a radio frequency (rf) source, the Laplace equation is solved to obtain the electric potential. The ion trajectories and the ion energy distribution (IED) at the bottom of the trench are obtained self-consistently by tracking the ions in the trench. The results show that the aspect ratio of depth- to-width of the photoresist trench and the voltage amplitude of the rf source applied to the electrode are important parameters. The larger the aspect ratio and the smaller the amplitude are, the more ions hit the sidewalls, which results in a notching phenomenon. Meanwhile, there are a higher high-energy peak and a lower low-energy peak in the IED with the increase in aspect ratio.

In order to investigate the mechanism of etching in low pressure radio-frequency (rf) plasmas, we adopt a two-dimensional Monte-Carlo (MC) cellular method to simulate the profile evolution, in which the ion reflection, the ion angular distribution (IAD) etc. are considered. It is found that the phenomenon of microtrenching results from the reflection of particles on the sidewall and the IAD is responsible for round corners at the bottom of the trench. The deeper the trench is, the more easily microtrenching or notching appear. In addition, the neutral particles can destroy the anisotropic etching of the trench and lead to bowling. On the other hand, by means of solving the Laplace equation near and in the trench with an iterative procedure, we obtain a stable or periodic stable electric field biased by a dc or rf source, in which the charging effect on the photoresist sidewall of the trench is considered. It is observed that both the dc and rf biases applied to the substrate can influence the profiles of etching, and the better etching profiles on the sidewall of the trench can be obtained with the rf bias than those with the dc bias.