M.T. Bell et al., Quantum Superinductor with Tunable Non-Linearity, Phys. Rev. Lett. 109, (2012). Many Josephson circuits intended for quantum computing would benefit from the realization of a “superinductor”: a decoherence-free element whose impedance exceeding the resistance quantum R Q =h/(2e) 2 at microwave frequencies. We have implemented the superinductor as a specially designed one-dimensional “ladder” of nanoscale Josephson junctions. The inductance of this micron-scale circuit, tunable by the magnetic field, can be as large as the inductance of a several- meters-long wire! The magnitude of the inductance and its non-linearity can be easily tuned by a weak magnetic field. These properties open new possibilities for the development of fault tolerant superconducting qubits and controllable coupling between qubits. Micrograph of the Josephson ladder: a chain of asymmetric dc-SQUID-like cells with several large Josephson junctions (JJs) in one branch shunted by a single small JJ in the other branch. Josephson junctions are formed at the intersections of sub-micron aluminum strips. t Rabi ~ 2.5 μs The Josephson ladder, being connected to a capacitor, operates as a qubit with a relatively long coherence time (> 2  s). The plot shows Rabi oscillations in a superinductor-based qubit. 1 Quantum Superinductors Michael Gershenson, Rutgers University New Brunswick, DMR

The impact of superinductors spreads well beyond the field of quantum computing. Due to the magnetic- field-tunable criticality, the Josephson ladders have potential to become a unique experimental platform for the study of the quantum phase transitions in one dimension (1D). The low-energy physics of the ladders can be mapped on the  4 model, which is relevant to a wide spectrum of physical phenomena, from quark confinement to ferromagnetism. Near the critical point this model shares many common features with the integrable model of a 1D Ising spin chain in the transverse magnetic field, which serves as a paradigm in the context of nonequilibrium thermodynamics and quantum critical phenomena. Our recent experiments show that the spectrum of low-energy excitations in these systems is consistent with the predictions for the Ising quantum critical model in which the excitations are described by emergent Majorana fermions. 2 Quantum Superinductors Michael Gershenson, Rutgers University New Brunswick, DMR

Broad Impact. The ideas generated in the course of this research will have a predictive power across a broad spectrum of fields, including physics and engineering. Within the physics sub-fields, our results advance the understanding of quantum phase transitions and decoherence in large closed quantum systems. The research is relevant to the nascent field of quantum computing that can be viewed as a battle field between the quantum behavior and emergent classicality. Development of fault-tolerant qubits is crucial for the practical implementation of quantum logical circuitry and, more generally, for the realization of novel ideas that will allow Nanoelectronics to maintain its progress beyond the era of Silicon Nanotechnology. The interdisciplinary science and technological components of this research project provide excellent educational opportunities for two graduate students, two undergrads, and one post-doc involved in this research. The multi-component Educational and Outreach Program, an essential part of the project, is designed to nurture an appreciation for nanoscience, and develop innovative curricula with a view of creating a more scientifically literate general public. The PI is a member of the team of Rutgers instructors working on transformative changes in large introductory science courses. The goal is to replace the traditional (passive) format of large lecture courses with the evidence-based teaching methods and interactive and collaborative formats that would promote the interactive learning environment and lead to better learning outcomes. 3 Quantum Superinductors Michael Gershenson, Rutgers University New Brunswick, DMR