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Topics in the theory of excitations in granular matter

Rakesh P. Tiwari

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

We use theoretical methods to study properties of excitations in various granular materials.We begin with three topics involving superconducting qubits.First, a three Josephson-junction persistent-current qubit is considered, with two junctions being identical, and the third junction differing from the other two by a factor of α in Josephson energy and capacitance.We show that when α > 1 and the bias voltages [6] Rakesh P Tiwari and Alok Shukla, "A basis set based Fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps", Comp.Phys.Commun.

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arXiv:2405.19658•Materials for Quantum Technology•Dec 1, 2024•2 citations
We use theoretical methods to study properties of excitations in various granular materials.We begin with three topics involving superconducting qubits.First, a three Josephson-junction persistent-current qubit is considered, with two junctions being identical, and the third junction differing from the other two by a factor of α in Josephson energy and capacitance.We show that when α > 1 and the bias voltages [6] Rakesh P Tiwari and Alok Shukla, "A basis set based Fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps", Comp.Phys.Commun.
The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit.
Abstract Josephson junctions supply the nonlinear inductance element in superconducting qubits. In the widely used transmon configuration, where the junction is shunted by a large capacitor, the low charging energy minimizes the sensitivity of the qubit to charge noise while maintaining the necessary anharmonicity to qubit states. We report here low-frequency transport measurements on small standalone junctions and identically fabricated capacitively-shunted junctions that show two distinct features normally attributed to small capacitance junctions near zero bias: reduced switching currents and prominent finite resistance associated with phase diffusion in the current–voltage characteristic. Our transport data reveals the existence of phase fluctuations in transmons arising from intrinsic junction capacitance.