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arXiv:cond-mat/0405320 · Physical Review E

Control of multilevel voltage states in a hysteretic superconducting-quantum-interference-device ring-resonator system

P. B. Stiffell, M. J. Everitt, Terrence D. Clark, Jason F. Ralph

Published Nov 1, 2005• 1 citation
arXivHTMLPDF

Abstract

In this paper we study numerical solutions to the quasiclassical equations of motion for a superconducting-quantum-interference device ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g., 10 state), multilevel logic and memory.

DOI
10.1103/physreve.72.056201

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In this paper we study numerical solutions to the quasiclassical equations of motion for a superconducting-quantum-interference device ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g., 10 state), multilevel logic and memory.
In this article, we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic superconducting quantum interference device (SQUID) ring, coupled to a rf tank circuit resonator, display relaxation oscillations. We demonstrate that the overall form of these characteristics, together with the relaxation oscillations, can be modeled accurately by solving the quasiclassical nonlinear equations of motion for the system. We suggest that in these very strongly hysteretic regimes, SQUID ring-resonator systems may find application in logic and memory devices.
In this paper we consider new and remarkable dynamical behavior displayed by a strongly hysteretic SQUID (Superconducting QUantum Interference device)-a single Josephson weak link enclosed by a thick superconducting ring inductively coupled to a radio frequency (rf) parallel LC tank circuit resonator. Experimentally, we show that in the strongly hysteretic regime this coupled system can display remarkable level structure in its dynamics, quite different to that normally associated with rf driven SQUID ring systems. We demonstrate theoretically that this level structure arises when the SQUID ring responds non-adiabatically to time dependent changes in its potential, i.e. so that the ring no longer stays at or very close to the minimum in this potential as it changes in time.
We consider the coupling of an electromagnetic wave to a split-ring Josephson oscillator or radio-frequency superconducting quantum interference device in the hysteretic regime. This device is similar to an atomic system in that it has a number of steady states. We show that one can switch between these with a suitable short external microwave pulse. The steady states can be characterized by their resonant lines which are of the Fano type. Using a static magnetic field, we can shift these spectral lines and lift their degeneracy.
Superconducting quantum multilevel systems coupled to resonators have recently been considered in some applications such as microwave lasing and high-fidelity quantum logical gates. In this work, using an rf-SQUID type phase qudit coupled to a microwave coplanar waveguide resonator, we study both theoretically and experimentally the energy spectrum of the system when the qudit level spacings are varied around the resonator frequency by changing the magnetic flux applied to the qudit loop. We show that the experimental result can be well described by a theoretical model that extends from the usual two-level Jaynes-Cummings system to the present four-level system. It is also shown that due to the small anharmonicity of the phase device a simplified model capturing the leading state interactions fits the experimental spectra very well. Furthermore we use the Lindblad master equation containing various relaxation and dephasing processes to calculate the level populations in the simpler qutrit-resonator system, which allows a clear understanding of the dynamics of the system under the microwave drive. Our results help to better understand and perform the experiments of coupled multilevel and resonator systems and can be applied in the case of transmon or Xmon qudits having similar anharmonicity to the present phase device.
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