R. Whiteman

Reactive probing of macroscopically quantum mechanical SQUID rings

Abstract In this paper we demonstrate that the energy level structure of ultra small capacitance SQUID rings can be probed adiabatically at radio frequency using both dynamical and quasistatic reactive techniques.

Solutions of the time dependent Schrödinger equation for a SQUID ring

In this paper we consider a quantum mechanical model for a SQUID ring subjected to a classical harmonic time varying perturbation. We describe a computational scheme for solving the time dependent Schrodinger equation for this system using a time dependent basis. We demonstrate that over a range of perturbation amplitudes and frequencies the time dependent wavefunction can be calculated accurately using 2, 3 or 4 basis states in the expansion. We calculate the time average of the expectation value of the energy as a function of quasi-static applied magnetic flux and show from these calculations that the system appears to be able to make transitions between states at specific values of this bias flux, even when the microwave frequency is well off resonance.

Opposed (hammerhead) Bifurcations in the Resonant Lineshape of a Strongly Driven SQUID Ring - Tank Circuit System

In this paper we describe very unusual paired bifurcations which can appear in the resonance curve of a coupled SQUID ring-radio frequency (rf) tank circuit system when the rf flux at the ring is comparable to Fo (= h/2e). We demonstrate that the position of these bistabilities is controlled by the static magnetic flux Fxstat applied to the ring, with simple bistable regions being observed on the lower or upper side of the resonance when (for n integer) Fxstat is close to nFo or (n + 1/2) Fo, respectively. More interestingly, we show that for values of Fx close to (n ± 1/4) Fo this resonance exhibits bistability on both its lower and upper sides. We discuss this very unusual phenomenon in terms of the non-linear equation of motion for the coupled system.

Observation of Quantum Jumps in Squid Rings

In this paper we describe an experimental technique which we have used to probe the low lying energy levels of a quantum mechanical SQUID ring and to observe transitions between these levels.

Microwave-induced quantum transitions in a superconducting quantum interference device

In this paper we consider the interaction of a quantum-mechanical superconducting quantum interference device (SQUID) with a classical monochromatic electromagnetic (EM) field. We solve the time-dependent Schrodinger equation for the SQUID ring in this EM field. We demonstrate that non-perturbative transitions between the low-lying states of the ring, due to coherent multiphoton absorption processes, dominate, even when the single-photon energy is small compared with the energy separation between these states. We present experimental data on small-capacitance SQUID rings, interacting with microwave fields, which point to the existence of such non-perturbative transitions.

Giant relaxation oscillations in a very strongly hysteretic superconductive quantum interference device ring-tank circuit system

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.

Adiabatic modulation of a superconducting quantum interference device (SQUID) ring by an electromagnetic field

In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrodinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.

Bistability in the frequency response of a driven SQUID ring-radio frequency resonator system

Abstract We discuss the experimental observation of the frequency response of a parallel LC tank circuit inductively coupled to a SQUID ring. We show that when the rms rf flux that couples to the ring is a significant fraction of the superconducting flux quantum, Φ o (= h 2e ) , the resonance exhibits a cyclic fold bistability.

Pinch resonances in a radio-frequency-driven superconducting-quantum-interference-device ring-resonator system

In this paper we present experimental data on the frequency domain response of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency (rf) tank circuit resonator. We show that with the ring weakly hysteretic the resonance lineshape of this coupled system can display opposed fold bifurcations that appear to touch (pinch off). We demonstrate that for appropriate circuit parameters these pinch off lineshapes exist as solutions of the non-linear equations of motion for the system.

SQUID rings as macroscopic quantum objects: The quantum‐classical interface

We consider the interaction of a SQUID ring in the ultra small capacitance quantum limit. We show that the energy level structure of such a SQUID ring, arising from its quantum mechanical behaviour, leads to a novel spectroscopy. We give examples of the way in which this spectroscopy is made manifest through the interation of SQUID ring with a classical circuit apparatus. (AIP)