J. Diggins

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.

Limits to the observation of coherent oscillations in a SQUID ring

Using the quantum mechanical, lumped component model of a SQUID ring we compute the onset of tunnelling and macroscopic superposition behaviour in the parameter space of the ring. In addition, we make a quantitative estimate of the stability required in the environmental flux to sustain a superposition state. Both these features are of crucial importance to the realisation of experiments aimed at revealing such behaviour.

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.

Macroscopic quantum phenomena: Study of the flux and charge uncertainties of a superconducting weak link ring in the flux mode regime

Abstract We propose a new method to manipulate the Schrodinger equation governing a superconducting weak link ring (SQUID) operating in the flux mode limit. We show how this method can be used to treat other equations, provided they still contain a quadratic part. Graphical results are presented for the energy levels and flux and charge uncertainties in the ring.

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.

The energy band structure of ultra small capacitance weak links — QED in condensed matter circuits

Abstract We consider various superconducting weak link circuits in which quantum effects dominate. We show that in this quantum regime these circuits take on a quantum electrodynamic description, at least as far as the electromagnetic field contribution is concerned.

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.

Flux and voltage periodic behaviour in a superconducting weak-link ring

Starting with a simple Lagrangian for the electromagnetic field with broken gauge symmetry, we derive an effective circuit Hamiltonian for a superconducting weak-link ring. The energy eigenstates of this Hamiltonian exhibit sensitivity to both external magnetic flux and an applied Faraday law voltage. We show that the flux periodicity of the rf SQUID ring, and the voltage periodic behaviour found in ultra-small-capacitance weak-link rings, can be seen as limiting cases of a more general phenomenon.

Capacitance in a radio-frequency-SQUID magnetometer

We use a discrete-field model for the quantum evolution of distributed superconducting circuits to calculate the effective capacitance for a radio-frequency-SQUID magnetometer: a large-capacitance superconducting ring containing an ultra-small-capacitance weak link. We demonstrate that the self-capacitance of the weak link can dominate the behaviour of the circuit.