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Journal of Physics Condensed Matter

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

R. Whiteman, Volker Schöllmann, M. J. Everitt, Terrence D. Clark, Robert J. Prance, Helen Prance, J. Diggins, G. Buckling, Jason F. Ralph

Published Nov 9, 1998• 6 citations
Publisher

Abstract

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 Schrödinger 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.

DOI
10.1088/0953-8984/10/44/004

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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 Schrödinger 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.
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.
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 Schrödinger 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.
The recovery of classical nonlinear and chaotic dynamics from quantum systems has long been a subject of interest.Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing.In this paper, we discuss the quantum to classical crossover of a superconducting quantum interference device (SQUID) ring.Such devices comprise a thick superconducting loop enclosing a Josephson weak link and are currently strong candidates for many applications in quantum technologies.The weak link brings with it a nonlinearity such that semiclassical models of this system can exhibit nonlinear and chaotic dynamics.For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics.Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear dynamics.
The recovery of classical chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper we discuss the quantum to classical crossover of a superconducting quantum inference device (SQUID) ring. Such devices comprise of thick superconducting loop enclosing a Josephson weak link. These devices are currently strong candidates for many applications in quantum technologies. The weak link brings with it a non-linearity such that semi-classical models of this system can exhibit chaotic dynamics. For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics. Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical chaotic dynamics.
This paper considers the behavior of a model persistent current qubit in the presence of a time-dependent electromagnetic field. A semi-classical approximation for the electromagnetic field is used to solve the time- dependent Schrodinger equation (TDSE) for the qubit, which is treated as a macroscopic quantum object. The qubit is describe3d by a Hamiltonian involving the enclosed magnetic flux (Phi) and the electric displacement flux Q, which obey the quantum mechanical commutation relation. The paper includes a brief summary of recent work on quantum mechanical coherence in persistent current circuits, and the solution of the TDSE in superconducting rings. Of particular interest is the emergence of strongly non-perturbative behavior that corresponds to transitions between the energy levels of the qubit. These transitions are due to the strong coupling between the electromagnetic fields and the superconducting condensate and can appear at frequencies predicted by conventional methods based on perturbations around the energy eigenstate of the time-independent system. The relevance of these non-perturbative processes to the operation of quantum logic gates based on superconducting circuits and the effect of the resultant non linearities on the environmental degrees of freedom coupled to the qubit are considered.
We present solutions of the time dependent Schrodinger equation for a SQUID ring coupled to an electromagnetic field, both treated quantum mechanically. We that show the SQUID ring can be used to create a maximally entangled state with the em field that without dissipation remains constant in time. Using methods familiar in quantum optics, we extend the model to include the effects of coupling this system to a dissipative environment. With this model we show that although such an environment makes a noticeable difference to the time evolution of the system, it need not destroy the the entanglement of this coupled system over time scales required for quantum technologies.