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arXiv:0706.1549 · Physical Review B

Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

A. J. Skinner, B. L. Hu

Published Jul 24, 2008• 3 citations
arXivHTMLPDF

Abstract

We develop a ``chain-boson model'' master equation, within the Born-Markov approximation, for a few superconducting quantum interference devices (SQUIDs) coupled into a chain and exchanging their angular momenta with a low-temperature phonon bath. Our master equation has four generators; we concentrate on the damping and diffusion and use them to study the relaxation and decoherence of a Heisenberg SQUID chain whose spectrum exhibits critical-point energy-level crossings, entangled states, and pairs of resonant transitions. We note that at an energy-level crossing, the relevant bath wavelengths are so long that even well-spaced large SQUIDs can partially exhibit collective coupling to the bath, dramatically reducing certain relaxation and decoherence rates. Also, transitions into entangled states can occur even in the case of an independent coupling of each SQUID to the bath. Finally, the pairs of resonant transitions can cause decaying oscillations to emerge in a lower-energy subspace.

DOI
10.1103/physrevb.78.014302

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In this paper we consider the modeling and simulation of open quantum systems from a device engineering perspective. We derive master equations at different levels of approximation for a superconducting quantum interference device (SQUID) ring coupled to an ohmic bath. We demonstrate that the master equations we consider produce decoherences that are qualitatively and quantitatively dependent on both the level of approximation and the ring's external flux bias. We discuss the issues raised when seeking to obtain Lindbladian dissipation and show, in this case, that the external flux (which may be considered to be a control variable in some applications) is not confined to the Hamiltonian, as often assumed in quantum control, but also appears in the Lindblad terms.
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