Dissipative effects in Multilevel Systems

Solomon, Allan I. and Schirmer, Sonia G. (2007). Dissipative effects in Multilevel Systems. Journal of Physics: Conference Series, 87 pp. 1–11.

DOI: https://doi.org/10.1088/1742-6596/87/1/012015


Dissipation is sometimes regarded as an inevitable and regrettable presence in the real evolution of a quantum system. However, the effects may not always be malign, although often non-intuitive and may even be beneficial. In this note we we display some of these effects for N-level systems, where N = 2,3,4.

We start with an elementary introduction to dissipative effects on the Bloch Sphere, and its interior, the Bloch Ball, for a two-level system. We describe explicitly the hamiltonian evolution as well as the purely dissipative dynamics, in the latter case giving the t-> infinity limits of the motion. This discussion enables us to provide an intuitive feeling for the measures of control-reachable states. For the three-level case we discuss the impossibility of isolating a two-level (qubit) subsystem; this is a Bohm-Aharonov type consequence of dissipation.

We finally exemplify the four-level case by giving constraints on the decay of two-qubit entanglement.

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