Exact dynamics in the inhomogeneous central-spin model

Details Exact dynamics in the inhomogeneous central-spin model Exact dynamics in the inhomogeneous central-spin model

2006-12-15

arxiv.org/abs/cond-mat/0612382v3

Phys. Rev. B 76 (2007) 014304

Physics

Condensed Matter

Statistical Mechanics

7 pages, 3 figures

Scientific paper

10.1103/PhysRevB.76.014304

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$, the oscillation frequency is proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.

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