Universal and measurable entanglement entropy in the spin-boson model

Abstract

We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin $E(\alpha ,\Delta ,h)$, where $\alpha$ is the dissipation strength, $\Delta$ is the tunneling amplitude between qubit states, and $h$ is the level asymmetry. For $1-\alpha \gg \Delta /{\omega }_c$ and $(\Delta ,h)\ll {\omega }_c$, we show that the Kondo energy scale $T_K$ controls the entanglement between the qubit and the bosonic environment (${\omega }_c$ is a high-energy cutoff). For $h\ll T_K$, the disentanglement proceeds as $(h/T_K{)}^2$; for $h\gg T_K$, $E$ vanishes as $(T_K/h{)}^{2-2\alpha }$, up to a logarithmic correction. For a given $h$, the maximum entanglement occurs at a value of $\alpha$ which lies in the crossover regime $h\sim T_K$. We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.

arXiv comment4 pages and 4 figures; updated version to appear in Physical Review Letters

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