Universal and measurable entanglement entropy in the spin-boson model

TL;DR

This paper derives a universal, measurable formula for entanglement entropy in the spin-boson model, linking it to the Kondo energy scale and enabling potential experimental measurement in charge qubits.

Contribution

It provides an explicit, universal expression for entanglement entropy in the spin-boson model, connecting it to the Kondo scale and suggesting experimental measurement methods.

Findings

Entanglement entropy depends on dissipation strength, tunneling amplitude, and level asymmetry.

Maximum entanglement occurs near the crossover regime where level asymmetry matches the Kondo scale.

Entanglement vanishes in the limits of large level asymmetry, following specific power laws.

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.