Kondo Resonance of a Microwave Photon

We emulate renormalization group models, such as the Spin-Boson Hamiltonian or the anisotropic Kondo model, from a quantum optics perspective by considering a superconducting device. The infra-red confinement involves photon excitations of two tunable transmission lines entangled to an artificial spin-1/2 particle or double-island charge qubit. Focusing on the propagation of microwave light, in the underdamped regime of the Spin-Boson model, we identify a many-body resonance where a photon is absorbed at the renormalized qubit frequency and reemitted forward in an elastic manner. We also show that asymptotic freedom of microwave light is reached by increasing the input signal amplitude at low temperatures which allows the disappearance of the transmission peak.Comment: Final Version: Main text and Supplementary Materia

Universal and measurable entanglement entropy in the spin-boson model

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.Comment: 4 pages and 4 figures; updated version to appear in Physical Review Letter