Inelastic Microwave Photon Scattering off a Quantum Impurity in a Josephson-Junction Array

Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version.

Figure 1

Diagram of the system. The dotted box surrounds the quantum impurity. See the text for further details.

Figure 2

Elastic transmission, elastic reflection, and total inelastic scattering probabilities at the Toulouse point $\alpha =1$ with left-right symmetry (hence the lead index $\ell$ was omitted) and $B_z=T=0$ (see Supplemental Material, Sec. SM.D [9]). See the text for further details.

Figure 3

The inelastic spectrum normalized by the total inelastic probability at the Toulouse point $\alpha =1$ with left-right symmetry (hence the lead indices $\ell$, ${\ell }^{\prime }$ were omitted), for $\omega /T_K=10.0$, and $B_z=T=0$. The continuous line is the exact result; see Supplemental Material, Eqs. (S43) and (S48) [9]. The dashed line corresponds to Eq. (16), valid for ${\omega }^{\prime }$, $\omega -{\omega }^{\prime }\gg T_K$. See the text for further details. The peak at ${\omega }^{\prime }\sim T_K$ sharpens, and a broad peak develops around $\omega -{\omega }^{\prime }\sim T_K$ for smaller $\alpha$; cf. Supplemental Material, Figs. S2 [9].