Fig. 4: One and two-photon spectroscopy as a function of voltage.
From: Quantum bath engineering of a high impedance microwave mode through quasiparticle tunneling
a Reflected signal measured with an injected microwave power of −140 dBm (η ≈ 2π × 2 MHz) as a function of frequency and bias voltage. The power is sufficiently low to mostly probe the 0 → 1 transition. The vertical lines are the same as in Fig. 1. b Reflected signal in the presence of a second microwave tone tuned at the frequency measured in a. This two-photon spectroscopy probes the 1 → 2 transition, which shifts differently than the 0 → 1 transition, showing the non-linearity induced by the Lamb shift. In both cases, the dashed blue lines correspond to the prediction of an ab initio quantum model. The dashed green line in a corresponds to the classical approximation, keeping only terms of order λ2 in the expression of the frequency shift. The hatched area was not measured.
