Multiphoton spectroscopy of a hybrid quantum system

We report on experimental multiphoton spectroscopy of a hybrid quantum system consisting of a superconducting phase qubit coherently coupled to an intrinsic two-level system (TLS). We directly probe hybridized states of the combined qubit-TLS system in the strongly interacting regime, where both the qubit-TLS coupling and the driving cannot be considered as weak perturbations. This regime is described by a theoretical model which incorporates anharmonic corrections, multiphoton processes and decoherence. We present a detailed comparison between experiment and theory and find excellent agreement over a wide range of parameters.

Figure 1

(Color online) Sketch of the experimental setup and circuit of the phase qubit with the TLS residing inside the qubits Josephson junction.

Figure 2

(Color online) (a) Experimental and (b) theoretical spectroscopic scans as a function of flux bias and drive frequency, showing both the anticrossing due to single-photon transitions and the resonance line associated with the weaker two-photon transition. The colorscale indicates the probability to find the qubit not in the ground state. We use the same colorscale for both plots. Inset: energy-level structure of the qubit/TLS system including the hybridized states $|1\pm ⟩$, which are split by the coupling $v_{\perp }$. As well as the usual single-photon transitions (between $|0g⟩$ and $|1\pm ⟩$), a two-photon transition is allowed between the states $|1e⟩$ and $|0g⟩$.

Figure 3

(Color online) Detailed power dependence of both the single (top, solid blue) and two-photon (lower, dashed red) transitions close to resonance with the TLS (as shown in Fig. 2). The amplitudes and associated uncertainties are obtained by fitting the experimental data with Lorentzian functions. The scaling of the saturation curves is as expected for both single- and two-photon transitions, as indicated by the fitted lines (see text).

Figure 4

(Color online) At higher microwave powers and over a wider region of parameter space, processes involving higher lying states of the qubit become important. (a) Experimental and (b) theoretical spectroscopic scans as a function of flux bias, showing both the transitions to the hybridized states $|1\pm ⟩$ (as per Fig. 2) and the states $|2\pm ⟩$. The colorscale is the same for both graphs. Inset: level structure including higher lying states of the qubit including further hybridized states which can be excited via a two-photon process, as indicated.

Figure 5

(Color online) Level structure of the coupled system of qubit and TLS for ${\omega }_d\approx {ϵ}_f\approx \frac{1}{2}{ϵ}_{02}$, illustrating the high degree of symmetry. Possible microwave induced transitions at this driving frequency are indicated by arrows.

Figure 6

(Color online) Using higher frequency excitations, the hybridized states $|2\pm ⟩$ can be directly excited via a one-photon process. (a) Experimental and (b) theoretical spectra showing the clear anticrossing due to the $|0g⟩\leftrightarrow |2\pm ⟩$ transition. The colorscale is the same for both graphs. (Inset) The corresponding energy-level diagram shows this direct transition which is typically ignored within the usual simplified models of such a system.