Charge Qubit Coupled to an Intense Microwave Electromagnetic Field in a Superconducting Nb Device: Evidence for Photon-Assisted Quasiparticle Tunneling

We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths, exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-Stückelberg interference structure of a longitudinally driven two-level system. For even stronger drives, we observe a significant change in the Landau-Zener-Stückelberg pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of quasiparticle poisoning, and leads to an enhanced interferometric response. The interference pattern becomes robust to quasiparticle poisoning and has a good potential for accurate charge sensing.

Figure 1

Optical image and scanning electron micrograph of the sample. Bottom right: Colored close-up of a segment of the resonator (red, central area) and nearby vortex-free ground plane (blue, peripheral areas). Top right: Circuit representation of the sample.

Figure 2

(a) Measured frequency shift of the microwave cavity as a function of gate charge and microwave amplitude. The frequency shift indicates the time-averaged projections of the qubit state onto ${\sigma }_z$; $T=20\mathrm{mK}$. (b) Numerical simulation. (c) Simplified quasiclassical energy diagram in the charge basis illustrating the process of restoring the parity of the box. (d) Cross section of the raw data (blue thin line), sampled at a rate of 50 kHz and averaged 8 times over a total time of 2.2 s per gate trace, and simulation (red thick line) taken at the thick green line indicated in (a). For the best fit, a longitudinal Gaussian convolution with the width ${\sigma }_n=0.0052e$ is applied to the theoretical result, consistent with slow fluctuations of nearby charges at the given measurement time scale. Dashed lines show the center of the seventh and sixth photon resonances. In our sample, we extract $C_G/C_J=1/15$, $C_J=0.741\mathrm{fF}$, ${\omega }_0/2\pi =6.94\mathrm{GHz}$, $E_J=4.82\mathrm{GHz}$, and $E_C=24.4\mathrm{GHz}$. The near-critically coupled cavity is excited with a microwave power of $-90$ to $-100\mathrm{dBm}$. To fit the experimental data, we use an effective charge fluctuator and quasiparticle temperature $T_{\mathrm{CF}}=100\mathrm{mK}$ and $T_{\mathrm{qp}}=200\mathrm{mK}$, a high frequency Ohmic coupling constant [30] $\alpha =1.2\times {10}^{-4}$, quasiparticle tunneling asymmetry ${\Gamma }_{\mathrm{odd}}={10}^7\Theta (E_i-E_f)\mathrm{Hz}$, and $G=0.1$.

Figure 3

(a) Calculated frequency shift as a function of photon number and charge offset for the coupled cavity CPB for two values of the superconducting gap $\Delta$. (b) Calculated transition rate between dressed states of the two subspaces as a function of the number of dissipated photons evaluated for $A_{ng}=0.9$ and $m=4$. The two directions (note the different scaling) are shifted by one photon due to small charging energy differences. (c) Energy-level representation for the photon-assisted relaxation via the quasiparticle subspace that results in population inversion (when ${\gamma }_2^{\mathrm{qp}}>{\Gamma }_2^{\mathrm{qp}}$) and fast recovery of the even parity.

Figure 4

(a) Calculated occupation probability for the even (solid line) and odd (dashed line) dressed states at the $m=7$ even photon resonance for $A_{ng}=0.65$. (b) Calculated occupation probability of the even-parity state (summed over all even charge states). At low drive, the incorrect parity (the parity that does not result in coherent dynamics) is dominating, while the proper parity is almost completely recovered at strong drives.