Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit

Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a continuously observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of Rabi spectroscopy enabled a long coherence time of about $2.5\mu \mathrm{s}$, corresponding to an effective qubit quality factor $\sim 7000$.

Figure 1

Measurement setup. The flux qubit is inductively coupled to a tank circuit. The dc source applies a constant flux ${\Phi }_{\mathrm{e}}\approx \frac{1}{2}{\Phi }_0$. The HF generator drives the qubit through a separate coil at a frequency close to the level separation $\Delta /h=868\mathrm{M}\mathrm{H}\mathrm{z}$. The output voltage at the resonant frequency of the tank is measured as a function of HF power.

Figure 2

The Al qubit inside the Nb pancake coil.

Figure 3

The spectral amplitude of the tank voltage for HF powers $P_a<P_b<P_c$ at 868 MHz, detected using the setup of Fig. 1. The bottom curve corresponds to the background noise without an HF signal. The inset shows normalized voltage spectra for seven values of HF power, with background subtracted. The shape of the resonance, being determined by the tank circuit, is essentially the same in each case. Remaining tiny variations visible in the main figure are due to the irradiated qubit modifying the tank’s inductance and hence its central frequency, and in principle similarly for dissipation in the qubit increasing the tank’s linewidth [7]; these are inconsequential for our analysis.

Figure 4

(a) Comparing the data to the theoretical Lorentzian. The fitting parameter is $g\approx 0.02$. Letters in the figure correspond to those in Fig. 3. (b) The Rabi frequency extracted from (a) versus the applied HF amplitude. The straight line is the predicted dependence ${\omega }_{\mathrm{R}}/{\omega }_{\mathrm{T}}=\sqrt{P/P_0}$. The good agreement provides strong evidence for Rabi oscillations.