Coherent Quasiclassical Dynamics of a Persistent Current Qubit

A new regime of coherent quantum dynamics of a qubit is realized at low driving frequencies in the strong driving limit. Coherent transitions between qubit states occur via the Landau-Zener process when the system is swept through an energy-level avoided crossing. The quantum interference mediated by repeated transitions gives rise to an oscillatory dependence of the qubit population on the driving-field amplitude and flux detuning. These interference fringes, which at high frequencies consist of individual multiphoton resonances, persist even for driving frequencies smaller than the decoherence rate, where individual resonances are no longer distinguishable. A theoretical model that incorporates dephasing agrees well with the observations.

Figure 1

(a) Schematic of the PC qubit surrounded by a dc SQUID readout. dc and rf fields control the state of the qubit. (b) A rf pulse of duration $\Delta t\gg {\nu }^{-1}$ drives the qubit, and its state is inferred from the voltage $V_{\mathrm{SQ}}$ across the SQUID pulsed with current $I_{\mathrm{SQ}}$. (c) The qubit experiences two Landau-Zener transitions over a single rf period, accumulating a relative phase $\Delta {\theta }_{12}$ between them. (d) The resulting interference fringes in qubit population for $\nu =270$ and 90 MHz, and $V_{\mathrm{rms}}=240$ and 171 mV, respectively, (vertical lines on Fig. 2).

Figure 2

Measured qubit population at strong driving in two regimes. (a) $\nu =270\mathrm{MHz}$. Multiphoton resonances of order up to $n=45$ can be discerned ($\nu T_2>1$). (b) $\nu =90\mathrm{MHz}$. Individual resonances are no longer distinguishable ($\nu T_2\lesssim 1$), but coherent interference is still observed. Vertical lines indicate the scans displayed in Fig. 1d. A pulse of duration $\Delta t=3\mu s$ was used in both cases.

Figure 3

(a) Time evolution of excited state population ($\nu =90\mathrm{MHz}$, $V_{\mathrm{rms}}=171\mathrm{mV}$) obtained by varying the pulse width $\Delta t$. (b) The characteristic rate $\Gamma$ as a function of flux detuning $\delta f$ obtained by fitting to the exponential time dependence [Eq. (9)] (inset shows examples of fits for the points I, II, III and IV).

Figure 4

Comparison of experiment (blue) and theory (red). (a) The transition rate from the right half of Fig. 3b fitted with $\Gamma$ defined by Eqs. (5, 9). (b) State $|1⟩$ occupation taken from Fig. 3a, compared to the model, Eq. (9).

Figure 5

Simulation of qubit population using model parameters extracted from data. (a) $\nu =270\mathrm{MHz}$. (b) $\nu =90\mathrm{MHz}$.