Coherent control of a superconducting qubit with dynamically tunable qubit-cavity coupling

We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe $T_1$ and $T_2$ times of 1.6 and 1.9 $\mu$s, respectively. This work demonstrates how this qubit can be incorporated into quantum architectures.

Figure 1

Energy level diagram for the TCQ showing the hybridized energy levels when $g_{10–00}\approx 0$. The transitions that have a high probability of occurring are indicated by arrows. The red, solid arrows indicate transitions with low coupling strengths and the blue, dashed arrows indicate transitions with high coupling strengths. The levels shown here are for the bare energy levels of the device; there are no effects of coupling to a cavity. In this work the $|00\rangle$ and $|\widetilde{10}\rangle$ states are used as the logical states of the qubit.

Figure 2

(a) Observed cavity transmission vs the two control voltages with a fixed spectroscopy tone at $7.5\mathrm{GHz}$. Both the dressed qubit frequency and coupling strength are functions of the control voltages. The contour shows where the qubit is resonant with the $7.5\mathrm{GHz}$ tone and is therefore driven between the ground and excited states. (b) Measured dressed frequency response of the qubit while moving along the $7.5\mathrm{GHz}$ contour in Fig. 1. The dressed qubit frequency remains constant at $7.5\mathrm{GHz}$. The amplitude of the response is related to the coupling strength between the qubit and the superconducting resonator. The point where the signal disappears corresponds to coupling strengths where the qubit cannot be driven by the spectroscopy tone. The dotted and dashed lines indicate $g_{10–00}$ control values where the measurements were performed for Fig. 3.

Figure 3

Rabi oscillations for three different qubit-cavity coupling strengths and a fixed dressed qubit frequency of $7.5\mathrm{GHz}$. The transition is driven using a Gaussian pulse with a fixed width $\sigma =6$ ns of varying amplitude. (a), (b), and (c) correspond to the dashed, dot-dash, and dotted lines in Fig. 2, respectively. In (a) a spectroscopy power of $-$32 dBm is used. To keep the number of oscillations approximately the same for the lower qubit-cavity coupling strength in (b), the spectroscopy power is increased to $-$22 dBm. In (c) 27 dBm more power than that in (a) is applied and no oscillations are observed. Given the measurement noise, we put a bound of $1/10$ of a Rabi oscillation.

Figure 4

(a) Observed Rabi oscillations when the qubit starts in the $g_{10–00}=0$ state and is simultaneously moved to a large $g_{10–00}$ state and driven by a $7.5\mathrm{GHz}$ Gaussian spectroscopy pulse $\sigma =6$ ns of varying amplitude. The fast flux pulse is 60 ns in duration and is followed by an identical pulse of the opposite sign so that the total pulse integral is zero; these zero integral pulses help reduce slow transients. (b) Pulsed measurements showing the probability of the qubit being in the excited state as a function of delay following a $\pi$ pulse. The qubit starts in the $g_{10–00}=0$ state and is excited with a $\pi$ pulse in the manner described in (a); a pulsing scheme is included as an inset to the figure. The measured $T_1$ is 1.6 $\mu$s. (c) Hahn echo measurements with the qubit starting in the $g_{10–00}=0$ state. Each of the pulses in the Hahn sequence is synchronized with a pair of fast flux pulses. A pulsing scheme is included as an inset to the figure. The measured $T_2$ time is 1.9 $\mu$s.