Observation of Quantum Jumps in a Superconducting Artificial Atom

We continuously measure the state of a superconducting quantum bit coupled to a microwave readout cavity by using a fast, ultralow-noise parametric amplifier. This arrangement allows us to observe quantum jumps between the qubit states in real time, and should enable quantum error correction and feedback—essential components of quantum information processing.

Figure 1

Experimental setup. Readout photons (black arrow, “1”) enter from the input port and are directed through a microwave circulator to a 180° hybrid, which converts the single-ended microwave signal into a differential one. The photons interact with the readout cavity and the reflected signal (purple arrows, “2”) carries information about the qubit state toward the parametric amplifier (paramp) through three circulators, which isolate the readout and qubit from the strong pump of the paramp. A directional coupler combines this signal with pump photons (green arrow, “3”) from the drive port. The paramp amplifies the readout signal, and the amplified signal (magenta arrow, “4”) is reflected and sent through the third circulator to the output port. Qubit manipulation pulses are also sent via the input port.

Figure 2

Parametric amplifier response. In (a), we plot the measured average phase of the reflected pump as a function of pump power with the qubit prepared in the ground (blue, open circles) or excited (red, solid circles) states and an average readout cavity occupation of about one photon. Panel (b) shows the same curves for higher average photon number ($\overline{n}\approx 30$) in the readout cavity, which increases the relative separation. The vertical dashed line shows the optimal bias point.

Figure 3

Quantum jumps. (a) shows the pulse sequence used to generate (b) and (c). The qubit is excited with a pulse of varying amplitude (red), and the readout (black) is immediately energized, causing the cavity population (purple) to rise and effect a measurement. Time $t=0$ corresponds to two cavity time constants after the readout is energized. (b) shows 20 representative single-shot traces for three different qubit rotations (0, $\pi$, and $2\pi$). Abrupt quantum jumps from the excited state (white) to the ground state (blue) are clearly visible for the data corresponding to the $\pi$ pulse, while the traces corresponding to 0 and $2\pi$ indicate that the qubit is mostly in the ground state. (c) shows single-shot time traces following a $\pi$ (red and green) and $2\pi$ (blue) pulse. (d) shows the pulse sequence used to generate (e) and (f). Here the readout is energized with the qubit in the ground state, and then a continuous qubit drive is applied after a $3\mu \mathrm{s}$ delay. (e) and (f) show 60 traces and one trace, respectively, of the qubit jumping between the ground and excited state under the influence of both the qubit drive and measurement pinning.

Figure 4

Jump statistics. (a) shows a histogram of $2\times {10}^4$ individual measurements with the qubit prepared with a $\pi$ pulse and $\overline{n}\approx 30$ readout photons. The excited state signal, centered around 0.6 V, is clearly resolved from the ground state signal at $-0.3\mathrm{V}$; the dashed line shows the discrimination threshold. The ensemble population is predominately in the excited state at $t=0$, and decays to the ground state with a time constant [(b), inset] $\tau =290\mathrm{ns}$. (b) shows a histogram of jump times from the excited state to the ground state extracted from individual measurements. The solid line is an exponential fit with a time constant ${\tau }_{\mathrm{jump}}=270\mathrm{ns}$. We do not plot jumps that occur less than two cavity time constants after the readout is energized. The pulse protocol used is shown in Fig. 3a.