RF-Driven Josephson Bifurcation Amplifier for Quantum Measurement

We have constructed a new type of amplifier whose primary purpose is the readout of superconducting quantum bits. It is based on the transition of a rf-driven Josephson junction between two distinct oscillation states near a dynamical bifurcation point. The main advantages of this new amplifier are speed, high sensitivity, low backaction, and the absence of on-chip dissipation. Pulsed microwave reflection measurements on nanofabricated Al junctions show that actual devices attain the performance predicted by theory.

Figure 1

Schematic diagram of the Josephson bifurcation amplifier. A junction with critical current $I_0$, parametrically coupled to the input port, is driven by a rf signal which provides the power for amplification. In the vicinity of the dynamical bifurcation point $i_{\mathrm{r}\mathrm{f}}=I_B$, the phase of the reflected signal phase $\varphi$ depends critically on the input signal. Inset: example of a parametric input coupling circuit.

Figure 2

Poincaré section of a rf-driven Josephson junction in the bistable regime $[\alpha =(1-\omega /{\omega }_p)=0.122,i_{\mathrm{r}\mathrm{f}}/I_B=0.87]$. The coordinates ${\delta }_{\parallel }$ and ${\delta }_{\perp }$ are the in-phase and quadrature-phase components of the junction gauge-invariant phase difference $\delta$. The color code gives the magnitude of the error current $i_e$ [18], which describes the “force” on $\delta$. The two stable oscillation states, labeled by 0 and 1, are indicated by white line segments. The basins of attraction corresponding to the two states are separated by the blue dotted line (separatrix). Point $S$, which lies on the separatrix, is the saddle point at which the escape trajectory from state 0 (dashed line) meets the retrapping trajectory into state 1 (solid line).

Figure 3

Hysteretic variation of the reflected signal phase $\varphi$ with drive current $i_{\mathrm{r}\mathrm{f}}/I_0$. Symbols denote the mode of $\varphi$, with up and down triangles corresponding to increasing and decreasing $i_{\mathrm{r}\mathrm{f}}$, respectively. The dotted line is $⟨\varphi ⟩$. The calculated bifurcation points, $I_{\overline{B}}$ and $I_B$, are marked on the horizontal axis. The 0 and 1 phase states are reminiscent of the superconducting and dissipative states of the dc current-biased junction.

Figure 4

Histograms of the reflected signal phase $\varphi$ at $i_{\mathrm{r}\mathrm{f}}/I_0=0.145$. The histogram contains $1.6\times {10}^6$ counts with an analysis time ${\tau }_a=20\mathrm{n}\mathrm{s}$. Data here have been taken under the same operating conditions as in Fig. 3. The dashed line represents the discrimination threshold between the 0 and 1 state.

Figure 5

Switching probability curves at $T=340\mathrm{m}\mathrm{K}$ as a function of the drive current $i_{\mathrm{r}\mathrm{f}}$. The discrimination power $d=0.57$ is the maximum difference between the two curves. The measurement protocol is the same as shown in the upper panel of Fig. 4. Though the two curves differ by approximately 1% in $I_0$, they are shifted by 6% in drive current.