Josephson Directional Amplifier for Quantum Measurement of Superconducting Circuits

We realize a microwave quantum-limited amplifier that is directional and can therefore function without the front circulator needed in many quantum measurements. The amplification takes place in only one direction between the input and output ports. Directionality is achieved by multipump parametric amplification combined with wave interference. We have verified the device noise performances by using it to read out a superconducting qubit and observed quantum jumps. With an improved version of this device, the qubit and preamplifer could be integrated on the same chip.

Figure 1

Setup used in measuring the performances of the JDA, whose schematic is shown in the inset. A superconducting cavity-qubit system is connected to the input of the JDA with no intermediate circulator or isolator stages. A low-pass filter and a directional coupler are inserted in between the cavity-qubit system and the JDA. The filter protects the cavity-qubit system from high-frequency pump photons that can possibly bounce off the JDA, while the directional coupler enables biasing the JDA at a desired working point using the input ${\mathrm{Probe}}_1$. Similarly, the circulator connected at the output of the JDA enables measuring the reflection off port 2 of the JDA using the input ${\mathrm{Probe}}_2$. The output signal is further amplified using a cryogenic HEMT amplifier and is demodulated at room temperature using a quadrature modulation mixer. The inset displays vector network analyzer measurements of $S_{21}$ and $S_{22}$ of the JDA as a function of frequency detuning relative to the read-out frequency $f_d$, taken at the working point employed in the read-out of the qubit-cavity system.

Figure 2

A comparison between the decoherence times of the qubit measured with the JDA off (left column) versus on (right column). Plots (a) and (b) show $T_1$ and $T_2$ Ramsey measurement results, respectively. The red filled circles are data points while the blue curves are fits. From the fits we get values for $T_1$ of $13.8\mu \mathrm{s}$ and $14.4\mu \mathrm{s}$, and values for $T_{2R}$ of $0.62\mu \mathrm{s}$ and $0.52\mu \mathrm{s}$ for the JDA-off versus -on cases, respectively.

Figure 3

Histograms of the qubit state measured after applying a $\pi$ pulse or no pulse to the qubit. Panels (a) and (b) show the histograms measured with the JDA off and on, respectively. In the left and middle columns, we depict two-dimensional histograms of the qubit state as a function of the $I$ and $Q$ quadratures of the microwave field, expressed in units of the square root of the average number of photons in the read-out pulse at the output of the JDA. The right column depicts projections of the two-dimensional histograms for the ground and excited states onto the $I$ quadrature.

Figure 4

Selected individual measurement records of the JDA-on output. The qubit state traces versus time exhibit quantum jumps between the ground and excited states of the qubit. The red and blue dashed lines—which indicate the excited and ground signal levels of the qubit, respectively—are guides for the eye.