Wideband Isolation by Frequency Conversion in a Josephson-Junction Transmission Line

Nonreciprocal transmission and isolation at microwave frequencies are important in many practical applications. In particular, compact isolators are useful in protecting sensitive quantum circuits operating at cryogenic temperatures from amplifier backaction and other environmental noise such as black-body radiation from higher temperature stages. However, the size of commercial cryogenic isolators limits the ability to measure multiple quantum circuits because of space constraints in typical dilution refrigerator systems. Furthermore, isolators usually require the use of ferrite components that cannot be integrated at the chip level and, since they also need large biasing magnetic fields, are incompatible with superconducting quantum circuits. In this work we show one way to accomplish isolation in a superconducting chip-scale device, a traveling-wave unidirectional frequency converter based on a parametrically pumped superconducting Josephson-junction transmission line, demonstrating better than 4.8 dB of inferred signal isolation from 6.6 to 11.4 GHz, with a maximum of 12 dB at 9.5 GHz. By using frequency diplexing techniques a conventional isolator could be implemented over this bandwidth.

Figure 1

On-chip traveling-wave isolation scheme. A nonlinear superconducting microwave line is formed by concatenating $N$ unit sections, each one composed of a transmission-line segment in series with an array of five Josephson junctions. A pump tone at ${\omega }_p$ periodically modulates the line inductance, allowing for frequency conversion of a signal copropagating with the pump. If the signal counterpropagates with respect to the pump, no frequency conversion occurs due to phase mismatch. (Inset) Circuit model of a unit section where $C_0$ is the transmission-line section capacitance. By externally dc biasing the device at approximately half of the junction’s critical current, the total section inductance is first-order sensitive to the pump current. This results in a pump-dependent inductance modulation amplitude $M$ and a pump-independent inductance $L_{\sec }$. The traveling pump wave is characterized by a $k$ vector ${\beta }_p$, frequency ${\omega }_p$, and phase ${\varphi }_p$.

Figure 2

Results of numerical calculations for the device in Fig. 1 for different modulation amplitudes $M$. (a) $N=40$ sections and (b) $N=160$ sections. See text for physical parameters.

Figure 3

(a) Micrograph of the frequency converter-isolator circuit. Each chip holds a meandered coplanar waveguide interrupted by strings of five Josephson junctions. The line contains 74 sections. The data in this article are measured with two of these chips connected in series (see text). The inset shows a magnified image of an angle-deposited junction array that forms the modulated inductor in the unit cell (see Fig. 1). (b) Measurement setup: through-reflect-line standards are measured for calibration.

Figure 4

(a) Measured forward-reverse transmission and input return loss for a pump frequency $f_p=4.8\mathrm{GHz}$ and pump power $P_p=-67.4\mathrm{dBm}$. The resonance peaks are due to impedance mismatch as well as parasitic electromagnetic modes. Pump-off plots of $|S_{21}|$ and $|S_{12}|$ are shown for reference, demonstrating reciprocal behavior absent the pump. (b) Device nonreciprocity $|S_{12}|/|S_{21}|$ with and without parametric pump. We estimate better than 4.7 dB of wideband isolation from 6.6 GHz to 11.4 GHz, with a maximum of 12 dB at 9.5 GHz (see text). Theory in Eq. (8) for a transmission line with 148 sections is shown by the dashed black line with the pump modulation index $M/L_{\sec }$ being the only fit parameter rendering $M/L_{\sec }=0.0714(3)$.

Figure 5

Coupling rate-length product $gL$ inferred from measured reverse transmission $|S_{12}|$ at two different pump frequencies (see text). Full power conversion is obtained when $gL=\pi /2$. Dashed lines are linear fits based on Eq. (3) rendering inductance modulation per unit section values of $M=8.2$, 15, and 21.1 pH.