Widely Tunable On-Chip Microwave Circulator for Superconducting Quantum Circuits

We report on the design and performance of an on-chip microwave circulator with a widely (GHz) tunable operation frequency. Nonreciprocity is created with a combination of frequency conversion and delay, and requires neither permanent magnets nor microwave bias tones, allowing on-chip integration with other superconducting circuits without the need for high-bandwidth control lines. Isolation in the device exceeds 20 dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at select operation frequencies. Furthermore, the device is linear with respect to input power for signal powers up to hundreds of fW ($\approx {10}^3$ circulating photons), and the direction of circulation can be dynamically reconfigured. We demonstrate its operation at a selection of frequencies between 4 and 6 GHz.

Popular Summary

As experiments on superconducting qubits (the quantum equivalent of a digital bit) clear a possible path to viable quantum computing processors, further signal processing innovations are needed to preserve a high level of control over the quantum information. One bottleneck is ensuring that signals travel in only one direction, which is critical for protecting the quantum hardware from the noisy environment. Devices engineered to enforce this requirement, known as circulators, are traditionally made with permanent magnets, which makes these magnetic circulators about the size of an engagement-ring box and impractical to miniaturize. We designed and tested an alternate method for building a circulator that uses time-varying circuit parameters to simulate circulation.

Our circulator is integrated onto a chip thousands of times smaller than a magnetic circulator and built from superconducting materials. Unlike other on-chip superconducting circulators, the device has a widely tunable operation frequency and can circulate a thousand photons at a time—many more than the several-photon signals typically emitted by a single qubit. We demonstrate isolation exceeding 20 dB over a bandwidth of tens of megahertz and are able to dynamically reconfigure the circulation direction.

Circulators allow energy and information to flow out of qubits for amplification and measurement, but they strongly suppress the reverse process, where energy and information flow from the environment can damage the fragile state of the qubit. Our device offers a tunable, integrable, scalable solution that can be used in a wide variety of quantum information technologies.

Figure 1

A four-port circulator (gray cylinder) routes fields incident on one of its ports out a neighboring port, as indicated by the arrow. In circuit quantum electrodynamics, these devices are used to separate incoming and outgoing fields for quantum reflection amplifiers, and to isolate fragile quantum systems from the backaction of classical amplifiers. Here, we use “quantum” and “classical” to mean amplifiers with added noise equal to and much greater than half a photon, respectively [9].

Figure 2

Conceptual diagram of nonreciprocity generated with frequency conversion and delay. (a) Lumped-element network that forms a gyrator. The insets show how fields are transformed by the network’s two components: multiplying elements and delays. In the upper inset, an input field at frequency ${\omega }_p$ (top panel) is multiplied by $\cos (\mathrm{\Omega }t)$ to create a field with spectral components at ${\omega }_p\pm \mathrm{\Omega }$ (bottom panel). The real and imaginary axes of the plot show the phase of these spectral components in a frame rotating at ${\omega }_p$. In the lower inset, a delay of length $\tau =\pi /2\mathrm{\Omega }$ advances or retards the phase of spectral components at ${\omega }_p+\mathrm{\Omega }$ or ${\omega }_p-\mathrm{\Omega }$ by $\pi /2$. (b) Calculation of the forward-scattering parameter for the network in (a), by following an incident field at frequency ${\omega }_p$ as it propagates through the device. Purple (green) arrows indicate fields propagating in the left (right) arm of the network. Fields are forward transmitted with amplitude and frequency unchanged, but phase shifted by $\pi$. (c) Backward transmission through the network in (a). Fields are transmitted with amplitude, frequency, and phase unchanged.

Figure 3

Multiplying elements and delays realized in a superconducting lumped-element circuit. (a) The model system [Fig. 2] is constructed from two parallel instances of this network. (b) A lumped-element version of the network in (a), created with capacitors and tunable inductors arranged in a bridge geometry. (c) To create an inductive bridge circuit in a superconducting microwave environment, four series arrays of SQUIDs are arranged in a figure-eight geometry and tuned with an off-chip magnetic coil producing a uniform flux ${\mathrm{\Phi }}_u$ and an on-chip bias line creating a gradiometric flux $\pm {\mathrm{\Phi }}_g$. (d) Simulated group delay for the circuit in (b) when its ports are connected to $50\text{ohm}$ transmission lines. The bridge inductors are parametrized according to Eq. (2), with $c=1\mathrm{pF}$, $l_0=1\mathrm{nH}$, and $\delta =0.2$.

Figure 4

Superconducting realization of a four-port circulator. (a) Lumped-element schematic of the circulator, constructed with four inductive bridge circuits and two capacitors. Bias lines (not shown) tune the imbalance $\delta$ of the four bridge circuits dynamically. (b) The schematic in (a) redrawn to better match the device layout. The rearrangement allows biasing of the bridge circuits with a pair of straight flux-control lines. (c) False-color optical micrograph of the circulator chip. A dashed black box indicates one of the four bridge circuits, created with four 12-SQUID arrays (green) arranged in the figure-eight geometry described in Fig. 3. Parallel-plate capacitors (purple) provide the capacitance needed for the resonant delay. Bias lines (red and blue) traverse the chip and imbalance the bridge circuits with a gradiometric flux.

Figure 5

Simplified experimental schematic for circulator measurements in a ${}^3\mathrm{He}$ cryostat (attenuation, filtering, and isolation omitted). Two switches and a directional coupler allow measurement of four of the circulator’s scattering parameters with a vector network analyzer (VNA).

Figure 6

Performance of an on-chip superconducting circulator tuned to operate near 4 GHz. (a) Frequency dependence of four of the circulator’s 16 scattering parameters, when configured as a counterclockwise circulator (blue traces) and a clockwise circulator (orange traces). (b) Transmission spectrum of the circulator at ${\omega }_p=2\pi \times 4.044\mathrm{GHz}$, measured at frequencies ${\omega }_p\pm m\mathrm{\Omega }$ with $m$ a positive integer. Spectral components are normalized by the power transmitted at ${\omega }_p$. Spurious sidebands are suppressed by approximately 20 dB. (c) Transmission as a function of probe power, with probe frequency fixed at ${\omega }_p=2\pi \times 4.044\mathrm{GHz}$. 1-dB compression occurs around 1 pW.

Figure 7

Performance of a widely tunable on-chip circulator. The insertion loss [(a), solid lines], dissipation [(a), dotted lines], maximum isolation (b), isolation bandwidth (c), sideband suppression (d), and power handling (e) are plotted at operation frequencies between 4 and 6 GHz when the device is configured as a clockwise (orange rectangles) or counterclockwise (blue circles) circulator. Isolation bandwidth refers to the bandwidth over which isolation exceeds 20 dB. Sideband suppression refers to the contrast between transmitted spectral components at the input frequency ${\omega }_p$ and the largest spurious sideband of the form ${\omega }_p\pm n\mathrm{\Omega }$. In (e), dotted lines indicate the device’s 1-dB compression point and solid lines indicate the 20-dB expansion point, where isolation drops below 20 dB.

Figure 8

Measurements of the circulator’s group delay $\tau$ (color, log scale) as a function of the probe frequency and a static gradiometric flux ${\mathrm{\Phi }}_u$ applied to all four of the bridge circuits. The duration and center frequency of the resonant delay depend on the uniform and gradiometric flux, allowing the circulator’s operation frequency to be tuned between 4 and 6 GHz. Dashed gray lines are predictions of Eq. (4) which use the mapping in Appendix pp1. To account for geometric inductance in the circuit (which is not present in the model), the dashed lines are calculated with effective uniform fluxes ${\tilde{\mathrm{\Phi }}}_u/{\mathrm{\Phi }}_0=0.38$, 0.33, and 0.28 chosen to match the frequency of the measured and predicted delays when ${\mathrm{\Phi }}_g=0$.

Figure 9

Measurements of a dynamically reconfigurable circulator. The phase $\varphi$ between the gradiometric flux lines determines the direction of circulation. Counterclockwise (a) and clockwise (b) transmission as a function of the probe frequency and the phase $\varphi$. Vertical and horizontal lines indicate the location of line cuts plotted in (c) and Fig. 6. (c) Counterclockwise (dashed line) and clockwise (solid line) transmission at probe frequency ${\omega }_p=2\pi \times 4.044\mathrm{GHz}$.

Figure 10

(a) Schematic illustrating the symmetrization of the parallel-plate capacitors used in the device. To create a capacitor $c$, two capacitors with half the desired capacitance are connected in parallel, such that the upper (lower) plate of the first capacitor is galvanically connected to the lower (upper) plate of the second. This procedure gives each side of the capacitor the same parasitic capacitance to the ground plane. (b) False-color scanning electron microscope image showing one of the $c/2$ capacitors used in the device (blue), and the joint connecting it to another $c/2$ capacitor (green), as described in (a). The plates in both capacitors are formed from narrow niobium strips of width $w=5\mu \mathrm{m}$ to prevent trapping flux vortices [45].

Figure 11

(a) Schematic showing the position of normal metal resistors in the inductive bridges and the routing of a quadrupole-source bias line that couples strongly to the SQUIDs it encloses and weakly to surrounding loops of the circuit. (b) False-color scanning electron microscope image showing two adjacent SQUID arrays (green) and the microstrip lines (pink) that flux bias them. (c) Schematic illustrating the challenge of coupling a bias line strongly to a small SQUID loop while coupling it weakly to a larger circuit loop.

Figure 12

Measurements (a),(b) and theoretical predictions (c),(d) of $|S_{21}|$ and $|S_{12}|$, as a function of probe frequency and amplitude of the oscillatory gradiometric flux, when the device is configured as a counterclockwise circulator. Theoretical predictions are made with the expressions in Ref. [19] and the mapping in Appendix pp1. Circuit parameters are fixed at their design targets ($l_0=1\mathrm{nH}$, $c=1\mathrm{pF}$) and the flux controls are set to match the measurements in (a) and (b): $\mathrm{\Omega }=2\pi \times 120\mathrm{MHz}$, ${\mathrm{\Phi }}_u=0.38{\mathrm{\Phi }}_0$.