A persistent-current-biased and current-actuated switch for superconducting circuits

Abstract

Broadband and low-loss superconducting switches can facilitate large-scale quantum information processors and cryogenic detectors by dynamically reconfiguring the connectivity of their circuits. The time dependent connectivity is enabled by the nonlinearity of lossless Josephson junctions, which are often wired into superconducting loops to be controlled by magnetic flux. However, this approach needs a power-consuming constant flux bias and dynamic flux actuation, both of which are hard to isolate from other switches or flux sensitive elements, limiting their integration density. Here, we design and characterize a microwave switch that implements a persistent current bias and direct current actuation to reduce static power consumption, actuation energy and potential crosstalk to other devices. We show that persistent current associated with tens of flux quanta is stable and long-lived, reducing the need for on-the-fly tuning. We further demonstrate that our switch has desirable performance for superconducting-circuit-based quantum information processing, including an off mode with more than 20 dB isolation comparable to commercial ferrite isolators, power handling larger than 100 pW sufficient for resonator readout tones and amplifier pumps, and modulation bandwidth broader than 600 MHz useful for multiplexing schemes.

Figures (7)

• Figure 1: A current controlled switch concept and design. (a) The inductive Wheatstone bridge and its eigenmodes, $\text{X, Y, Z}$, expressed in terms of node flux variables $\phi_{\text{X}}= (\phi_{\text{W}} - \phi_{\text{E}})/\sqrt{2}$, $\phi_{\text{Y}}=(\phi_{\text{N}} - \phi_{\text{S}}) /\sqrt{2}$ and $\phi_{\text{Z}}=(\phi_{\text{N}} +\phi_{\text{S}} - \phi_{\text{E}} - \phi_{\text{W}})/2$Flurin_2014. The currents associated with these modes are represented with the cyan arrows. In addition, a circulating current $I_{\text{C}}$ (central cyan arrow) is associated with the accumulative phase $\phi_{\text{C}}$ around the bridge. Using both $I_{\text{Z}}$ and $I_{\text{C}}$ as control currents, the total currents in the inductors are the same for opposite inductors but different for adjacent ones, as indicated by their light and dark green colors. The differential $\text{X}$ and $\text{Y}$ modes are connected to the input and output ports respectively. (b) The circuit schematics for the bridge concept in (a) shown at two temperatures. The diamond-shaped bridge is twisted into a figure-8 shape to minimize the flux sensitivity to any uniform background magnetic field. The rf-SQUID arrays, labeled as "20 RFS", implement the tunable inductors of the bridge. A PCS directs which path the source current $I_{\text{src}}$ takes. When the device temperature is such that the aluminum patch (magenta) is resistive, the south node $\text{S}$ splits into $\text{S}+$ and $\text{S}-$ nodes, through which the intended-to-trap current $I_{\text{src}}=I_{\text{trg}}$ flows into the bridge. When superconducting, the aluminum patch acts as a low inductance shunt, approximately collapsing the $\text{S}+$ and $\text{S}-$ nodes to the $\text{S}$ node. In this state, the $I_{\text{C}}$ consists of the trapped current ($\approx I_{\text{trg}}$) and the contribution from $\phi_{\text{ext}}$. Inset: An aluminum patch (magenta) closes the superconducting loop of the bridge. An antisymmetric rf-SQUID (c) is one in a series of 20 SQUIDs that form a tunable inductor Miniature_Zimmerman_1971. In this compact design, there are two wiring layers shown in purple and gray, and they are connected by three parallel paths: 2 vias and a JJ. The middle trace inside the rf-SQUID and the trace connecting to the neighboring rf-SQUIDs interact with the spiral inductors ($L_{\text{sh}}$) through mutual inductance $M$ and $-M$, canceling the effect of each other.
• Figure 2: Demonstrating the control scheme with transmission measurements. (a) The switch's circuit diagram shows the bridge, the current control lines and the microwave ports for transmission measurements including the C bias (orange) and the Z actuation (blue). The bridge loop is closed with a heat activated PCS (magenta). The input and output ports are connected to the $\text{X}$ and $\text{Y}$ modes via baluns (purple) . The $10\ \text{m}\Omega$ Au resistors (brown) in the $\text{Z}$ lines and capacitors (red) break unwanted superconducting loops. (b) Transmission measurements sweeping $I_{\text{trg}}$ and the $I_{\text{Z}}$ are obtained by attempting to trap $I_{\text{trg}}$ using the PCS, followed by a sweep of $\tau(I_{\text{Z}})$. (c) A vertical linecut of (b) at $I_{\text{Z}}=0.1\ \text{mA}$ reveals the persistent current trapped in the bridge forms quantized steps, corresponding to integer numbers of trapped flux. (d) Two measurements of $\tau(I_{\text{Z}},\phi_{\text{ext}})$ are shown at different values of trapped flux, $\phi_{\text{C}}=0$ (left) and $\phi_{\text{C}}=22$ (right), where $\phi_{\text{ext}}$ is normalized by its experimentally determined period $\tilde{\phi}_{\text{C}}$. The red crosses with dashed lines label the centers of the grid structures (points about which $\tau$ is most approximately an even function of both arguments) showing a shift of the grid pattern in the $\phi_{\text{ext}}$ axis. (e) The figure shows the normalized correlation $\chi$ between the two sweeps of $\tau(I_{\text{Z}},\phi_{\text{ext}})$ in (d), where its maximum (red star) is used to extract the shift in $\phi_{\text{ext}}$ and the corresponding change in $I_{\text{C}}$. (f) This figure shows the result of repeatedly extracting the shift in $\phi_{\text{ext}}$ once an hour after intentionally trapping 34 flux quanta. The number of trapped flux remained constant until a jump (of unknown cause) occurred at the 104th hour. (g) The width of the steps shown in Fig. \ref{['fig:2']}b represents the amount of $\text{C}$ bias required to increment the trapped flux. The step width $I_{\text{stp}}$ as a function of $I_{\text{trg}}$ changes periodically, illustrating the bridge's current dependent differential inductance.
• Figure 3: Microwave performance of the switch. (a) Transmission as a function of input frequency and $I_{\text{Z}}$, with $I_{\text{trg}} = 2\text{0 μA}$, shows regions of $\text{re}(\tau)>0$ (cyan), $\text{re}(\tau)\approx0$ (white) and $\text{re}(\tau)<0$ (orange). The red and green arrows label the $I_{\text{Z}}$ corresponding to the on and off modes. Figure (b) shows $|\tau|$ as a function of input frequency for the on and off modes. The purple shading indicates the region for which the difference between on and off transmission exceeds $\text{20 dB}$. (c) The figure shows $|\tau|$ as function of input power of a $\text{5.1 GHz}$ tone for the on-mode bias point with the $\text{1 dB}$ compression point (annotated in blue) at $\text{-67 dBm}$.
• Figure 4: Sideband generation and modulation bandwidth. (a) The modulation gain of the first-order modulation sidebands (red/green) and the $\text{5.1 GHz}$ carrier tone (orange) is plotted versus modulation frequency. The $|\tau|$ in all other sidebands is less than carrier feedthrough. The inset conceptually illustrates the color scheme in the main figure. (b) Extracted scaling factor $\zeta$ as a function of modulation frequency $f_{\text{m}}$ is shown as the orange line. Additionally, the cyan line shows the expected frequency dependent attenuation of the cryostat cable ($\text{1 dB}$ at $\text{5 GHz}$). The inset is similar to that of (a), except that the $|\tau|$ of the feedthrough is the dominant peak with $I_{\text{trg}}=0$. The first order sidebands are further filtered by a low-pass filter, and are represented by the dashed lines.
• Figure Extended Data Fig. 1: The circuit model of the bridge arm (labeled by $l$) includes 20 rf-SQUIDs and stray inductance $L_{\text{str}}/4$. The phase drop across each rf-SQUID is $\phi_{\text{J}}$, which is controlled by the current in the arm $I_{l}$.