Tunable Josephson voltage source for quantum circuits

TL;DR

This work introduces a tunable, low-noise voltage source based on the ac Josephson effect that operates continuously in the 30–160 µV range while delivering over 100 nA at millikelvin temperatures. By calibrating the microwave drive amplitude A(ω) at each frequency, the device maintains stable phase locking to Shapiro steps and achieves $V = n\hbar\omega/2e$ over a broad voltage range without dc bias changes. The authors demonstrate device operation, calibration strategies (PAT-based and supercurrent suppression-based), and coupling to a mesoscopic load, achieving a measured load noise as low as 50 pV RMS and a frequency stability of about 2.4 ppm, showcasing metrologically accurate, tunable cryogenic voltage bias suitable for quantum devices. Potential extensions include higher voltage with junction arrays and lower voltage via increased shunt capacitance, enabling broad applicability in quantum information, sensing, and mesoscopic experiments.

Abstract

Noisy voltage sources can be a limiting factor for fundamental physics experiments as well as for device applications in quantum information, mesoscopic circuits, magnetometry, and other fields. The best commercial DC voltage sources can be programmed to approximately six digits and have intrinsic noise in the microvolt range. On the other hand the noise level in metrological Josephson-junction based voltage standards is sub-femtovolt. Although such voltage standards can be considered "noiseless," they are generally not designed for continuous tuning of the output voltage nor for supplying current to a load at cryogenic temperatures. We propose a Josephson effect based voltage source, as opposed to a voltage standard, operating in the 30-160 uV range which can supply over 100 nA of current to loads at milli-Kelvin temperatures. We describe the operating principle, the sample design, and the calibration procedure to obtain continuous tunability. We show current-voltage characteristics of the device, demonstrate how the voltage can be adjusted without DC control connections to room-temperature electronics, and showcase an experiment coupling the source to a mesoscopic load, a small Josephson junction. Finally we characterize the performance of our source by measuring the voltage noise at the load, 50 pV RMS, which is attributed to parasitic resistances in the cabling. This work establishes the use of the Josephson effect for voltage biasing extremely sensitive quantum devices.

Figures (9)

• Figure 1: (a) Circuit schematic of a Josephson tunnel junction driven by a microwave source showing locking to a Shapiro step at voltage $V = n\hbar\omega/2e$. Here, $I_c$ is the junction critical current and $C_s$ is a shunt capacitance. (b) Sketch of the current-voltage characteristic of the junction with (black) and without (light gray) microwave drive. When the drive amplitude is appropriately adjusted, Shapiro steps (thick vertical lines) appear. (c) After calibrating for the optimal microwave amplitude-frequency dependence $A(\omega)$ that maximizes the height of the first Shapiro step, the output voltage $V = \hbar\omega/2e$ can be continuously tuned without losing phase lock.
• Figure 2: (a) False-colored optical image of Josephson tunable voltage source and electron micrograph of the Josephson tunnel junction (inset). The shunt capacitor is highlighted in orange, and bonding pads are highlighted in blue (dc connections) and green (microwave bias connection). (b) Circuit schematic for measurement of device current-voltage characteristic. An applied dc voltage $V_0$ induces the current $I = (V_b-V)/R$ through the junction. Here, $V_b$ and $V$ are measured with differential voltage amplifiers and a microwave drive is applied via the signal generator $A\sin\omega t$.
• Figure 3: (a) Current-voltage characteristics of Josephson tunable voltage source for different microwave drive amplitudes $A$ at fixed frequency $\omega_0/2\pi=20\GHz$. Traces are offset by 0.5 for clarity. (b) Map of current as a function of microwave drive amplitude ($x$ axis) and voltage ($y$ axis) showing Shapiro step lobes. (c) Amplitudes of the supercurrent peak and first three Shapiro current steps, as extracted from the current-voltage map in (b), are plotted as a function of drive amplitude.
• Figure 4: (a) Current-voltage characteristics measured at optimal microwave amplitude $A_{0}^{c}(\omega)$ minimizing the supercurrent for $\omega/2\pi=\qtylist[list-units=single]{16;18;20}{\GHz}$. A reference $IV$ without microwave drive is shown in black. Data is measured with a positive sweep in bias voltage, resulting in smaller negative peaks. (b) Current voltage map measured at $A_{0}^{c}(\omega)$ plotted as a function of microwave drive frequency. The $IV$ characteristics in (a) are indicated by vertical dashed lines. (c) Height of Shapiro peaks of order $n$ extracted from (b) along the lines indicated by arrows.
• Figure 5: After switching to the first Shapiro step (blue), the frequency is modulated in the range 1040 with a triangular waveform having a period of 9.17 (bottom time scale). The power is adjusted according to the calibration to maintain the step amplitude. The measured junction voltage is continuous and follows the Josephson relation $V=\hbar\omega/2e$ without switching to other steps over a total time of 100. In orange the junction is locked to the second-order step at $V=2\hbar\omega/2e$, the sweep period is 1.036, and the measurement duration is approximately 9 (top time scale). The biasing circuit is disconnected with a cryogenic switch during the measurement (see main text).