Fast Charge Sensing of a Cavity-Coupled Double Quantum Dot Using a Josephson Parametric Amplifier

We demonstrate fast readout of a double quantum dot (DQD) that is coupled to a superconducting resonator. Utilizing a parametric amplifier beyond its range of linear amplification, we improve the signal-to-noise ratio (SNR) by a factor of 2000 compared to the situation with the parametric amplifier turned off. With an integration time of 400 ns comparable to the inverse effective bandwidth, we achieve a SNR of 76. By measuring the SNR as a function of the integration time, we extract an equivalent charge sensitivity of $8\times {10}^{-5}e/\sqrt{\mathrm{Hz}}$. The high SNR allows us to acquire a DQD charge-stability diagram in just 20 ms. At such a high data rate, it is possible to acquire charge-stability diagrams in a live “video mode,” enabling real-time tuning of the DQD confinement potential.

Figure 1

(a) Diagram of the experimental setup. A readout tone at frequency $f_{\text{in}}$ is applied to the cavity input port. The output field of the cavity is sent through a circulator, amplified using a JPA, and then demodulated into the $I$ and $Q$ quadratures. The amplification band of the JPA is flux tuned using a small coil that creates a magnetic field $B$. A directional coupler is used to couple in the pump field at frequency $f_{\text{pump}}$. (b) Illustration of the DQD cavity system. A single nanowire is placed on top of five depletion gates. Negative voltages on the gates establish a double-well potential forming the DQD. (c) Optical micrograph of the JPA, which is implemented as a quarter-wavelength resonator shunted by an array of five SQUIDs. The resonator is coupled to the input port using an interdigitated planar capacitor (outlined in green). A scanning electron micrograph showing the SQUID array is outlined in red. (d) Schematic of the magnetic shielding used to isolate the JPA from the superconducting magnet around the DQD. The JPA is housed in a copper box magnetically shielded by one aluminum and two Amumetal 4K cylinders.

Figure 2

(a) Reflected phase $\mathrm{\Phi }$ as a function of bias coil current $I$ and probe frequency $f$. The resonance frequency of the JPA is indicated by a large phase shift. (b) Gain as a function of frequency for the JPA configured as a linear amplifier in phase-insensitive mode. We achieve a gain of approximately 4000 (36 dB) with a bandwidth $B_w=3.8\mathrm{MHz}$. (c) Phase $\mathrm{\Phi }$ of the signal reflected off of the JPA as a function of the total incident power $P_{\mathrm{tot}}$. Grey area indicates the power range around $P_{\text{pump}}=-94\mathrm{dBm}$ for which amplification is approximately linear. Green- and red-shaded areas schematically represent noise-induced power fluctuations around the average $P_{\mathrm{tot}}$ associated with the DQD on and off state, respectively.

Figure 3

DQD charge-stability diagram extracted by plotting the normalized $Q$ quadrature amplitude as a function of gate voltages $V_{\mathrm{L}}$ and $V_{\mathrm{R}}$. The plot is taken with the JPA turned on and takes only 2 min to acquire. Dashed lines are guides to the eye.

Figure 4

(a),(b) $Q$ quadrature amplitude plotted as a function of $V_{\mathrm{L}}$ and $V_{\mathrm{R}}$ near the $(n,m+1)\leftrightarrow (n-1,m+2)$ interdot charge transition. (a) Data taken with the JPA on, and (b) with the JPA off. For both cases, each point of the color map is integrated for $\tau =42\mu \mathrm{s}$. (c),(d) Traces of the $Q$ quadrature amplitude showing the interdot charge transition for different per-point integration times $\tau$. (c) Data taken with the JPA on (traces are offset by 1 for clarity), and (d) with the JPA off (traces are offset by 1.5 for clarity). (e) SNR for the interdot charge transition as a function of the integration time $\tau$. Amplification with the JPA results in a factor of 2000 improvement in the SNR. Solid lines are fits to Eq. (2).

Figure 5

Normalized $Q$ quadrature amplitude as a function of $V_{\mathrm{L}}$ and $V_{\mathrm{R}}$. The scan is acquired by rastering the gate voltages over a 20-ms period. The rastering scheme is illustrated in the lower inset. Starting in the lower left-hand corner of the stability diagram, $V_{\mathrm{R}}$ is repeatedly ramped with a $40\text{−}\mu \mathrm{s}$ period. At the same time, $V_{\mathrm{L}}$ is ramped up with a 20-ms period. The rastering configuration is similar to cathode-ray-tube monitors. The high SNR then allows for real-time tuning of the DQD, which is accomplished using an intuitive user interface pictured in the upper inset.

Figure 6

Complete circuit diagram. All microwave sources and the Alazar data acquisition card are phase locked using a SRS FS725 frequency standard. The gray-colored components are not used in the present experiment.