1 Introduction

Our Center has been actively engaged in axion search experiments based on the haloscope concept [1]. In these experiments, our detector consists of a microwave cavity immersed in a high magnetic field and cooled to temperatures as low as a few millikelvin. The interaction of axions with the magnetic field can cause their conversion into photons, and the cavity serves to resonantly enhance these photons. If the signal frequency aligns closely with the cavity resonance, the signal becomes detectable with low-noise readout equipment. The expected signal levels fall within the range of 10\(^{-24}\)–10\(^{-22}\) W, imposing stringent requirements on the first stage of our readout system.

The converted signal power depends on the axion mass, which is currently unknown. Therefore, we must scan across a vast frequency range to detect this signal. The speed of this frequency scan follows:

$$\begin{aligned} S\propto \frac{g_\gamma ^4}{(\textrm{SNR})^2}\eta \frac{1}{{T_s}^2}{B_0}^4V^2{C}^2Q^2 \end{aligned}$$
(1)

In this formula, \(g_\gamma\) corresponds to the model-dependent coupling coefficient, taking the values of 0.97 and 0.36 for the Kim–Shifman–Vainshtein–Zakharov (KSVZ) [2, 3] and DFSZ [4, 5] models, respectively. \(\textrm{SNR}\) represents the signal-to-noise ratio, while \(\eta\) signifies the overall data acquisition (DAQ) efficiency. \(T_s\) denotes the system noise temperature, \(B_0\) stands for the external magnetic field, V represents the cavity volume, C characterizes the form factor associated with the resonant mode, indicating the alignment of the external magnetic field with the cavity electric field for the relevant mode, and Q indicates the cavity quality factor.

As Eq. (1) shows, the scanning speed is inversely proportional to the square of the system noise temperature. Therefore, our objective is to minimize system noise temperature to enhance our scanning rate. The system noise comprises the noise from the cavity and other components in our setup and the added noise from the amplifiers, which at best can achieve quantum-limited noise. Currently, in our center, we employ flux-driven JPAs, which exhibit noise levels close to the quantum limit [6].

2 Josephson parametric amplifier

Figure 1 presents the equivalent circuit diagram of a flux-driven JPA. This circuit consists of a \(\lambda /4\) coplanar-waveguide resonator coupled through a capacitor \(C_c\) to the transmission line outside, with a superconducting quantum interference device (SQUID) attached at the resonator’s end. The SQUID functions as a variable inductance, with its value depending on the magnetic flux passing through the SQUID’s loop. To adjust the resonance frequency \(f_r\), a superconducting coil introduces the DC flux \(\Phi\) through the SQUID loop. Parametric amplification is achieved by modulating the flux within the SQUID using a separate pump signal introduced through a dedicated transmission line and coupled to the SQUID.

The JPA operates in a three-wave mixing mode where the frequencies of the pump \(f_p\), the signal \(f_s\), and the idler \(f_i\) satisfy the relationship \(f_p = f_s + f_i\). The signal is first directed to the coupling capacitor to reach the JPA. The reflected and amplified signal then travels back through the same capacitor to be transmitted to the external circuitry. To separate incoming and outgoing waves, a circulator is employed (see Fig. 2).

Fig. 1
figure 1

Flux-driven Josephson parametric amplifier diagram. Components arranged from left to right: coupling capacitor, \(\lambda /4\) resonator, SQUID, flux bias, and pump lines

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Fig. 2
figure 2

JPA readout diagram. Components arranged from left to right: noise source for Y-factor noise measurements; directional coupler DC to inject test signals; RF circulator C with JPA; RF isolator (IS; cold amplifiers AMP1-AMP2, room temperature amplifier AMP3

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3 Readout

The readout chain used for the tests is shown in Fig. 2. On the left, there is a noise source described in [7]. A directional coupler (DC) follows admitting test signals from a vector network analyzer VNA into the system. An RF circulator (C) is used to separate the JPA input and output signals. An RF isolator (IS) prevents unwanted signal reflection from HEMT amplifiers and reduces the transmission of HEMT noise to the JPA. Two cold HEMT amplifiers (AMP1) and (AMP2), optimized for low-temperature operation, enhance the JPA output signal. Finally, a room temperature RF amplifier (AMP3) handles the final stage of signal amplification before the signal is directed to the switch, which applies the output signal to either the input of the VNA or a spectrum analyzer (SA), depending on the test. The VNA and SA connected to the computer with GPIB interfaces for further processing.

4 Extending the amplification bandwidth by using multiple JPAs

Our JPAs, designed for frequencies between 1 and 1.5 GHz, exhibit an instantaneous bandwidth exceeding 150 kHz at 20 dB gain. With a flux bias applied to the SQUIDs, we can tune their central frequency within the range of 45–60 MHz [8]. The cavity bandwidth is 5–8 times larger, and to cover the entire frequency range of the CAPP-MAX cavity, we would have needed to replace our JPA multiple times. Given the complexity of our cryogenic system, need to ramp the magnet up and down, and capacity of our helium recovery system, this would have resulted in significant downtime. Typically, the process of replacing a JPA necessitates two to three weeks of intensive work on the cryogenic fridge before we can resume the experiment. Furthermore, every cooldown of the cryogenic system consumes a significant amount of liquid helium (LHe). This is a growing concern due to the escalating costs of acquiring and managing LHe.

These challenges prompted us to seek solutions to extend the tuning range of our system, reduce downtime, and optimize helium usage. The following sections will elaborate on the strategies we explored and implemented to overcome these issues effectively.

Fig. 3
figure 3

Left: Simplified readout diagram based on a JPA. Right: Diagram of readout based on parallel connection of 3 JPAs

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We propose a new method to extend the scanning bandwidth, by the parallel connection of JPAs designed for different frequency ranges (Fig. 3). This approach leverages the fact that, within the 1 to 2 GHz range, the size of our device and package structures remains considerably smaller than the wavelength, making long-line effects negligible. We have developed a specialized printed circuit board (PCB) (see Fig. 4) that enables us to continue utilizing the same JPA holder as previously described in [8].

Fig. 4
figure 4

The left image shows the PCB for the parallel connection of 3 JPAs, with arrows indicating the contact pads for signal input/output and applying the pump. The DC flux bias is common for all of the JPAs and is created by a 200-turn coil wound with superconducting wire around the PCB holder (not shown). The right image depicts the dependence of resonance frequency on bias current for three JPAs connected in parallel, with the JPA pumps switched off

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5 Tests and Results

For our tests, we positioned the JPAs within a three-layer magnetic shield, as described in [8], to protect them from external magnetic fields and interferences. The shield was then cooled down to 36 mK inside a dry dilution refrigerator. This temperature is intentionally set slightly above the fridge’s base temperature of 11 mK with a PID controller to ensure temperature stability and prevent any unwanted fluctuations during the testing process. These temperature fluctuations can lead to undesirable variations in the JPA’s gain and noise, potentially compromising the test results.

In our initial tests, we determined the resonance frequency of each of the three JPAs in the assembly by measuring the S21 phase using a VNA (Fig. 2). These measurements were conducted in passive mode, where no pump is applied, and were repeated for different DC bias currents (Fig. 4, right).

In the second test, we disconnected the VNA and connected the output of AMP3 to the SA, following the procedure detailed in [9]. Initially, we measured gain dependence (paramap) from pump frequency and power. In the frequency ranges shown in Table 1, all three JPAs exhibited peak gains of approximately 20 dB, aligning with the desired JPA gain for our experiments. Finally, we conducted measurements of the frequency-dependent system noise temperatures using the Y-factor method by changing the temperature of the noise source. As shown in Table 1, there are small band overlaps between the JPAs. In these cases, we selected the JPA with the lower noise temperature. As illustrated in Fig. 5, the JPAs demonstrated effective operations without visible mutual interference, resulting in a system noise temperature of about 150 mK.

Table 1 Operation frequency range and bandwidth of JPAs
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Fig. 5
figure 5

Dependence of the total system noise temperature on the frequency, with each JPA represented by a different color. The input of the chain is terminated with a 50 \(\Omega\) noise source that is thermally stabilized at 36 mK. The brown line corresponds to the quantum noise limit

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6 Conclusion

Our parallel JPA configuration has proven to be a promising solution for extending the scanning range in a single cooldown for our experiment. By connecting three JPAs with operating frequency band 48–52 MHz and different central frequencies in parallel, we have effectively expanded our coverage up to 140 MHz, approximately three times the original range, and reduced the need for frequent JPA replacements. These developments did not negatively affect JPA behavior compare to using a single JPA. This approach enhances our scanning capabilities by reducing the downtime associated with JPA replacements and minimizes the loss of expensive liquid helium during cooldowns.