We describe the first implementation of a Josephson Traveling Wave Parametric Amplifier (JTWPA) in an axion dark matter search. The operation of the JTWPA for a period of about two weeks achieved sensitivity to axion-like particle dark matter with axion–photon couplings above 10−13 Ge V−1 over a narrow range of axion masses centered around 19.84 µeV by tuning the resonant frequency of the cavity over the frequency range of 4796.7–4799.5 MHz. The JTWPA was operated in the insert of the axion dark matter experiment as part of an independent receiver chain that was attached to a 0.56-l cavity. The ability of the JTWPA to deliver high gain over a wide (3 GHz) bandwidth has engendered interest from those aiming to perform broadband axion searches, a longstanding goal in this field.
I. MOTIVATION
We aim to compose 85%2 of the matter content of the universe, dark matter appears necessary to explain a variety of observations, from galactic rotation curves and gravitational lensing to the anisotropies of the cosmic microwave background and the properties of galaxy cluster collisions.2–5 Despite the scope of these observations, the nature of dark matter remains a mystery. One particularly promising candidate is the axion, which has the unique ability not only to account for all the dark matter6–8 but also to solve the so-called strong-CP problem.9–12
One method to render the axion visible is called the resonant cavity haloscope, first proposed by Pierre Sikivie.13,14 The Axion Dark Matter eXperiment (ADMX) is one such experiment that is unique in its ability to detect Dine–Fischler–Srednicki–Zhitnitsky (DFSZ) axions.1,15,16 Other haloscopes have achieved sensitivity to the band around the Kim–Schifman–Vainshtein–Zakharov (KSVZ) model of the axion.17–27 Of the two, the DFSZ axion is the more difficult to detect, with signals of an order of magnitude smaller than the KSVZ axion. Sensitivity to the DFSZ axion is therefore a noteworthy achievement. Such progress is attributable to the advent of ultra-low-noise quantum amplifiers, such as the Microstrip SQUID Amplifier (MSA)28 and the Josephson Parametric Amplifier (JPA).29,30 A limitation of these amplifiers is their narrowband nature. Recent developments have enabled the fabrication of modified JPAs that can provide bandwidth over as much as 640 MHz.31 Nevertheless, the subsequently developed Josephson Traveling Wave Parametric Amplifier (JTWPA)32 provides power gain over a much wider bandwidth of several GHz, which could further enable broadband axion searches. We note that one other experiment implemented a JTWPA in a receiver chain intended for axion searches,33 though no axion search was performed as it was not placed in a magnetic field.
A. Josephson traveling wave parametric amplifier
The JTWPA consists of a lumped element transmission line, where Josephson junctions are the non-linear inductive element. When a microwave signal travels down the line, the non-linear inductance causes four-wave mixing. This feature enables the JTWPA to provide broadband power gain.32 Because of this feature, it is recognized that the JTWPA is generally well-suited for axion searches that aim to cover a wider range of the axion parameter space.34 Broadband experiments are ideal for axion searches involving transient signals appearing off-resonance and allow for the possibility of multimode searches.35,36 Another advantage of the JTWPA is that it does not require a circulator to separate incoming and outgoing modes, enabling a compact receiver design. This helpful feature is ideal for axion searches aiming to take advantage of any extra space in a volume that is typically constrained by the diameter of a magnet bore. This characteristic may be especially advantageous in the case of multi-cavity searches that require a scaling up of microwave components contained within a field-cancellation coil.
II. JTWPA DEMONSTRATION
In an effort to integrate a JTWPA into an axion search, a prototype experiment was operated within the ADMX magnet bore. The “sidecar” cavity is mounted on top of the ADMX main cavity,1 residing in a magnetic field of about 3.83 T just above the main experiment’s superconducting magnet.37 Although it uses an independent receiver chain, its operation is secondary to the main experiment. Data-taking is therefore likely to cease when technical issues pertaining to the main experiment are encountered. The 0.56-ℓ sidecar cavity can be disassembled into two halves, thus allowing a single tuning rod to be mounted inside with ease. Typical measurements of the sidecar loaded quality factor, QL, were ∼700. The quality factor was lower than expected due to larger than expected material losses in the alumina axles as well as leakage through the RF feedthrough holding the readout antenna. The form factor, representing the overlap of the static magnetic and axion electric field, was computed to be 0.41 ± 0.06 using detailed simulations performed in both CST (Computer Simulation Technology) Microwave Studio Suite38 and COMSOL.39 The cavity is coupled by an antenna to a receiver chain that exists independently of the main experiment.
At present, the current iteration of the sidecar uses a JTWPA as its first-stage amplifier and a heterostructure field-effect transistor (HFET) amplifier as its second-stage amplifier.40 The diagram of the receiver chain for the sidecar cavity is shown in Fig. 1. The receiver chain allows for transmission and reflection measurements to determine the cavity frequency, quality factor, and antenna coupling. The JTWPA is located on the output line, acting as the first-stage amplifier and conduit for power coming from the cavity. The JTWPA is operated by providing a pump tone coming from a local oscillator in the warm electronics space. The particular JTWPA used in this search was fabricated at and acquired from MIT Lincoln Laboratory.41 It is made from niobium, with a critical temperature of 9.3 K.
RF schematic of the sidecar cavity for this run. The JTWPA resides between two circulators on the output line. These two circulators are used to prevent power from reflecting into the cavity. All these components are mounted within a so-called quantum amplifier package that is thermally sunk and bolted to the main ADMX cavity via a cold finger. The package itself resides in a low-field region that is maintained using a field cancellation coil, and the amplifiers are protected with an additional mu metal shielding.
RF schematic of the sidecar cavity for this run. The JTWPA resides between two circulators on the output line. These two circulators are used to prevent power from reflecting into the cavity. All these components are mounted within a so-called quantum amplifier package that is thermally sunk and bolted to the main ADMX cavity via a cold finger. The package itself resides in a low-field region that is maintained using a field cancellation coil, and the amplifiers are protected with an additional mu metal shielding.
Data were acquired for about two weeks with the sidecar cavity until the main experiment required a magnet ramp down. Our first implementation investigated only a narrow frequency range that was accessible with the sidecar cavity due to a sticking tuning rod. Nevertheless, these results represent the first demonstration of an axion search with a JTWPA.
A. Noise performance
Wideband power gain of the JTWPA from 4 to 7 GHz, measured during data-taking operations. The magnetic field is on, and the JTWPA temperature is 100 mK. The JTWPA provided gain with pump tone frequencies roughly between 7 and 8.5 GHz.
Wideband power gain of the JTWPA from 4 to 7 GHz, measured during data-taking operations. The magnetic field is on, and the JTWPA temperature is 100 mK. The JTWPA provided gain with pump tone frequencies roughly between 7 and 8.5 GHz.
Transmission measurements through the JTWPA, acquired by routing power from the cavity bypass line through the output line, with two different pump frequencies applied to the JTWPA, shown in solid (blue) and dashed (orange) curves. The gain peaks are spaced roughly 38 MHz apart. The JTWPA was biased so that the 2-MHz power spectrum was centered on a region with maximum gain.
Transmission measurements through the JTWPA, acquired by routing power from the cavity bypass line through the output line, with two different pump frequencies applied to the JTWPA, shown in solid (blue) and dashed (orange) curves. The gain peaks are spaced roughly 38 MHz apart. The JTWPA was biased so that the 2-MHz power spectrum was centered on a region with maximum gain.
Mean digitized power of sidecar as a function of the temperature of the final stage attenuator for two frequencies off resonance: 4.6 GHz (left) and 4.9 GHz (right). Data were acquired on either side of the resonance because THFET can easily be determined using Eq. (4) off-cavity resonance. The value of THFET on resonance can then be computed by interpolating between the two off-resonance values for THFET. The actual temperature sensor for the x-axis was mounted to the quantum amplifier package, which is thermally connected to the final stage attenuator on the bypass line. The gain of the second-stage and downstream electronics and their associated noise temperature were extracted from the fit. Each data point consisted of an integration time of 10 s. Data are not evenly spaced in temperature space because of the non-linear warming of the ADMX insert. This value of THFET, along with the JTWPA SNRI, was used to compute the system noise.
Mean digitized power of sidecar as a function of the temperature of the final stage attenuator for two frequencies off resonance: 4.6 GHz (left) and 4.9 GHz (right). Data were acquired on either side of the resonance because THFET can easily be determined using Eq. (4) off-cavity resonance. The value of THFET on resonance can then be computed by interpolating between the two off-resonance values for THFET. The actual temperature sensor for the x-axis was mounted to the quantum amplifier package, which is thermally connected to the final stage attenuator on the bypass line. The gain of the second-stage and downstream electronics and their associated noise temperature were extracted from the fit. Each data point consisted of an integration time of 10 s. Data are not evenly spaced in temperature space because of the non-linear warming of the ADMX insert. This value of THFET, along with the JTWPA SNRI, was used to compute the system noise.
Downstream receiver noise temperature (THFET) as a function of frequency. To obtain the downstream receiver noise temperature at any given frequency, power was sampled and integrated for 10 s while the final stage attenuator on the bypass line was heated. The resulting data were fit using Eq. (4). The value of THFET at 4.798 GHz, shown in red, was computed by interpolating between the two nearest values for THFET. This value of THFET, along with the JTWPA SNRI, were used to compute the system noise. The uncertainties on THFET are a combination of the statistical uncertainty and the temperature sensor uncertainty.
Downstream receiver noise temperature (THFET) as a function of frequency. To obtain the downstream receiver noise temperature at any given frequency, power was sampled and integrated for 10 s while the final stage attenuator on the bypass line was heated. The resulting data were fit using Eq. (4). The value of THFET at 4.798 GHz, shown in red, was computed by interpolating between the two nearest values for THFET. This value of THFET, along with the JTWPA SNRI, were used to compute the system noise. The uncertainties on THFET are a combination of the statistical uncertainty and the temperature sensor uncertainty.
The SNRI is continuously optimized throughout data-taking to minimize the system noise. The wide bandwidth of the JTWPA simplifies the amplifier optimization process. A JTWPA requires only the adjustment of the pump frequency and power, an advantage over a JPA that requires the adjustment of the former together with a bias current to tune its resonant frequency. A feature of the JTWPA is that its gain is not flat across a wide range. Instead, there are oscillations in the gain of about 10 dB, with peaks spaced roughly 38 MHz apart. This feature arises from imperfect impedance matching to the Josephson junctions in the transmission line that constitutes the JTWPA. The exact spacing and height of the peaks depend on the individual JTWPA. Adjusting the frequency of the JTWPA pump tone adjusts the frequencies of these peaks and, therefore, optimizes the gain at a particular frequency. A demonstration of this effect is shown in the plot of the receiver gain as a function of frequency, as shown in Fig. 3. In-situ measurements of the JTWPA gain were acquired by reversing the warm RF switch in Fig. 1 toward the VNA. Likewise, power measurements were made by reversing it toward the warm receiver. The SNRI associated with a given spectrum was computed by smoothing and interpolating between measurements of the JTWPA SNRI before and after sampling power from the cavity to acquire a reasonable value over the time duration of data acquisition.
We measured the attenuation of all cables and components between the cavity and the JTWPA in liquid nitrogen. We then scaled the measured attenuation to 100 mK, the temperature stage of the quantum amplifier package, using the temperature scaling ratios described in the cable specifications sheet.46 The value of ɛ, which we measured to be 0.40 ± 0.04 in linear units, was then used to compute the system noise. This measurement includes attenuation from the JTWPA, which has an associated insertion loss of −3.0 ± 0.3 dB47 at 4.798 GHz. Assuming an average JTWPA SNRI of 8.25 dB, the average system noise was measured to be 1.38 ± 0.08 K, with the dominant uncertainty coming from the uncertainty in the attenuation from the cavity to the JTWPA. This value is within the expected range of the system noise using a JTWPA.48 At a frequency of about 4.798 GHz, the standard quantum limit is 226 mK. The measured total system noise is therefore about 6 times the standard quantum limit. The JTWPA contributes about 1.5 ± 1.7 noise photons in this setup.33
III. AXION DATA-TAKING
Padé approximant fit an individual raw spectrum for the sidecar. A strong peak in the spectrum was determined to be interference coming from IF electronics, as it appeared always in the same bins, even in power spectra acquired far off cavity resonance. It was removed by masking bins 2800–4000, explaining the gap in the data, above.
Padé approximant fit an individual raw spectrum for the sidecar. A strong peak in the spectrum was determined to be interference coming from IF electronics, as it appeared always in the same bins, even in power spectra acquired far off cavity resonance. It was removed by masking bins 2800–4000, explaining the gap in the data, above.
Noise distribution (blue) and Gaussian fit (red) of the data after removing the receiver shape for the sidecar. After background subtraction, the distribution of powers measured is well represented by a Gaussian, as expected for white noise. The mean of the fit was computed to be −0.007, with a sigma of 0.990.
Noise distribution (blue) and Gaussian fit (red) of the data after removing the receiver shape for the sidecar. After background subtraction, the distribution of powers measured is well represented by a Gaussian, as expected for white noise. The mean of the fit was computed to be −0.007, with a sigma of 0.990.
A strong peak between 4797.5 and 4797.75 MHz was determined to be due to radio-frequency interference by examining scans far from cavity resonance and observing that the peak occupied the same IF bins of the power spectrum regardless of the cavity frequency. A mask was created to exclude these frequencies from the final limit plot. The total bandwidth that was excluded from any individual raw spectrum due to the mask was 120 kHz.
Axion candidates were defined as any power excesses greater than a 3σ fluctuation above the average power level from the flattened spectrum. Two candidates were flagged but were not identified as axion-like due to a lack of persistence between scans. The systematic uncertainties are shown in Table I. The dominant systematic uncertainties come from the quality factor. The sensitivity achieved by this experiment can be seen in Fig. 8, which excludes axion dark matter with an assumption that axions constitute all of the dark matter, taken to have a density of 0.45 Ge V/cm3.50 The sensitivity can be seen in the larger context of axion searches in Fig. 9. Optimal filtering was used with the assumption of a Maxwell–Boltzmann line shape.51 The shape of the excluded region shown in Fig. 8 arises from the fact that the frequency of the TM010 mode shifted during the course of data-taking. These frequency shifts coincided with a filling of the liquid helium reservoir, which is known to induce mechanical vibrations in the insert. The mechanical vibrations cause small shifts in the positions of the antenna and tuning rod. These vibrations resulted in slight shifts in the resonant frequency of the cavity, despite the fact that the cavity was not intentionally tuned during the period of this data acquisition. The resonant frequency of the cavity drifted from about 4.7975 to 4.7990 GHz throughout the course of data-taking.
Dominant sources of systematic uncertainty. The uncertainties were added in quadrature to attain the uncertainty on the total axion power from the cavity, shown in the bottom row. For the first entry, B is the magnetic field, V is the volume, and C010 is the form factor. The last row shows the total uncertainty of the axion power from the cavity.
| Source | Fractional |
|---|---|
| uncertainty | |
| B2VC010 | 0.15 |
| Q | 0.2 |
| Antenna coupling | 0.01 |
| THFET/ɛ | 0.11 |
| SNRI measurement | 0.11 |
| Total on power | 0.26 |
| Source | Fractional |
|---|---|
| uncertainty | |
| B2VC010 | 0.15 |
| Q | 0.2 |
| Antenna coupling | 0.01 |
| THFET/ɛ | 0.11 |
| SNRI measurement | 0.11 |
| Total on power | 0.26 |
Sensitivity plot from the sidecar data with a JTWPA, assuming an axion density of 0.45 GeV/cm3, equal to the total dark matter density at the Earth. The two lines represent DFSZ and KSVZ models. The prior limit from the CAST experiment is also shown.52
Sensitivity plot from the sidecar data with a JTWPA, assuming an axion density of 0.45 GeV/cm3, equal to the total dark matter density at the Earth. The two lines represent DFSZ and KSVZ models. The prior limit from the CAST experiment is also shown.52
Sensitivity plot in the context of nearby searches. Green shows prior exclusions from the ADMX Collaboration. Red shows this work.
Sensitivity plot in the context of nearby searches. Green shows prior exclusions from the ADMX Collaboration. Red shows this work.
IV. CONCLUSION
In conclusion, we have demonstrated the sustained operation of a JTWPA for axion searches. While the data analyzed in this run were acquired in about 2 weeks, the JTWPA provided reasonable gain for a period of several months during engineering runs prior to data acquisition. Furthermore, an incident occurred in which an accidental increase in the magnet current led to a magnetic field of about 0.41 T in the vicinity of the JTWPA. As a result, the JTWPA was temporarily disabled, but its operation was fully restored after the insert temperature was raised above the critical temperature of niobium. We note that a similar recovery is expected for both the MSA and JPA. Such resilience against inadvertently applied fields bodes well for future axion experiments. This work sets the stage for broadband axion searches, in which we take full advantage of the ability of the JTWPA to operate with high gain over a wider bandwidth. The wide bandwidth of the JTWPA may be useful in frequency-multiplexed axion searches.53 It is clear that improvements to the noise performance can be made, and studies of JTWPA performance in small magnetic fields are warranted. Future searches that aim to use a JTWPA should continue to improve the means by which we measure the system noise temperature, and consider including an RF line to bypass the JTWPA. This bypass would provide some ability to isolate the JTWPA and, therefore, study its impact on the receiver chain. Finally, increasing the gain of the JTWPA would allow for a lower system noise temperature. It remains true that a big advantage of JPA over JTWPA is its near quantum-limited noise performance, which is valuable in extremely sensitive measurements such as the axion search. Improvements to the gain may be possible if magnetic field flux penetration into the amplifier package could be further reduced, and the gain optimization script improved. Although the JTWPA noise performance is less optimal than that of other quantum amplifiers, it remains true that it achieves wideband sensitivity that could be used in future axion search applications.
ACKNOWLEDGMENTS
This work was supported by the U.S. Department of Energy through Grants Nos. DE-SC0009800, DESC0009723, DE-SC0010296, DE-SC0010280, DE-SC0011665, DEFG02-97ER41029, DEFG02-96ER40956, DEAC52-07NA27344, DEC03-76SF00098, and DE-SC0017987. Fermilab is a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. Additional support was provided by the Heising-Simons Foundation and the Lawrence Livermore National Laboratory and Pacific Northwest National Laboratory LDRD offices (LLNL Release No. LLNL-JRNL-825283). UWA was funded by the ARC Center of Excellence for Engineered Quantum Systems (Grant No. CE170100009) and Dark Matter Particle Physics (Grant No. CE200100008). Ben McAllister was funded by the Forrest Research Foundation. Tatsumi Nitta was supported by JSPS Overseas Research Fellowships No. 202060305. MIT Lincoln Laboratory acknowledges support from the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), under Air Force Contract No. FA8721-05-C-0002. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, or the U.S. Government.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
C. Bartram: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). T. Braine: Data curation (equal); Investigation (equal); Writing – review & editing (equal). R. Cervantes: Conceptualization (equal); Data curation (equal); Investigation (equal); Software (equal); Writing – review & editing (equal). N. Crisosto: Data curation (equal); Investigation (equal); Writing – review & editing (equal). N. Du: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). G. Leum: Data curation (equal); Investigation (equal). P. Mohapatra: Data curation (equal); Investigation (equal). T. Nitta: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). L. J. Rosenberg: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal). G. Rybka: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). J. Yang: Data curation (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). John Clarke: Writing – review & editing (equal). I. Siddiqi: Resources (equal). A. Agrawal: Writing – review & editing (equal). A. V. Dixit: Writing – review & editing (equal). M. H. Awida: Writing – review & editing (equal). A. S. Chou: Formal analysis (equal); Writing – review & editing (equal). M. Hollister: Writing – review & editing (equal). S. Knirck: Writing – review & editing (equal). A. Sonnenschein: Project administration (equal); Resources (equal); Writing – review & editing (equal). W. Wester: Writing – review & editing (equal). J. R. Gleason: Conceptualization (equal); Writing – review & editing (equal). A. T. Hipp: Writing – review & editing (equal). S. Jois: Writing – review & editing (equal). P. Sikivie: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). N. S. Sullivan: Methodology (equal); Writing – review & editing (equal). D. B. Tanner: Conceptualization (equal); Investigation (equal); Methodology (equal); Writing – review & editing (equal). E. Lentz: Formal analysis (equal); Writing – review & editing (equal). R. Khatiwada: Investigation (equal); Writing – review & editing (equal). C. Cisneros: Writing – review & editing (equal). N. Robertson: Writing – review & editing (equal). N. Woollett: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Writing – review & editing (equal). L. D. Duffy: Writing – review & editing (equal). C. Boutan: Conceptualization (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – review & editing (equal). M. Jones: Writing – review & editing (equal). B. H. LaRoque: Conceptualization (equal); Data curation (equal); Methodology (equal); Software (equal); Writing – review & editing (equal). N. S. Oblath: Software (equal); Writing – review & editing (equal). M. S. Taubman: Writing – review & editing (equal). E. J. Daw: Writing – review & editing (equal). M. G. Perry: Writing – review & editing (equal). J. H. Buckley: Writing – review & editing (equal). C. Gaikwad: Writing – review & editing (equal). J. Hoffman: Conceptualization (equal); Investigation (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). K. Murch: Writing – review & editing (equal). M. Goryachev: Writing – review & editing (equal). B. T. McAllister: Writing – review & editing (equal). A. Quiskamp: Writing – review & editing (equal). C. Thomson: Investigation (equal); Writing – review & editing (equal). M. E. Tobar(ADMX Collaboration): Writing – review & editing (equal). V. Bolkhovsky: Resources (equal); Writing – review & editing (equal). G. Calusine: Resources (equal); Writing – review & editing (equal). W. Oliver: Resources (equal); Writing – review & editing (equal). K. Serniak: Resources (equal); Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.
