New results from HAYSTAC’s phase II operation with a squeezed state receiver

A search for dark matter axions with masses $>10\mathrm{\mu }\mathrm{eV}/{\mathrm{c}}^2$ has been performed using the HAYSTAC experiment’s squeezed state receiver to achieve subquantum limited noise. This work includes details of the design and operation of the experiment previously used to search for axions in the mass ranges 16.96–17.12 and $17.14–17.28\mathrm{\mu }\mathrm{eV}/{\mathrm{c}}^2$ (4.100–4.140 GHz and 4.145–4.178 GHz) as well as upgrades to facilitate an extended search at higher masses. These upgrades include improvements to the data acquisition routine which have reduced the effective dead time by a factor of 5, allowing for the new region to be scanned $\sim 1.6$ times faster with comparable sensitivity. No statistically significant evidence of an axion signal is found in the range $18.44–18.71\mathrm{\mu }\mathrm{eV}/{\mathrm{c}}^2$ (4.459–4.523 GHz), leading to an aggregate upper limit exclusion at the 90% level on the axion-photon coupling of $2.06\times g_{\gamma }^{\mathrm{KSVZ}}$.

Figure 1

(a) Simplified illustration of the cavity coupled to the SSR outlining the main components and (b)–(e) how they transform the state in quadrature phase space. (b) An initially unsqueezed vacuum state (orange) sourced by a $50\Omega$ terminator is (c) sent to the SQ JPA, which squeezes the $\widehat{Y}$ quadrature. The state is then (d) reflected off of the cavity, thereby adding cavity noise (green), which would include any axion-induced signal. (e) The state is then routed to the AMP JPA, which is operated $\pi /2$ out of phase of the SQ JPA such that it amplifies the previously squeezed $\widehat{Y}$ quadrature, which contains both cavity noise and squeezed vacuum noise.

Figure 2

Top: CAD model of the main cavity installed inside the magnet’s bore. Bottom: a detailed view of the top of the cavity highlighting the tuning rod design. The axle used to tune the cavity is segmented such that only the small sections outside of either end cap are conducting, with the sections inside the cavity made of alumina. The tuning rod is further cooled by inserting a copper stem through the hollow axle, from the top, bottom, or both ends. Also shown is the JPA housing located $\sim 60\mathrm{cm}$ above the main cavity. The magnet’s 70 K and 4 K shields, and the fridge’s 4 K and 1 K shields are omitted for simplicity.

Figure 3

Schematic of HAYSTAC’s electronics including both the IF and rf components. The electronics are divided by their temperature stage, with the top stage held at room temperature, the middle at 4 K, and the bottom at 61 mK. Input lines into the system (black) are used to send signals for calibration and characterization of the system, while output lines (purple) are used to transfer signals from the output of the cavity to the DAQ to be recorded. The lines providing the pump tone to the JPAs and mixer (green) and the lines for the JPA bias currents (orange) are also shown.

Figure 4

Example transmission (top) and reflection (bottom) measurements (black) taken with the VNA in Phase IIb along with the fit (red) to Eq. (7) used to extract the relevant cavity parameters. The profile for both is normalized, with the transmission profile normalized to have unit peak power and the reflection normalized to unit power off resonance.

Figure 5

Measured values of $Q_L$ and $\beta$ as a function of ${\nu }_c$ for every run taken during the original scans in both Phase IIa (left) and Phase IIb (right) with the average value over each phase shown as a dashed line. The discontinuous jumps in both values correspond to adjustments of the antenna position to maintain $\beta$ near the optimal value.

Figure 6

Example flux tuning curves of the SQ JPA (left) and the AMP JPA (right) produced from measuring the phase response as a function of frequency $\nu$ with the VNA while varying the current $I_{\mathrm{JPA}}$ in one of the JPA’s bias coils. The resonance of the JPA at a given $I_{\mathrm{JPA}}$ is the frequency at which the phase undergoes a $\pi$ phase shift. In the tuning curve for the SQ, the AMP ’s curve is also present at $\sim 5.3\mathrm{GHz}$ but stays roughly constant due to reverse biasing the AMP’s current. The observed residual variation is due to an initially imperfect compensation and was corrected before axion data were taken. The SQ curve is also present in the AMP’s curve, but it is below the lowest frequency plotted here. Additionally, the nonsmooth regions in the curves are likely due to nonuniformity of the magnetic flux penetrating each JPA.

Figure 7

Example plot of delivered squeezing mapped over both the voltage of the variable phase shifter $V_{\theta }$ and the variable attenuator $V_A$. This mapping allows for the identification of the $V_{\theta }$ and $V_A$ which maximize squeezing, where the optimal $V_{\theta }$ corresponds to a $\pi /2+n\pi$ phase difference between the SQ and AMP, and the optimal $V_A$ corresponds to the largest SQ gain before saturation. Additionally, beyond a certain gain this fully saturates the chain, causing regions of fake squeezing seen here as the disconnected points at $V_A<2.1\mathrm{V}$.

Figure 8

Example 2Q gain profiles of the AMP and the SQ as measured by the VNA (solid lines) and their fits to a Lorentzian (dashed lines). Because the data are taken through rfl and the JPA is centered on the cavity’s resonant frequency, the cavity’s reflection profile appears as a dip at 0 MHz. When fitting the profile the $\sim 2\mathrm{MHz}$ region where this effect is most prominent is ignored so as not to distort the fit.

Figure 9

Example steps of the analysis procedure described in the text for a single spectrum taken during Phase IIb. (a) Raw data (solid blue) for a single tuning step compared to the average baseline (dashed red) calculated from the full data set. The shape of both follow from the cavity’s transmission profile, with differences between the two arising from variations of experimental properties between each tuning step. (b) Same spectrum after dividing out the average baseline (solid blue) and removing IF contaminated bins, along with the calculated residual baseline (dashed red). (c) Same spectrum after removing the residual baseline and normalized such that each bin is approximately sampled from a normal distribution with $\mu =0$ and $\sigma =1$. (d) Distribution of the observed power in each frequency bin (blue points) from (c), showing good agreement with $\mathcal{N}(0,1)$ (solid red).

Figure 10

Diagram of the relevant frequencies for HAYSTAC’s data taking and analysis, showing the relative shape of the cavity (black), AMP (red), and SQ (purple) profiles as a function of detuning and normalized to the same peak height. The measurement is taken in a homodyne configuration, with all the profiles centered at 0 MHz. As a result, each bin contains power from both positive and negative detunings (Appendix pp1-s2), and the double-sided profile is recovered by mirroring (gray cross-hatches) the spectrum around 0 MHz. Also shown is the analysis band (blue shaded region) and the probe tone (green) at 10 kHz used to monitor gain fluctuations over the course of each measurement.

Figure 11

Axion exclusions showing the two-dimensional prior update $\mathcal{U}$ in grayscale (top panel) for (a) Phase IIa [24] and (b) Phase IIb. This includes the 10% prior update contour (solid red) as well as the 90% aggregate exclusion (dashed red). (c) Results of this work shown alongside previous exclusion results from HAYSTAC Phase I [31, 32] as well as from other haloscopes RBF [58], UF [59], ADMX [19, 60, 61, 62], CAPP [18, 63, 64, 65, 66], CAST-CAPP [67], and TASEH [68]. The QCD axion model band representing the most natural KSVZ and DFSZ models is shown in yellow [69], with the benchmark KSVZ [10, 11] and DFSZ [12, 13] model lines shown as black dashed lines.

Figure 12

Plot of the cavity’s form factor for the $T{M}_{010}$ mode over the band of interest in this paper. The regions with sharp drops in $C_{010}$ are due to mode crossings and are avoided during the axion search.

Figure 13

Model of the HAYSTAC detector used for calibration measurements described in the text. Noise is sourced from a 50Ω load which can be switched between a cold ($T_{\mathrm{mc}}$) and hot ($T_{\mathrm{VTS}}$) load. This noise is transmitted through a series of discrete components, including loss elements ($\alpha$, $\rho$ and $\lambda$), gain elements ($G_S$, $G_A$, and $G_H$), and the cavity, which adds noise proportional to ${|{\chi }_{rfl}|}^2$ at its effective temperature $T_c$. The signal is then mixed down into the IF by half the JPA pump frequency (${\nu }_p$), equivalent to the cavity’s frequency (${\nu }_c$).

Figure 14

Example set of calibration spectra taken periodically to extract parameters for determining the system noise, shown for both on-resonant (solid lines) and off-resonant (dashed lines) measurements. The spectra are smoothed to remove expected statistical fluctuations and normalized relative to the on-resonant power of the “g” measurement, which is taken in the same configuration as that used to search for axions.

Figure 15

Average value over the analysis band of the three model parameters extracted from the periodic calibrations used to determine the system noise, shown for all of Phase II as a function of the cavity frequency. Error bars are the result of the systematic uncertainty on each parameter shown in Table 2.

Figure 16

Contributions to $N_{\mathrm{sys}}$ in the IF, plotted in units of power spectral density as a function of detuning using the average calibration parameters from Phase IIb shown in Table 2.