Gram-scale cryogenic calorimeters for rare-event searches

The energy threshold of a cryogenic calorimeter can be lowered by reducing its size. This is of importance since the resulting increase in signal rate enables new approaches in rare-event searches, including the detection of MeV mass dark matter and coherent scattering of reactor or solar neutrinos. A scaling law for energy threshold vs detector size is given. We analyze the possibility of lowering the threshold of a gram-scale cryogenic calorimeter to the few eV regime. A prototype 0.5 g ${\mathrm{Al}}_2{\mathrm{O}}_3$ device achieved an energy threshold of $E_{\text{th}}=(19.7\pm 0.9)\mathrm{eV}$, the lowest value reported for a macroscopic calorimeter.

Figure 1

Nuclear-recoil spectra on ${\mathrm{CaWO}}_4$ for CNNS of antineutrinos from a 4 GW nuclear reactor at a distance of 40 m, for $200\mathrm{MeV}/{\mathrm{c}}^2$ mass DM ($\sigma =1\mathrm{pb}$), and for CNNS of solar neutrinos. The grey area indicates a range of measured background levels for shallow sites [3, 4] and at a deep-underground location (dotted line) [5]. Closed circles indicate previous cryogenic detector technology [2, 6]; the performance of the detector presented here is depicted as an open circle (surface operation). The expected threshold of the presented detector at a deep-underground location is shown as a diamond.

Figure 2

The scaling law for ${\mathrm{CaWO}}_4$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$ cubes fitted to results of cryogenic ${\mathrm{CaWO}}_4$ (triangles) and ${\mathrm{Al}}_2{\mathrm{O}}_3$ (cross) detectors [2, 11, 12]. The lines show the $M^{2/3}$ behavior according to Eq. (3). The expected values for the prototype described here under low-background conditions are shown by the red stars. There is agreement with the expected performance of 24 g ${\mathrm{CaWO}}_4$ detectors (green error bar) [6]. The result presented here is shown by a blue circle.

Figure 3

Randomly chosen pulses from different energy ranges fitted with the truncated template (red lines). Upper frame: An event with an energy of about 100 eV where the detector response is entirely linear. Lower frame: A saturated 5.9 keV pulse. Above 0.4 V the pulse shapes deviate significantly from the template pulse.

Figure 4

Main frame: Goodness of the template fit (TF; rms value). The truncation level is 0.4 V and the truncated template fit (TTF) yields an almost energy-independent rms value (black). The ${}^{55}\mathrm{Fe}$ ${\mathrm{K}}_{\alpha }$ x-ray line is reconstructed at a pulse height of $(3.925\pm 0.003)\mathrm{V}$. The impact of pulse saturation on the energy reconstruction is demonstrated by a classic TF without truncation (red). The rms value rises significantly for energies above the linear region. Inset: Ratio of the reconstructed energy by the TTF and the optimum filter method (OFM). In the linear region both methods agree on the 1% level (see the text). Above the truncation limit the OFM fails to reconstruct the correct energy, as expected, due to a different pulse shape caused by saturation.

Figure 5

Final energy spectrum up to 10 keV acquired with the prototype ${\mathrm{Al}}_2{\mathrm{O}}_3$ detector in the presence of a ${}^{55}\mathrm{Fe}$ calibration source.

Figure 6

Left: Pulse sample and optimum filter output in the time domain. Right: Comparison of the baseline noise derived by the TTF (black histogram) and the OFM (red dots). Gaussian fits to the data are shown.

Figure 7

Demonstration of the optimum trigger. Upper plot: A 19.7 eV standard pulse is superimposed on a randomly chosen noise sample (onset at sample 2000). Lower plot: Output of the optimum filter applied to the sample. The pulse is clearly triggered while noise contributions are suppressed sufficiently below threshold, which is set at a pulse height of 13.0 mV (see the text).

Figure 8

Determination of the trigger threshold. Randomly chosen noise samples are superimposed with template pulses of different discrete energies (red crosses). The optimum trigger is applied to these samples yielding the energy-dependent trigger efficiency (left y axis). The data are fitted by an error function, giving an energy threshold of $E_{\text{th}}=(19.7\pm 0.1)\mathrm{eV}$ for 50% efficiency. The width ${\sigma }_{th}=(3.82\pm 0.15)\mathrm{eV}$ is in agreement with the variance of the baseline noise. The reconstructed energy of pure noise samples after filtering is shown in a histogram (black, right y axis).