CERES: A Cryogenic Experiment to Reconstruct Energy Systematics in TeO$_{2}$ bolometers

This paper presents the design, current status, and future upgrade plans for the CERES experiment, a dedicated cryogenic setup developed to directly measure and characterize the position-dependent systematic effects on energy scale and resolution in TeO$_2$ bolometers used for rare event searches.

The Gist

Imagine you are trying to listen to a whisper in a giant, empty cathedral. If you stand right next to the person whispering, you hear it clearly. If you stand at the back of the room, the sound is fainter and arrives a split-second later. Now, imagine that the cathedral itself is a crystal, and the "whisper" is a tiny burst of energy from a radioactive particle.

This paper introduces CERES, a new experiment designed to figure out exactly how the "sound" of that energy changes depending on where it happens inside a crystal.

Here is the breakdown of what the scientists are doing, using simple analogies:

The Big Picture: Why Do We Care?

Scientists are building massive, super-cold detectors to catch incredibly rare events (like a specific type of nuclear decay that could explain why the universe exists). These detectors are like ultra-sensitive microphones.

For a long time, scientists assumed these microphones heard everything the same way, no matter where the sound came from inside the crystal. They thought, "If a particle hits the top, bottom, or middle, the detector reads the exact same energy."

However, recent hints suggest this isn't true. The "sound" might change slightly depending on the location. If you don't account for this, your measurements might be slightly off, or you might mistake background noise for a real discovery. CERES is built to map out these differences.

The Experiment: The "Crystal Guitar"

To test this, the team built a special setup using Tellurium Dioxide (TeO2) crystals.

1. The Crystal: Instead of using huge blocks, they cut the crystals into thin strips (like slices of bread) and slabs.
2. The Microphones: They attached two very sensitive sensors (called NTDs) to the ends of the crystal strips. Think of these as microphones placed at opposite ends of a long hallway.
3. The "Whisper": Instead of using actual radioactive particles (which are hard to control precisely), they use a UV LED connected to a fiber optic cable. They shine a tiny, precise dot of light onto specific spots on the crystal. This light acts like a tiny hammer, creating a vibration (a "phonon") that travels through the crystal.

How It Works: The "Harp" Mechanism

One of the tricky parts of this experiment is that the whole thing must be kept at temperatures colder than outer space (near absolute zero). You can't just stick a motor inside to move the light around; the heat from the motor would ruin the experiment.

So, the team built a clever device called a "harp."

• Imagine a copper frame with slots in it, like a harp.
• They can slide the fiber optic cable (the "light source") into different slots.
• This allows them to "tap" the crystal at different precise locations without moving any heavy machinery or adding heat.

What They Found (So Far)

In their first test, they shone the light on three different spots: the center of the crystal, and spots closer to each of the two sensors.

• Timing: When the light hit the center, the "sound" reached both sensors at almost the same time. When it hit near one sensor, that sensor heard it first. They measured this time difference to be about 86 microseconds (a tiny fraction of a second). This proves that time can tell you where the event happened.
• Energy: They also checked if the "loudness" (energy) changed based on location. They found the sensors agreed on the energy level to within 1.4%. This is very precise, but the tiny differences they see are exactly what they want to study.
• Shape: The shape of the "sound wave" (the pulse) looked slightly different depending on where the light hit.

The Future: Mapping the Crystal

The paper concludes that CERES is just getting started. Now that they have proven the setup works, they plan to:

• Map the whole crystal: Systematically tap the crystal at hundreds of spots to create a full "heat map" of how the detector responds.
• Use computers: They will run simulations to predict how vibrations travel through the crystal to match their real-world data.
• Try new sensors: They plan to test faster sensors to see if they can catch even more subtle details.
• Upgrade the "Harp": They are planning to install a tiny, cryogenic mirror system (like a laser pointer on a remote control) to scan the crystal automatically without having to open the freezer every time.

In short: CERES is a high-tech "ear" that is learning to tell exactly where a sound came from inside a crystal, ensuring that future experiments searching for the secrets of the universe don't get confused by the crystal's own quirks.

Technical Summary

Technical Summary: CERES – A Cryogenic Experiment to Reconstruct Energy Systematics in TeO2 Bolometers

Problem Statement
Low-temperature crystal calorimetry (bolometry) is a premier tool for rare event searches, such as neutrinoless double beta decay ($0\nu\beta\beta$), due to its high energy resolution and low intrinsic background. However, current detectors, such as those in the CUORE and CUPID experiments, utilize Neutron-Transmutation-Doped (NTD) Germanium sensors that have long been assumed to possess a position-independent response. Recent studies suggest this assumption may be flawed; both energy scale and energy resolution may vary based on the spatial location and topology of energy deposition within the detector. These uncharacterized systematic effects could limit the ability to define a fiducial volume to reject surface backgrounds (e.g., degraded alpha particles) or to perform topological identification of multi-site gamma events. Furthermore, while fast sensors (e.g., in AMORE-II) have shown position-dependent effects, the specific impact of event topology on the response of TeO$_2$ crystals equipped with NTD sensors remains to be precisely quantified.

Methodology and Experimental Design
The Cryogenic Experiment to Reconstruct Energy Systematics (CERES) is a dedicated experiment designed to directly measure and characterize the position dependence of calorimetric response in Tellurium Dioxide (TeO$_2$) crystals. The experiment reduces the effective dimensionality of the crystals to perform one- and two-dimensional surface scans using "strip" (5 cm $\times$ 3 mm $\times$ 3 mm) and "slab" (5 cm $\times$ 5 cm $\times$ 3 mm) wafers.

Key design features include:

• Radiation Source: Instead of traditional silicon heaters, CERES uses a 255 nm UV LED coupled to single-ended optical fibers. This choice ensures the excitation of electron-hole pairs (above the TeO$_2$ band gap) to produce a phonon spectrum similar to ionizing radiation, while isolating position-dependent effects inherent to the crystal, thermal links, and sensors without adding significant heat capacity.
• Positioning Mechanism: To avoid the high heat load of motors at cryogenic temperatures, the experiment utilizes a custom copper "harp" with multiple slots. Optical fibers are secured in these slots above the crystal, allowing for precise, configurable localization of the radiation source without moving parts inside the cryostat.
• Sensors: The setup employs NTD sensors and is designed to accommodate Transition Edge Sensors (TES). Sensors are placed on the ends of the crystal surface, closer to the energy deposition site than the weak thermal links, to enhance phonon collection.
• Observables: The experiment targets three primary observables: timing, amplitude, and pulse shape. Timing differences (expected to be on the order of 10 $\mu$s given the speed of sound in TeO$_2$) and amplitude ratios are used to reconstruct position and energy sharing.

Initial Commissioning and Results
The initial validation run utilized a strip crystal with two NTDs mounted on the face normal to the [001] direction. Three optical fibers (OF1, OF2, OF3) were positioned symmetrically, with OF1 at the center and OF2/3 closer to the respective sensors. Data were collected at 15–16 mK in a dilution refrigerator. To ensure stability, data acquisition occurred during 250-second intervals with the pulse-tube cooler off, using a 4 Hz LED pulse rate.

Key findings from the commissioning phase include:

• Linearity: A scan of LED pulse widths (50–500 $\mu$s) revealed that NTDs deviate from linearity at 300 $\mu$s. Consequently, a pulse width of 200 $\mu$s was selected for subsequent operations to remain within the linear regime.
• Energy Sharing Resolution: Using the amplitude ratio between the two NTDs as a proxy for energy sharing, the experiment measured a resolution of $\sigma(A_1/A_2) = 0.59\%$, corresponding to a Full Width at Half Maximum (FWHM) of 1.4%.
• Timing Resolution: By defining arrival time as the point where the pulse reaches 10% of its maximum amplitude, the timing resolution for the difference between NTD1 and NTD2 was measured as $\sigma(t) = 86$ $\mu$s (FWHM = 203 $\mu$s).
• Pulse Shape: Amplitude-normalized average pulses showed distinct shape differences depending on the fiber location (OF1 vs. OF2/3), though further analysis is required to fully quantify the contribution of position to these variations.

Significance and Future Work
The paper claims that CERES provides a novel framework for measuring and parameterizing position-dependent effects in TeO$_2$ crystals, which is a critical step toward improving the energy resolution of current and future $0\nu\beta\beta$ experiments. By characterizing these systematics, the experiment aims to enable the development of position and topological reconstruction capabilities in macro-calorimeters.

Future work outlined in the paper includes:

• Simulation: Performing Monte Carlo simulations of ballistic phonon propagation (Geant4) and finite-element simulations of thermal phonon propagation (COMSOL) to model the observed effects.
• Expanded Radiation Sources: Broadening the study to include gamma, x-ray, and alpha sources to investigate single- and multi-site topologies.
• Sensor Upgrades: Extending the methodology to Li$_2$MoO$_4$ crystals (relevant for CUPID) and integrating TES sensors to study ballistic-to-thermal phonon conversion effects.
• System Upgrades: Implementing a cryo-compatible MEMS mirror optical system for high-resolution scanning without repeated thermal cycles and installing an anti-vibrational suspension system to allow stable data-taking while the pulse-tube cooler is active.