Search

The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 5$\;$cm$\times$5$\;$cm$\times$5$\;$cm TeO$_2$ crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in $^{130}$Te. Unprecedented in size amongst cryogenic calorimetric experiments, CUORE provides a promising setting for the study of exotic through-going particles. Using the first tonne-year of CUORE's exposure, we perform a search for hypothesized fractionally charged particles (FCPs), which are well-motivated by various Standard Model extensions and would have suppressed interactions with matter. No excess of FCP candidate tracks is observed over background, setting leading limits on the underground FCP flux with charges between $e/24-e/5$ at 90\% confidence level. Using the low background environment and segmented geometry of CUORE, we establish the sensitivity of tonne-scale sub-Kelvin detectors to diverse signatures of new physics., Comment: 7 pages, 5 figures

We present the model we developed to reconstruct the CUORE radioactive background based on the analysis of an experimental exposure of 1038.4 kg yr. The data reconstruction relies on a simultaneous Bayesian fit applied to energy spectra over a broad energy range. The high granularity of the CUORE detector, together with the large exposure and extended stable operations, allow for an in-depth exploration of both spatial and time dependence of backgrounds. We achieve high sensitivity to both bulk and surface activities of the materials of the setup, detecting levels as low as 10 nBq kg$^{-1}$ and 0.1 nBq cm$^{-2}$, respectively. We compare the contamination levels we extract from the background model with prior radio-assay data, which informs future background risk mitigation strategies. The results of this background model play a crucial role in constructing the background budget for the CUPID experiment as it will exploit the same CUORE infrastructure.

The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta ($0\nu \beta\beta$) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta\beta$ decay of $^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for $0\nu \beta\beta$ decay and place a lower limit on the half-life of T$_{1/2}$ $>$ 3.8 $\times$ 10$^{25}$ years (90% C.I.) with over 2 tonne$\cdot$year TeO$_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for $0\nu \beta\beta$ decay across multiple isotopes.

A Kinetic Inductance Traveling Wave amplifier (KIT) utilizes the nonlinear kinetic inductance of superconducting films, particularly Niobium Titanium Nitride (NbTiN), for parametric amplification. These amplifiers achieve remarkable performance in terms of gain, bandwidth, compression power, and frequently approach the quantum limit for noise. However, most KIT demonstrations have been isolated from practical device readout systems. Using a KIT as the first amplifier in the readout chain of an unoptimized microwave SQUID multiplexer coupled to a transition-edge sensor microcalorimeter we see an initial improvement in the flux noise. One challenge in KIT integration is the considerable microwave pump power required to drive the non-linearity. To address this, we have initiated efforts to reduce the pump power by using thinner NbTiN films and an inverted microstrip transmission line design. In this article, we present the new transmission line design, fabrication procedure, and initial device characterization -- including gain and added noise. These devices exhibit over 10 dB of gain with a 3 dB bandwidth of approximately 5.5-7.25 GHz, a maximum practical gain of 12 dB and typical gain ripple under 4 dB peak-to-peak. We observe an appreciable impedance mismatch in the NbTiN transmission line, which is likely the source of the majority of the gain ripple. Finally we perform an initial noise characterization and demonstrate system-added noise of three quanta or less over nearly the entire 3 dB bandwidth.

Recent advancements in quantum technologies and advanced detection experiments have underscored the pressing need for the detection of exceedingly weak signals within the microwave frequency spectrum. Addressing this challenge, the Josephson Traveling Wave Parametric Amplifier (JTWPA) has been proposed as a cryogenic front-end amplifier capable of approaching the quantum noise limit while providing a relevant bandwidth. This research is centered on a comprehensive numerical investigation of the JTWPA, without resorting to simplifications regarding the nonlinearity of the essential components. Specifically, this study focuses on a thorough examination of the system, characterized by coupled nonlinear differential equations representing all components of the device. Proper input and output signals at the device's boundaries are considered. The analysis of the output signals undergoing the parametric amplification process involves a detailed exploration of phase-space dynamics and Fourier spectral analysis of the output voltage. This study is conducted while considering the parameters ruling the response of the device under pump and signal excitations. In addition to the expected signal amplification, the findings reveal that the nonlinear nature of the system can give rise to unforeseen phenomena, depending on the system's operational conditions, which include: the generation of pump tone harmonics, modulation of the signal gain, and incommensurate frequency generation-effects that are not easily accommodated by simplistic linearized approaches, Comment: 5 pages, 4 figures, DARTWARS project - INFN (Italy)

Noise at the quantum limit over a broad bandwidth is a fundamental requirement for future cryogenic experiments for neutrino mass measurements, dark matter searches and Cosmic Microwave Background (CMB) measurements as well as for fast high-fidelity read-out of superconducting qubits. In the last years, Josephson Parametric Amplifiers (JPA) have demonstrated noise levels close to the quantum limit, but due to their narrow bandwidth, only few detectors or qubits per line can be read out in parallel. An alternative and innovative solution is based on superconducting parametric amplification exploiting the travelling-wave concept. Within the DARTWARS (Detector Array Readout with Travelling Wave AmplifieRS) project, we develop Kinetic Inductance Travelling-Wave Parametric Amplifiers (KI-TWPAs) for low temperature detectors and qubit read-out. KI-TWPAs are typically operated in a threewave mixing (3WM) mode and are characterised by a high gain, a high saturation power, a large amplification bandwidth and nearly quantum limited noise performance. The goal of the DARTWARS project is to optimise the KI-TWPA design, explore new materials, and investigate alternative fabrication processes in order to enhance the overall performance of the amplifier. In this contribution we present the advancements made by the DARTWARS collaboration to produce a working prototype of a KI-TWPA, from the fabrication to the characterisation.

Superconducting parametric amplifiers offer the capability to amplify feeble signals with extremely low levels of added noise, potentially reaching quantum-limited amplification. This characteristic makes them essential components in the realm of high-fidelity quantum computing and serves to propel advancements in the field of quantum sensing. In particular, Traveling-Wave Parametric Amplifiers (TWPAs) may be especially suitable for practical applications due to their multi-Gigahertz amplification bandwidth, a feature lacking in Josephson Parametric Amplifiers (JPAs), despite the latter being a more established technology. This paper presents recent developments of the DARTWARS (Detector Array Readout with Traveling Wave AmplifieRS) project, focusing on the latest prototypes of Kinetic Inductance TWPAs (KITWPAs). The project aims to develop a KITWPA capable of achieving $20\,$ dB of amplification. To enhance the production yield, the first prototypes were fabricated with half the length and expected gain of the final device. In this paper, we present the results of the characterization of one of the half-length prototypes. The measurements revealed an average amplification of approximately $9\,$dB across a $2\,$GHz bandwidth for a KITWPA spanning $17\,$mm in length.

A quantum-limited amplification chain is a fundamental advantage for any application that may benefit from the detection of very faint signals. Reading out arrays of superconducting detectors (TESs or MKIDs), resonant cavities, or qubits, calls for large bandwidth amplifiers in addition to having the lowest possible noise. At millikelvin temperatures, Kinetic Inductance Traveling-Wave Parametric Amplifiers (KI-TWPAs) working in 3-wave-mixing (3WM) and fabricated from a 20 nm thick NbTiN film have shown promising noise performances, as they can operate close to the quantum limit. However, they still require fairly high pump power. Devices that would require lower pump power would be easier to implement in readout chains, could reach the quantum limit and they would be compatible with qubit readout. A possible solution for obtaining this optimal configuration is to use a thinner superconducting film. In this work we explore the properties of NbTiN films with a thickness less than 20 nm and we report the obtained experimental characterizations in terms of critical temperature, normal resistivity, and kinetic inductance. A new design for a 3WM KI-TWPA amplifier, based on these developed superconducting films, is introduced and discussed.

A wide-bandwidth and low-noise amplification chain in the microwave regime is crucial for the efficient read-out of quantum systems based on superconducting detectors, such as Microwave Kinetic Inductance Detectors (MKIDs), Transition Edge Sensors (TESs), Magnetic Microcalorimeters (MMCs), and RF cavities, as well as qubits. Kinetic Inductance Travelling Wave Parametric Amplifiers (KI-TWPAs) operated in a three-wave mixing fashion have demonstrated exceptional dynamic range and low-noise performance, approaching the quantum limit. These amplifiers can be fabricated using a single layer of a high kinetic inductance film as weakly dispersive artificial transmission lines, with the ability to control the phase-matched bandwidth through dispersion engineering. In this study, we present the optimisation of the rf sputter-deposition process of NbTiN films using a Nb80%T20 target, with the goal of achieving precise control over film characteristics, resulting in high kinetic inductance while maintaining a high transition temperature. The parameter landscape related to the different sputtering conditions, such as pressure, power, and nitrogen flow, has been explored and the film thickness has been used as a fine-tuning parameter to adjust the properties of the final NbTiN films used for the fabrication of KI-TWPAs. As a final result, we have obtained a NbTiN film with a kinetic inductance of 8.5 pH/sq which we have exploited to fabricate KI-TWPA prototype devices, showing promising amplification performance.

Quantum Sensing is a rapidly expanding research field that finds one of its applications in Fundamental Physics, as the search for Dark Matter. Devices based on superconducting qubits have already been successfully applied in detecting few-GHz single photons via Quantum Non-Demolition measurement (QND). This technique allows us to perform repeatable measurements, bringing remarkable sensitivity improvements and dark count rate suppression in experiments based on high-precision microwave photon detection, such as for Axions and Dark Photons search. In this context, the INFN Qub-IT project goal is to realize an itinerant single-photon counter based on superconducting qubits that will exploit QND for enhancing Axion search experiments. In this study, we present Qub-IT's status towards the realization of its first superconducting qubit device, illustrating design and simulation procedures and the characterization of fabricated Coplanar Waveguide Resonators (CPWs) for readout. We match target qubit parameters and assess a few-percent level agreement between lumped and distributed element simulation models. We reach a maximum internal quality factor of 9.2x10^5 for -92 dBm on-chip readout power.

DARTWARS (Detector Array Readout with Traveling Wave AmplifieRS) is a three years project that aims to develop high-performing innovative Traveling Wave Parametric Amplifiers (TWPAs) for low temperature detectors and qubit readout (C-band). The practical development follows two different promising approaches, one based on the Josephson junctions (TWJPA) and the other one based on the kinetic inductance of a high-resistivity superconductor (KITWPA). This paper presents the advancements made by the DARTWARS collaboration to produce a first working prototype of a KITWPA., Comment: 3 pages, 4 figures. Proceeding of Pisa15th Meeting conference

The DARTWARS project has the goal of developing high-performing innovative travelling wave parametric amplifiers with high gain, large bandwidth, high saturation power, and nearly quantum-limited noise. The target frequency region for its applications is 5 - 10 GHz, with an expected noise temperature of about 600 mK. The development follows two different approaches, one based on Josephson junctions and one based on kinetic inductance of superconductors. This contribution mainly focuses on the Josephson travelling wave parametric amplifier, presenting its design, preliminary measurements and the test of homogeneity of arrays of Josephson junctions., Comment: 4 pages, 5 figures. Proceeding of Pisa15th Meeting conference. arXiv admin note: text overlap with arXiv:2111.03409

Quantum sensing is a rapidly growing field of research which is already improving sensitivity in fundamental physics experiments. The ability to control quantum devices to measure physical quantities received a major boost from superconducting qubits and the improved capacity in engineering and fabricating this type of devices. The goal of the QUB-IT project is to realize an itinerant single-photon counter exploiting Quantum Non Demolition (QND) measurements and entangled qubits, in order to surpass current devices in terms of efficiency and low dark-count rates. Such a detector has direct applications in Axion dark-matter experiments (such as QUAX[1]), which require the photon to travel along a transmission line before being measured. In this contribution we present the design and simulation of the first superconducting device consisting of a transmon qubit coupled to a resonator using Qiskit-Metal (IBM). Exploiting the Energy Participation Ratio (EPR) simulation we were able to extract the circuit Hamiltonian parameters, such as resonant frequencies, anharmonicity and qubit-resonator couplings.

The Cryogenic Underground Observatory for Rare Events (CUORE) is the most sensitive experiment searching for neutrinoless double-beta decay ($0\nu\beta\beta$) in $^{130}\text{Te}$. CUORE uses a cryogenic array of 988 TeO$_2$ calorimeters operated at $\sim$10 mK with a total mass of 741 kg. To further increase the sensitivity, the detector response must be well understood. Here, we present a non-linear thermal model for the CUORE experiment on a detector-by-detector basis. We have examined both equilibrium and dynamic electro-thermal models of detectors by numerically fitting non-linear differential equations to the detector data of a subset of CUORE channels which are well characterized and representative of all channels. We demonstrate that the hot-electron effect and electric-field dependence of resistance in NTD-Ge thermistors alone are inadequate to describe our detectors' energy dependent pulse shapes. We introduce an empirical second-order correction factor in the exponential temperature dependence of the thermistor, which produces excellent agreement with energy-dependent pulse shape data up to 6 MeV. We also present a noise analysis using the fitted thermal parameters and show that the intrinsic thermal noise is negligible compared to the observed noise for our detectors., Comment: 34 pages, 14 figures, 6 tables

The Cryogenic Underground Observatory for Rare Events (CUORE) at Laboratori Nazionali del Gran Sasso of INFN in Italy is an experiment searching for neutrinoless double beta (0$\nu\beta\beta$) decay. Its main goal is to investigate this decay in $^{130}$Te, but its ton-scale mass and low background make CUORE sensitive to other rare processes as well. In this work, we present our first results on the search for \nbb decay of $^{128}$Te, the Te isotope with the second highest natural isotopic abundance. We find no evidence for this decay, and using a Bayesian analysis we set a lower limit on the $^{128}$Te \nbb decay half-life of T$_{1/2} > 3.6 \times 10^{24}$ yr (90\% CI). This represents the most stringent limit on the half-life of this isotope, improving by over a factor 30 the previous direct search results, and exceeding those from geochemical experiments for the first time.

We discuss the consequences of the quantum uncertainty on the spectrum of the electron emitted by the $\beta$-processes of a tritium atom bound to a graphene sheet. We analyze quantitatively the issue recently raised in [Cheipesh et al., Phys. Rev. D 104, 116004 (2021)], and discuss the relevant time scales and the degrees of freedom that can contribute to the intrinsic spread in the electron energy. We perform careful calculations of the potential between tritium and graphene with different coverages and geometries. With this at hand, we propose possible avenues to mitigate the effect of the quantum uncertainty., Comment: 14 pages, 5 figures

CUORE is a large scale cryogenic experiment searching for neutrinoless double beta decay ($0\nu\beta\beta$) in $^{130}$Te. The CUORE detector is made of natural tellurium, providing the possibility of rare event searches on isotopes other than $^{130}$Te. In this work we describe a search for neutrinoless positron emitting electron capture ($0\nu\beta^+EC$) decay in $^{120}$Te with a total TeO$_2$ exposure of 355.7 kg $\cdot$ yr, corresponding to 0.2405 kg $\cdot$ yr of $^{120}$Te. Albeit $0 \nu \beta\beta$ with two final state electrons represents the most promising channel, the emission of a positron and two 511-keV $\gamma$s make $0\nu\beta^+EC$ decay signature extremely clear. To fully exploit the potential offered by the detector modularity we include events with different topology and perform a simultaneous fit of five selected signal signatures. Using blinded data we extract a median exclusion sensitivity of $3.4 \cdot 10^{22}$ yr at 90% Credibility Interval (C.I.). After unblinding we find no evidence of $0\nu\beta^+EC$ signal and set a 90% C.I. Bayesian lower limit of $2.9 \cdot 10^{22}$ yr on $^{120}$Te half-life. This result improves by an order of magnitude the existing limit from the combined analysis of CUORE-0 and Cuoricino.

While the mass differences between neutrino mass states are known, their absolute masses and mass hierarchy have not yet been determined. Determining the mass of neutrinos provides access to physics beyond the Standard Model and the resulting value has implications for the growth of large-scale structure in the universe over cosmic history. Because of the importance of the topic, a number of efforts are already underway to determine the mass of neutrinos including direct kinematic measurements and indirect measurements of astrophysical phenomena that constrain the sum of the mass eigenstates through models of cosmic evolution. Here, we advocate for a collaborative international effort to perform a kinematic determination of the effective electron neutrino mass using calorimetric measurements of the decay of 163Ho. This effort is justified by the success of current experiments using the technique, its high benefit-to-cost ratio, the value of approaches with different systematic errors, and the value of measuring the electron neutrino mass rather than the electron anti-neutrino mass., Comment: contribution to Snowmass 2021

Experiments aiming at high sensitivities usually demand for a very high statistics in order to reach more precise measurements. However, for those exploiting Low Temperature Detectors (LTDs), a high source activity may represent a drawback, if the events rate becomes comparable with the detector characteristic temporal response. Indeed, since commonly used optimum filtering approaches can only process LTDs signals well isolated in time, a non-negligible part of the recorded experimental data-set is discarded and hence constitute the dead-time. In the presented study we demonstrate that, thanks to the matrix optimum filtering approach, the dead-time of an experiment exploiting LTDs can be strongly reduced.

Noise at the quantum limit over a large bandwidth is a fundamental requirement for future applications operating at millikelvin temperatures, such as the neutrino mass measurement, the next-generation x-ray observatory, the CMB measurement, the dark matter and axion detection, and the rapid high-fidelity readout of superconducting qubits. The read out sensitivity of arrays of microcalorimeter detectors, resonant axion-detectors, and qubits, is currently limited by the noise temperature and bandwidth of the cryogenic amplifiers. The DARTWARS (Detector Array Readout with Traveling Wave AmplifieRS) project has the goal of developing high-performing innovative traveling wave parametric amplifiers (TWPAs) with a high gain, a high saturation power, and a quantum-limited or nearly quantum-limited noise. The practical development follows two different promising approaches, one based on the Josephson junctions and the other one based on the kinetic inductance of a high-resistivity superconductor. In this contribution we present the aims of the project, the adopted design solutions and preliminary results from simulations and measurements.

The advent of ultra-low noise microwave amplifiers revolutionized several research fields demanding quantum-limited technologies. Exploiting a theoretical bimodal description of a linear phase-preserving amplifier, in this contribution we analyze some of the intrinsic properties of a model architecture (i.e., an rf-SQUID based Josephson Traveling Wave Parametric Amplifier) in terms of amplification and noise generation for key case study input states (Fock and coherents). Furthermore, we present an analysis of the output signals generated by the parametric amplification mechanism when thermal noise fluctuations feed the device., Comment: 5 pages, 6 figures

The PTOLEMY transverse drift filter is a new concept to enable precision analysis of the energy spectrum of electrons near the tritium beta-decay endpoint. This paper details the implementation and optimization methods for successful operation of the filter. We present the first demonstrator that produces the required magnetic field properties with an iron return-flux magnet. Two methods for the setting of filter electrode voltages are detailed. The challenges of low-energy electron transport in cases of low field are discussed, such as the growth of the cyclotron radius with decreasing magnetic field, which puts a ceiling on filter performance relative to fixed filter dimensions. Additionally, low pitch angle trajectories are dominated by motion parallel to the magnetic field lines and introduce non-adiabatic conditions and curvature drift. To minimize these effects and maximize electron acceptance into the filter, we present a three-potential-well design to simultaneously drain the parallel and transverse kinetic energies throughout the length of the filter. These optimizations are shown, in simulation, to achieve low-energy electron transport from a 1 T iron core (or 3 T superconducting) starting field with initial kinetic energy of 18.6 keV drained to <10 eV (<1 eV) in about 80 cm. This result for low field operation paves the way for the first demonstrator of the PTOLEMY spectrometer for measurement of electrons near the tritium endpoint to be constructed at the Gran Sasso National Laboratary (LNGS) in Italy., Comment: 29 pages, 25 figures

The past few decades have seen major developments in the design and operation of cryogenic particle detectors. This technology offers an extremely good energy resolution - comparable to semiconductor detectors - and a wide choice of target materials, making low temperature calorimetric detectors ideal for a variety of particle physics applications. Rare event searches have continued to require ever greater exposures, which has driven them to ever larger cryogenic detectors, with the CUORE experiment being the first to reach a tonne-scale, mK-cooled, experimental mass. CUORE, designed to search for neutrinoless double beta decay, has been operational since 2017 at a temperature of about 10 mK. This result has been attained by the use of an unprecedentedly large cryogenic infrastructure called the CUORE cryostat: conceived, designed and commissioned for this purpose. In this article the main characteristics and features of the cryogenic facility developed for the CUORE experiment are highlighted. A brief introduction of the evolution of the field and of the past cryogenic facilities are given. The motivation behind the design and development of the CUORE cryogenic facility is detailed as are the steps taken toward realization, commissioning, and operation of the CUORE cryostat. The major challenges overcome by the collaboration and the solutions implemented throughout the building of the cryogenic facility will be discussed along with the potential improvements for future facilities. The success of CUORE has opened the door to a new generation of large-scale cryogenic facilities in numerous fields of science. Broader implications of the incredible feat achieved by the CUORE collaboration on the future cryogenic facilities in various fields ranging from neutrino and dark matter experiments to quantum computing will be examined., Comment: 45 pages, 14 figures

For a high source activity experiment, such as HOLMES, non-constant baseline pulses could constitute a great fraction of the data-set. We test the optimal filter matrix technique, proposed to process these pulses, on simulated responses of HOLMES microcalorimeters.

The possibility that neutrinos may be their own antiparticles, unique among the known fundamental particles, arises from the symmetric theory of fermions proposed by Ettore Majorana in 1937. Given the profound consequences of such Majorana neutrinos, among which is a potential explanation for the matter-antimatter asymmetry of the universe via leptogenesis, the Majorana nature of neutrinos commands intense experimental scrutiny globally; one of the primary experimental probes is neutrinoless double beta ($0 \nu \beta \beta$) decay. Here we show results from the search for $0 \nu \beta \beta$ decay of $^{130}$Te, using the latest advanced cryogenic calorimeters with the CUORE experiment. CUORE, operating just 10 millikelvin above absolute zero, has pushed the state of the art on three frontiers: the sheer mass held at such ultra-low temperatures, operational longevity, and the low levels of ionising radiation emanating from the cryogenic infrastructure. We find no evidence for $0 \nu \beta \beta$ decay and set a lower bound of $T_{1/2}^{0 \nu} > 2.2 \times 10^{25}$ years at a 90% credibility interval. We discuss potential applications of the advances made with CUORE to other fields such as direct dark matter, neutrino and nuclear physics searches and large-scale quantum computing, which can benefit from sustained operation of large payloads in a low-radioactivity, ultra-low temperature cryogenic environment.

The CUORE experiment is a large bolometric array searching for the lepton number violating neutrino-less double beta decay ($0\nu\beta\beta$) in the isotope $\mathrm{^{130}Te}$. In this work we present the latest results on two searches for the double beta decay (DBD) of $\mathrm{^{130}Te}$ to the first $0^{+}_2$ excited state of $\mathrm{^{130}Xe}$: the $0\nu\beta\beta$ decay and the Standard Model-allowed two-neutrinos double beta decay ($2\nu\beta\beta$). Both searches are based on a 372.5 kg$\times$yr TeO$_2$ exposure. The de-excitation gamma rays emitted by the excited Xe nucleus in the final state yield a unique signature, which can be searched for with low background by studying coincident events in two or more bolometers. The closely packed arrangement of the CUORE crystals constitutes a significant advantage in this regard. The median limit setting sensitivities at 90\% Credible Interval (C.I.) of the given searches were estimated as $\mathrm{S^{0\nu}_{1/2} = 5.6 \times 10^{24} \: \mathrm{yr}}$ for the ${0\nu\beta\beta}$ decay and $\mathrm{S^{2\nu}_{1/2} = 2.1 \times 10^{24} \: \mathrm{yr}}$ for the ${2\nu\beta\beta}$ decay. No significant evidence for either of the decay modes was observed and a Bayesian lower bound at $90\%$ C.I. on the decay half lives is obtained as: $\mathrm{(T_{1/2})^{0\nu}_{0^+_2} > 5.9 \times 10^{24} \: \mathrm{yr}}$ for the $0\nu\beta\beta$ mode and $\mathrm{(T_{1/2})^{2\nu}_{0^+_2} > 1.3 \times 10^{24} \: \mathrm{yr}}$ for the $2\nu\beta\beta$ mode. These represent the most stringent limits on the DBD of $^{130}$Te to excited states and improve by a factor $\sim5$ the previous results on this process., Comment: 13 pages, 6 figures