Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method.

Abstract Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytical…

Johnson-Nyquist Noise Effects in Neutron Electric-Dipole-Moment Experiments

Magnetic Johnson-Nyquist noise (JNN) originating from metal electrodes, used to create a static electric field in neutron electric-dipole-moment (nEDM) experiments, may limit the sensitivity of measurements. We present here the first dedicated study on JNN applied to a large-scale long-measurement-time experiment with the implementation of a co-magnetometry. In this study, we derive surface- and volume-averaged root-mean-square normal noise amplitudes at a certain frequency bandwidth for a cylindrical geometry. In addition, we model the source of noise as a finite number of current dipoles and demonstrate a method to simulate temporal and three-dimensional spatial dependencies of JNN. The c…

New constraints on Lorentz invariance violation from the neutron electric dipole moment

We propose an original test of Lorentz invariance in the interaction between a particle spin and an electromagnetic field and report on a first measurement using ultracold neutrons. We used a high sensitivity neutron electric dipole moment (nEDM) spectrometer and searched for a direction dependence of a nEDM signal leading to a modulation of its magnitude at periods of 12 and 24 hours. We constrain such a modulation to $d_{12} < 15 \times 10^{-25} \ e\,{\rm cm}$ and $d_{24} < 10 \times 10^{-25} \ e\,{\rm cm}$ at 95~\% C.L. The result translates into a limit on the energy scale for this type of Lorentz violation effect at the level of ${\cal E}_{LV} > 10^{10}$~GeV.

Optically pumped Cs magnetometers enabling a high-sensitivity search for the neutron electric dipole moment

An array of 16 laser-pumped scalar Cs magnetometers was part of the neutron electric dipole moment (nEDM) experiment taking data at the Paul Scherrer Institute in 2015 and 2016. It was deployed to measure the gradients of the experiment's magnetic field and to monitor their temporal evolution. The originality of the array lies in its compact design, in which a single near-infrared diode laser drives all magnetometers that are located in a high-vacuum chamber, with a selection of the sensors mounted on a high-voltage electrode. We describe details of the Cs sensors' construction and modes of operation, emphasizing the accuracy and sensitivity of the magnetic-field readout. We present two app…

Measurement of the permanent electric dipole moment of the neutron

We present the result of an experiment to measure the electric dipole moment (EDM) of the neutron at the Paul Scherrer Institute using Ramsey’s method of separated oscillating magnetic fields with ultracold neutrons. Our measurement stands in the long history of EDM experiments probing physics violating time-reversal invariance. The salient features of this experiment were the use of a 199Hg comagnetometer and an array of optically pumped cesium vapor magnetometers to cancel and correct for magnetic-field changes. The statistical analysis was performed on blinded datasets by two separate groups, while the estimation of systematic effects profited from an unprecedented knowledge of the magne…

Cyclotron radiation emission spectroscopy signal classification with machine learning in project 8

The Cyclotron Radiation Emission Spectroscopy (CRES) technique pioneered by Project 8 measures electromagnetic radiation from individual electrons gyrating in a background magnetic field to construct a highly precise energy spectrum for beta decay studies and other applications. The detector, magnetic trap geometry, and electron dynamics give rise to a multitude of complex electron signal structures which carry information about distinguishing physical traits. With machine learning models, we develop a scheme based on these traits to analyze and classify CRES signals. Understanding and proper use of these traits will be instrumental to improve cyclotron frequency reconstruction and help Pro…

Constraining interactions mediated by axion-like particles with ultracold neutrons

We report a new limit on a possible short range spin-dependent interaction from the precise measurement of the ratio of Larmor precession frequencies of stored ultracold neutrons and Hg199 atoms confined in the same volume. The measurement was performed in a ~1μT vertical magnetic holding field with the apparatus searching for a permanent electric dipole moment of the neutron at the Paul Scherrer Institute. A possible coupling between freely precessing polarized neutron spins and unpolarized nucleons of the wall material can be investigated by searching for a tiny change of the precession frequencies of neutron and mercury spins. Such a frequency change can be interpreted as a consequence o…

Copper coated carbon fiber reinforced plastics for high and ultra high vacuum applications

We have used copper-coated carbon fiber reinforced plastic (CuCFRP) for the construction of high and ultra-high vacuum recipients. The vacuum performance is found to be comparable to typical stainless steel used for this purpose. In test recipients we have reached pressures of 2E-8 mbar and measured a desorption rate of 1E-11 mbar*liter/s/cm^2; no degradation over time (2 years) has been found. Suitability for baking has been found to depend on the CFRP production process, presumably on the temperature of the autoclave curing. Together with other unique properties of CuCFRP such as low weight and being nearly non-magnetic, this makes it an ideal material for many high-end vacuum application…

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g−2 Experiment

The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the preces…

Results from the Project 8 phase-1 cyclotron radiation emission spectroscopy detector

The Project 8 collaboration seeks to measure the absolute neutrino mass scale by means of precision spectroscopy of the beta decay of tritium. Our technique, cyclotron radiation emission spectroscopy, measures the frequency of the radiation emitted by electrons produced by decays in an ambient magnetic field. Because the cyclotron frequency is inversely proportional to the electron's Lorentz factor, this is also a measurement of the electron's energy. In order to demonstrate the viability of this technique, we have assembled and successfully operated a prototype system, which uses a rectangular waveguide to collect the cyclotron radiation from internal conversion electrons emitted from a ga…

Bayesian Analysis of a Future Beta Decay Experiment's Sensitivity to Neutrino Mass Scale and Ordering

Bayesian modeling techniques enable sensitivity analyses that incorporate detailed expectations regarding future experiments. A model-based approach also allows one to evaluate inferences and predicted outcomes, by calibrating (or measuring) the consequences incurred when certain results are reported. We present procedures for calibrating predictions of an experiment's sensitivity to both continuous and discrete parameters. Using these procedures and a new Bayesian model of the $\beta$-decay spectrum, we assess a high-precision $\beta$-decay experiment's sensitivity to the neutrino mass scale and ordering, for one assumed design scenario. We find that such an experiment could measure the el…

Gravitational depolarization of ultracold neutrons : comparison with data

We compare the expected effects of so-called gravitationally enhanced depolarization of ultracold neutrons to measurements carried out in a spin-precession chamber exposed to a variety of vertical magnetic-field gradients. In particular, we have investigated the dependence upon these field gradients of spin depolarization rates and also of shifts in the measured neutron Larmor precession frequency. We find excellent qualitative agreement, with gravitationally enhanced depolarization accounting for several previously unexplained features in the data.

Determining the neutrino mass with cyclotron radiation emission spectroscopy—Project 8

The most sensitive direct method to establish the absolute neutrino mass is observation of the endpoint of the tritium beta-decay spectrum. Cyclotron Radiation Emission Spectroscopy (CRES) is a precision spectrographic technique that can probe much of the unexplored neutrino mass range with $\mathcal{O}({\rm eV})$ resolution. A lower bound of $m(\nu_e) \gtrsim 9(0.1)\, {\rm meV}$ is set by observations of neutrino oscillations, while the KATRIN Experiment - the current-generation tritium beta-decay experiment that is based on Magnetic Adiabatic Collimation with an Electrostatic (MAC-E) filter - will achieve a sensitivity of $m(\nu_e) \lesssim 0.2\,{\rm eV}$. The CRES technique aims to avoid…

A measurement of the neutron to 199Hg magnetic moment ratio

The neutron gyromagnetic ratio has been measured relative to that of the 199Hg atom with an uncertainty of 0.8 ppm. We employed an apparatus where ultracold neutrons and mercury atoms are stored in the same volume and report the result γn/γHg=3.8424574(30).

Dynamic stabilization of the magnetic field surrounding the neutron electric dipole moment spectrometer at the Paul Scherrer Institute

The Surrounding Field Compensation (SFC) system described in this work is installed around the four-layer Mu-metal magnetic shield of the neutron electric dipole moment spectrometer located at the Paul Scherrer Institute. The SFC system reduces the DC component of the external magnetic field by a factor of about 20. Within a control volume of approximately 2.5m x 2.5m x 3m disturbances of the magnetic field are attenuated by factors of 5 to 50 at a bandwidth from $10^{-3}$ Hz up to 0.5 Hz, which corresponds to integration times longer than several hundreds of seconds and represent the important timescale for the nEDM measurement. These shielding factors apply to random environmental noise f…

Demonstration of sensitivity increase in mercury free-spin-precession magnetometers due to laser-based readout for neutron electric dipole moment searches

International audience; We report on a laser based $^{199}$Hg co-magnetometer deployed in an experiment searching for a permanent electric dipole moment of the neutron. We demonstrate a more than five times increased signal to-noise-ratio in a direct comparison measurement with its $^{204}$Hg discharge bulb-based predecessor. An improved data model for the extraction of important system parameters such as the degrees of absorption and polarization is derived. Laser- and lamp-based data-sets can be consistently described by the improved model which permits to compare measurements using the two different light sources and to explain the increase in magnetometer performance. The laser-based ma…

PROJECT 8: A FREQUENCY-BASED APPROACH TO MEASURE THE ABSOLUTE NEUTRINO MASS SCALE

MC calculations for the nEDM experiment systematics

International audience; The nEDM experiment hosted at the Paul Scherrer Institute is the flagship project at the new ultracold neutron facility. Estimations of systematic effects for the determination of the neutron electric dipole moment play an important role in this project. Experimental studies are supported by Monte Carlo simulations using the MCUCN code. Here we briefly present first results on the experimental benchmark of the model, and on the evaluation of the storage time dependence of the centre of mass of UCN in the nEDM precession chamber. Such time dependence calculations will serve as consistency tests for future measurements involving field gradient corrections of the Ramsey…

Testing isotropy of the universe using the Ramsey resonance technique on ultracold neutron spins

Physics at the Planck scale could be revealed by looking for tiny violations of fundamental symmetries in low energy experiments. In 2008, a sensitive test of the isotropy of the Universe using has been performed with stored ultracold neutrons (UCN), this is the first clock-comparison experiment performed with free neutrons. During several days we monitored the Larmor frequency of neutron spins in a weak magnetic field using the Ramsey resonance technique. An non-zero cosmic axial field, violating rotational symmetry, would induce a daily variation of the precession frequency. Our null result constitutes one of the most stringent tests of Lorentz invariance to date.

Project 8 Phase III Design Concept

We present a working concept for Phase III of the Project 8 experiment, aiming to achieve a neutrino mass sensitivity of $2~\mathrm{eV}$ ($90~\%$ C.L.) using a large volume of molecular tritium and a phased antenna array. The detection system is discussed in detail.

Observation of Gravitationally Induced Vertical Striation of Polarized Ultracold Neutrons by Spin-Echo Spectroscopy.

We describe a spin-echo method for ultracold neutrons (UCNs) confined in a precession chamber and exposed to a $|B_0|=1~\text{\mu T}$ magnetic field. We have demonstrated that the analysis of UCN spin-echo resonance signals in combination with knowledge of the ambient magnetic field provides an excellent method by which to reconstruct the energy spectrum of a confined ensemble of neutrons. The method takes advantage of the relative dephasing of spins arising from a gravitationally induced striation of stored UCN of different energies, and also permits an improved determination of the vertical magnetic-field gradient with an exceptional accuracy of $1.1~\text{pT/cm}$. This novel combination …

Locust: C++ software for simulation of RF detection

The Locust simulation package is a new C++ software tool developed to simulate the measurement of time-varying electromagnetic fields using RF detection techniques. Modularity and flexibility allow for arbitrary input signals, while concurrently supporting tight integration with physics-based simulations as input. External signals driven by the Kassiopeia particle tracking package are discussed, demonstrating conditional feedback between Locust and Kassiopeia during software execution. An application of the simulation to the Project 8 experiment is described. Locust is publicly available at https://github.com/project8/locust_mc.

Electron Radiated Power in Cyclotron Radiation Emission Spectroscopy Experiments

The recently developed technique of Cyclotron Radiation Emission Spectroscopy (CRES) uses frequency information from the cyclotron motion of an electron in a magnetic bottle to infer its kinetic energy. Here we derive the expected radio frequency signal from an electron in a waveguide CRES apparatus from first principles. We demonstrate that the frequency-domain signal is rich in information about the electron's kinematic parameters, and extract a set of measurables that in a suitably designed system are sufficient for disentangling the electron's kinetic energy from the rest of its kinematic features. This lays the groundwork for high-resolution energy measurements in future CRES experimen…