Abstract At University College London (UCL), our group had the great privilege of working closely with Professor Basil Hiley in the pursuit of experiments exploring the foundations of quantum theory. Among the many projects we undertook with Basil, one held particular significance for all of us: the experimental observation of the Bohm velocity. It was a long-standing ambition of Basil’s to see the ideas he and David Bohm had developed put to the test in the laboratory. The experimental techniques used to obtain the results presented in this paper form the foundation of an ongoing theoretical and early-stage experimental investigation at UCL, in which a velocity-sensitive Raman population transfer scheme is employed to encode the Bohm velocity into an atomic system by coherently transferring populations between two quantum states using a pair of laser beams. In my talk, I briefly discussed several of the theoretical and experimental approaches that the group had developed together over the years. One such approach involves a subset of weak measurements, in which phase information that is normally inaccessible or lost in a strong projective measurement can instead be encoded into the transition amplitude probability density (TAPD). This paper focuses on this aspect of weak measurement theory and its experimental realisation. At UCL, the Quantum Foundations Group has demonstrated that such measurements can be implemented using atomic systems, specifically for metastable helium. These efforts represent a significant part of our time with Basil, and our ongoing attempt to bring foundational quantum ideas into the laboratory.

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study).

Gravitational waves proved hard to detect experimentally and yet carry high energy fluxes. Conversely, the technology for electromagnetic waves is sophisticated, easily available, and highly sensitive. Various proposals have been made to use the conversion of a gravitational wave into an electromagnetic wave to generate signals that could be detected. We present test results from a novel electromagnetic antenna, efficient at the very low frequencies needed to explore the signals from supermassive black holes mergers. These will eventually be studied by the laser interferometric space antenna (LISA) at wavelengths between $10<^>{8}$ and $10<^>{11}$ m. Common forms of electromagnetic antennae are only efficient when the ratio of wavelength, $\lambda$, to antenna length, L, is roughly between 0.1 and 10. This paper proposes a scheme for a realistic ground-based electromagnetic antenna, 'the resistive antenna', which operates efficiently at a ratio $\frac{\lambda }{L}$ of more than $10<^>{6}$. The first estimates of ambient noise at these low frequencies from field trials of such a device are presented. The measured levels of ambient noise result in this detection scheme having a sensitivity much worse than LISA. The antenna design described in this communication may also have application in other fields.

AbstractThe NEMO-3 results for the double-$$\beta $$ β decay of $$^{150}$$ 150 Nd to the 0$$^+_1$$ 1 + and 2$$^+_1$$ 1 + excited states of $$^{150}$$ 150 Sm are reported. The data recorded during 5.25 year with 36.6 g of the isotope $$^{150}$$ 150 Nd are used in the analysis. The signal of the $$2\nu \beta \beta $$ 2 ν β β transition to the 0$$^+_1$$ 1 + excited state is detected with a statistical significance exceeding 5$$\sigma $$ σ . The half-life is measured to be $$T_{1/2}^{2\nu \beta \beta }(0^+_1) = \left[ 1.11 ^{+0.19}_{-0.14} \,\left( \hbox {stat}\right) ^{+0.17}_{-0.15}\,\left( \hbox {syst}\right) \right] \times 10^{20}$$ T 1 / 2 2 ν β β ( 0 1 + ) = 1 . 11 - 0.14 + 0.19 stat - 0.15 + 0.17 syst × 10 20 year, which is the most precise value that has been measured to date. 90% confidence-level limits are set for the other decay modes. For the $$2\nu \beta \beta $$ 2 ν β β decay to the 2$$^+_1$$ 1 + level the limit is $$T^{2\nu \beta \beta }_{1/2}(2^+_1) > 2.42 \times 10^{20}~\hbox {year}$$ T 1 / 2 2 ν β β ( 2 1 + ) > 2.42 × 10 20 year . The limits on the $$0\nu \beta \beta $$ 0 ν β β decay to the 0$$^+_1$$ 1 + and 2$$^+_1$$ 1 + levels of $$^{150}$$ 150 Sm are significantly improved to $$T_{1/2}^{0\nu \beta \beta }(0^+_1) > 1.36 \times 10^{22}~\hbox {year}$$ T 1 / 2 0 ν β β ( 0 1 + ) > 1.36 × 10 22 year and $$T_{1/2}^{0\nu \beta \beta }(2^+_1) > 1.26 \times 10^{22}~\hbox {year}$$ T 1 / 2 0 ν β β ( 2 1 + ) > 1.26 × 10 22 year .

The NEMO-3 results for the double- β decay of ^150 Nd to the 0 ^+_1 and 2 ^+_1 excited states of ^150 Sm are reported. The data recorded during 5.25 year with 36.6 g of the isotope ^150 Nd are used in the analysis. The signal of the 2νββ transition to the 0 ^+_1 excited state is detected with a statistical significance exceeding 5 σ . The half-life is measured to be T_1/2^2νββ(0^+_1) = [ 1.11 ^+0.19_-0.14 ( stat) ^+0.17_-0.15 ( syst) ] × 10^20 year, which is the most precise value that has been measured to date. 90 2νββ decay to the 2 ^+_1 level the limit is T^2νββ_1/2(2^+_1) > 2.42 × 10^20 year . The limits on the 0νββ decay to the 0 ^+_1 and 2 ^+_1 levels of ^150 Sm are significantly improved to T_1/2^0νββ(0^+_1) > 1.36 × 10^22 year and T_1/2^0νββ(2^+_1) > 1.26 × 10^22 year .

The NEMO-3 results for the double-beta decay of150Nd to the 0+1and 2+1excited states of150Sm are reported The data recorded during 5.25 year with 36.6 g of the iso-tope150Nd are used in the analysis. The signal of the 2 nu beta beta transition to the 0+1excited state is detected with a statisti-cal significance exceeding 5 sigma. The half-life is measured tobeT(1/2)(0 nu beta beta)((0+1)=[1.11+0.19-0.14(stat)+0.17-0.15(syst)]x10(20) year, which is the most precise value that has been measuredto date. 90% confidence-level limits are set for the otherdecay modes. For the 2 nu beta beta decay to the 2+1level the limitisT2 nu beta beta 1/2(2+1)>2.42x10 (20) year. The limits on the 0 nu beta beta decay to the 0+1and 2+1levels of150Sm are significantlyimproved toT0 nu beta beta 1/2(0+1)>1.36x1022year and T-1/2(0 nu beta beta)(2+1)>1.26x10(22)year

Abstract The NEMO-3 results for the double- $$\beta $$ β decay of $$^{150}$$ 150 Nd to the 0 $$^+_1$$ 1 + and 2 $$^+_1$$ 1 + excited states of $$^{150}$$ 150 Sm are reported. The data recorded during 5.25 year with 36.6 g of the isotope $$^{150}$$ 150 Nd are used in the analysis. The signal of the $$2\nu \beta \beta $$ 2 ν β β transition to the 0 $$^+_1$$ 1 + excited state is detected with a statistical significance exceeding 5 $$\sigma $$ σ . The half-life is measured to be $$T_{1/2}^{2\nu \beta \beta }(0^+_1) = \left[ 1.11 ^{+0.19}_{-0.14} \,\left( \hbox {stat}\right) ^{+0.17}_{-0.15}\,\left( \hbox {syst}\right) \right] \times 10^{20}$$ T 1 / 2 2 ν β β ( 0 1 + ) = 1 . 11 - 0.14 + 0.19 stat - 0.15 + 0.17 syst × 10 20 year, which is the most precise value that has been measured to date. 90% confidence-level limits are set for the other decay modes. For the $$2\nu \beta \beta $$ 2 ν β β decay to the 2 $$^+_1$$ 1 + level the limit is $$T^{2\nu \beta \beta }_{1/2}(2^+_1) > 2.42 \times 10^{20}~\hbox {year}$$ T 1 / 2 2 ν β β ( 2 1 + ) > 2.42 × 10 20 year . The limits on the $$0\nu \beta \beta $$ 0 ν β β decay to the 0 $$^+_1$$ 1 + and 2 $$^+_1$$ 1 + levels of $$^{150}$$ 150 Sm are significantly improved to $$T_{1/2}^{0\nu \beta \beta }(0^+_1) > 1.36 \times 10^{22}~\hbox {year}$$ T 1 / 2 0 ν β β ( 0 1 + ) > 1.36 × 10 22 year and $$T_{1/2}^{0\nu \beta \beta }(2^+_1) > 1.26 \times 10^{22}~\hbox {year}$$ T 1 / 2 0 ν β β ( 2 1 + ) > 1.26 × 10 22 year .

We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies.

We describe the creation and characterisation of a velocity tunable, spin-polarized beam of slow metastable argon atoms. We show that the beam velocity can be determined with a precision below 1% using matter-wave interferometry. The profile of the interference pattern was also used to determine the velocity spread of the beam, as well as the Van der Waals (VdW) co-efficient for the interaction between the metastable atoms and the multi-slit silicon nitride grating. The VdW co-efficient was determined to be C 3 = 1.84 ± 0.17 a.u., in good agreement with values derived from spectroscopic data. Finally, the spin polarization of the beam produced during acceleration of the beam was also measured, demonstrating a spatially uniform spin polarization of 96% in the m = +2 state.

The SuperNEMO experiment will search for neutrinoless double-beta decay (0νββ), and study the Standard-Model double-beta decay process (2νββ). The SuperNEMO technology can measure the energy of each of the electrons produced in a double-beta (ββ) decay, and can reconstruct the topology of their individual tracks. The study of the double-beta decay spectrum requires very accurate energy calibration to be carried out periodically. The SuperNEMO Demonstrator Module will be calibrated using 42 calibration sources, each consisting of a droplet of ^207Bi within a frame assembly. The quality of these sources, which depends upon the entire ^207Bi droplet being contained within the frame, is key for correctly calibrating SuperNEMO's energy response. In this paper, we present a novel method for precisely measuring the exact geometry of the deposition of ^207Bi droplets within the frames, using Timepix pixel detectors. We studied 49 different sources and selected 42 high-quality sources with the most central source positioning.

Double-beta decays of $^{100}$Mo from the 6.0195-year exposure of a 6.914 kg high-purity sample were recorded by the NEMO-3 experiment that searched for neutrinoless double-beta decays. These ultra-rare transitions to $^{100}$Ru have a half-life of approximately $7\times10^{18}$ years, and have been used to conduct the first ever search for periodic variations of this decay mode. The Lomb-Scargle periodogram technique, and its error-weighted extension, were employed to look for periodic modulations of the half-life. Monte Carlo modeling was used to study the modulation sensitivity of the data over a broad range of amplitudes and frequencies. Data show no evidence of modulations with amplitude greater than 2.5% in the frequency range of $0.33225\,{\rm y^{-1}}$ to $365.25\,{\rm y^{-1}}$.

The double-beta decay of Se-82 to the 0(1)(+) excited state of Kr-82 has been studied with the NEMO-3 detector using 0.93 kg of enriched Se-82 measured for 4.75 y, corresponding to an exposure of 4.42 kg.y. A dedicated analysis to reconstruct the gamma-rays has been performed to search for events in the 2e2 gamma channel. No evidence of a 2 nu beta beta decay to the 0(1)(+) state has been observed and a limit of T-1/2(2 nu) (Se-82, 0(gs)(+) -> 0(1)(+)) > 1.3 x 10(21) y at 90% CL has been set. Concerning the 0 nu beta beta decay to the 0(1)(+)-state, a limit for this decay has been obtained with T-1/2(0 nu) (Se-82, 0(gs)(+) -> 0(1)(+)) > 2.3 x 10(22) y at 90% CL, independently from the 2 nu beta beta decay process. These results are obtained for the first time with a tracko-calo detector, reconstructing every particle in the final state. (C) 2020 Elsevier B.V. All rights reserved.

The full data set of the NEMO-3 experiment has been used to measure the half-life of the two-neutrino double beta decay of $^{100}$Mo to the ground state of $^{100}$Ru, $T_{1/2} = \left[ 6.81 \pm 0.01\,\left(\mbox{stat}\right) ^{+0.38}_{-0.40}\,\left(\mbox{syst}\right) \right] \times10^{18}$ y. The two-electron energy sum, single electron energy spectra and distribution of the angle between the electrons are presented with an unprecedented statistics of $5\times10^5$ events and a signal-to-background ratio of ~80. Clear evidence for the Single State Dominance model is found for this nuclear transition. Limits on Majoron emitting neutrinoless double beta decay modes with spectral indices of n=2,3,7, as well as constraints on Lorentz invariance violation and on the bosonic neutrino contribution to the two-neutrino double beta decay mode are obtained.

Abstract A radiochemical method for producing 82Se sources with an ultra-low level of contamination of natural radionuclides (40K, decay products of 232Th and 238U) has been developed based on cation-exchange chromatographic purification with reverse removal of impurities. It includes chromatographic separation (purification), reduction, conditioning (which includes decantation, centrifugation, washing, grinding, and drying), and 82Se foil production. The conditioning stage, during which highly dispersed elemental selenium is obtained by the reduction of purified selenious acid (H2SeO3) with sulfur dioxide (SO2) represents the crucial step in the preparation of radiopure 82Se samples. The natural selenium (600 g) was first produced in this procedure in order to refine the method. The technique developed was then used to produce 2.5 kg of radiopure enriched selenium (82Se). The produced 82Se samples were wrapped in polyethylene (12 μm thick) and radionuclides present in the sample were analyzed with the BiPo-3 detector. The radiopurity of the plastic materials (chromatographic column material and polypropylene chemical vessels), which were used at all stages, was determined by instrumental neutron activation analysis. The radiopurity of the 82Se foils was checked by measurements with the BiPo-3 spectrometer, which confirmed the high purity of the final product. The measured contamination level for 208Tl was 8–54 μBq/kg, and for 214Bi the detection limit of 600 μBq/kg has been reached.

A method for measuring the weak value of spin for atoms is proposed using a variant of the original Stern–Gerlach apparatus. A full simulation of an experiment for observing the real part of the weak value using the impulsive approximation has been carried out. Our predictions show a displacement of the beam of helium atoms in the metastable 23S1 state, Δw, that is within the resolution of conventional microchannel plate detectors indicating that this type of experiment is feasible. Our analysis also determines the experimental parameters that will give an accurate determination of the weak value of spin. Preliminary experimental results are shown for helium, neon and argon in the 23S1 and 3P2 metastable states, respectively.

Using data from the NEMO-3 experiment, we have measured the two-neutrino double beta decay ($2\nu\beta\beta$) half-life of $^{82}$Se as $T_{1/2}^{2\nu} = \left[ 9.39 \pm 0.17\,\left(\mbox{stat}\right) \pm 0.58\,\left(\mbox{syst}\right)\right] \times 10^{19}$ y under the single-state dominance hypothesis for this nuclear transition. The corresponding nuclear matrix element is $\left|M^{2\nu}\right| = 0.0498 \pm 0.0016$. In addition, a search for neutrinoless double beta decay ($0\nu\beta\beta$) using 0.93 kg of $^{82}$Se observed for a total of 5.25 y has been conducted and no evidence for a signal has been found. The resulting half-life limit of $T_{1/2}^{0\nu} > 2.5 \times 10^{23} \,\mbox{y} \,(90\%\,\mbox{C.L.})$ for the light neutrino exchange mechanism leads to a constraint on the effective Majorana neutrino mass of $\langle m_{\nu} \rangle < \left(1.2 - 3.0\right) \,\mbox{eV}$, where the range reflects $0\nu\beta\beta$ nuclear matrix element values from different calculations. Furthermore, constraints on lepton number violating parameters for other $0\nu\beta\beta$ mechanisms, such as right-handed currents, majoron emission and R-parity violating supersymmetry modes have been set.

There has been a recent revival of interest in the notion of a 'trajectory' of a quantum particle. In this paper, we detail the relationship between Dirac's ideas, Feynman paths and the Bohm approach. The key to the relationship is the weak value of the momentum which Feynman calls a transition probability amplitude. With this identification we are able to conclude that a Bohm 'trajectory' is the average of an ensemble of actual individual stochastic Feynman paths. This implies that they can be interpreted as the mean momentum flow of a set of individual quantum processes and not the path of an individual particle. This enables us to give a clearer account of the experimental two-slit results of Kocsis et al.

The NEMO-3 experiment measured the half-life of the 2 nu beta beta decay and searched for the 0 nu beta beta decay of Cd-116. Using 410 g of Cd-116 installed in the detector with an exposure of 5.26 y, (4968 +/- 74) events corresponding to the 2 nu beta beta decay of Cd-116 to the ground state of Sn-116 have been observed with a signal to background ratio of about 12. The half-life of the 2 nu beta beta decay has been measured to be T-1/2(2 nu) = [2.74 +/- 0.04(stat) +/- 0.18(syst)] x 10(19) y. No events have been observed above the expected background while searching for 0 nu beta beta decay. The corresponding limit on the half-life is determined to be T-1/2(0 nu) >= 1.0 x 10(23) y at the 90% C. L. which corresponds to an upper limit on the effective Majorana neutrino mass of < m(nu)> <= 1.4-2.5 eV depending on the nuclear matrix elements considered. Limits on other mechanisms generating 0 nu beta beta decay such as the exchange of R-parity violating supersymmetric particles, right-handed currents and majoron emission are also obtained.

A method for measuring the real part of the weak (local) value of spin is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises metastable helium in the 2^3S_1 state. A full simulation using the impulsive approximation has been carried out and it predicts a displacement of the beam by Δ_w = 17 - 33 μ m. This is on the limit of our detector resolution and we will discuss ways of increasing Δ_w. The simulation also indicates how we might observe the imaginary part of the weak value.