Abstract Bose-Einstein condensates subjected to modulation of the interaction between atoms exhibit the emergence of density waves and matter-wave jets with a velocity proportional to the square root of the modulation frequency. Matter-wave jets have been studied in two- and one-dimensional systems showing that for sufficiently strong modulation additional higher harmonic matter-wave jets emerge. Here we report the experimental observation of incommensurable “golden” $$\frac{1+\sqrt{5}}{2}$$ 1 + 5 2 matter-wave jets in a Bose-Einstein condensate exposed to a single frequency interaction modulation. We study the formation of higher-order jets in quasi-one-dimensional geometry with numerical one dimensional (1D) Gross-Pitaevskii equation simulation. We explore the process of jet formation experimentally and theoretically for a wide range of modulation amplitudes and frequencies and establish a phase diagram delineating different regimes of jet formation. The observation of incommensurate jets provides a new route to an aperiodic density modulation of the condensate without employing an external potential.

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).

Spin noise based quantum random number generators first appeared in 2008 and have since then garnered little further interest, in part because their bit rate is limited by the transverse relaxation time T_2 which for coated alkali vapour cells is typically in the kbit/s range. Here we present two advances. The first is an improved bit generation protocol that allows generating bits at rates exceeding 1/T_2 with only a minor increase of serial correlations. The second is a significant reduction of the time T_2 itself by removing the coating, increasing the vapour temperature and introducing a magnetic-field gradient. In this way we managed to increase the bit generation rate to 1.04 Mbit/s. We analyse the quality of the generated random bits using entropy estimation and we discuss the extraction methods to obtain high-entropy bitstreams. We accurately predict the entropy output of the device backed with a stochastic model and numerical simulations.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

Dynamical fluctuations of the elastic strain in strongly correlated systems are known to affect the onset of metal-to-insulator or superconducting transitions. Here we report their effect on the properties of a family of bandwidth-controlled alkali-intercalated fullerene superconductors. We introduce elastic strain through static local structural disorder in a systematic and controllable way in the fcc-structured K x Cs3-x C60 (with potassium content, 0.22 ≤ x K ≤ 2) series of compositions by utilizing the difference in size between the K+ and Cs+ co-dopants. The occurrence of the crossover from the Mott-Jahn-Teller insulating (MJTI) state into the strongly correlated Jahn-Teller metal (JTM) on cooling is evidenced for the compositions with x K < 1.28 by both synchrotron X-ray powder diffraction (SXRPD) - anomalous reduction of the unit cell volume - and 133Cs NMR spectroscopy - sudden suppression in the 133Cs spin-lattice relaxation rates. The emerging superconducting state with a maximum critical temperature, T c = 30.9 K shows a characteristic dome-like dependence on the unit-cell volume or equivalently, on the ratio between the on-site Coulomb repulsion, U, and the bandwidth, W. However, compared to the parent Cs3C60 composition in which cation disorder effects are completely absent, the maximum T c is lower by ∼12%. The reduction in T c displays a linear dependence on the variance of the tetrahedral-site cation size, σ T 2, thus establishing a clear link between structural-disorder-induced attenuation of critical elastic strain fluctuations and the electronic ground state.

We observe dark-state polariton collapses and revivals in a quantum memory based on electromagnetically induced transparency on a cloud of cold cesium atoms in a magnetic field. Using $\sigma^+$ polarized signal and control beams in the direction of the magnetic field, we suppress the dark-state polariton collapses by polarizing the atoms towards one of the stretched Zeeman states and optimizing the frequency detuning of the control beam. In this way, we demonstrate a quantum memory with only partial dark-state polariton collapses, making the memory usable at any storage time, not only at discretized times of revivals. We obtain storage time of more than 400 $\rm{\mu}$s, which is ten times longer than what we can achieve by trying to annul the magnetic field.

The aim of this study is to evaluate the method for the compensation of magnetic field interference from the mains, which consists primarily of components with a frequency of 50 (60) Hz and its multiples. The setup compensates for the interfering field using three Helmholtz coils, magnetic field sensors, a digital processing unit, and power amplifiers. The processing unit implements an adaptive least-mean-square (LMS) algorithm to calculate the currents through coils that are necessary for compensation. The prototype fully compensates for interfering with the magnetic field at 50, 150, 250, and 350 Hz down to the noise level of the sensor arrangement within 20 s and reduces higher harmonics. The overall reduction in the rms value of the interfering field is better than 28 dB, and a significantly better reduction is achieved in the frequency range from 0 Hz to 400 Hz.

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 use optical tweezers based on time-multiplexed acousto-optic deflectors to trap ultra-cold cesium atoms in one-dimensional arrays of atomic ensembles. For temperatures between 2.5 μK and 50 nK we study the maximal time between optical tweezer pulses that retains the number of atoms in a single trap. This time provides an estimate on the maximal number of sites in an array of time-multiplexed optical tweezers. We demonstrate evaporative cooling of atoms in arrays of up to 25 optical tweezer traps and the preparation of atoms in a box potential. Additionally, we demonstrate three different protocols for the preparation of atomic-ensemble arrays by transfer from an expanding ultra-cold atomic cloud. These result in the preparation of arrays of up to 74 atomic ensembles consisting of ∼100 atoms on average.

In frustrated spin-1/2 chains the competition between the nearest- and next-nearest-neighbor exchange interactions leads to a rich phase diagram that becomes even richer in the presence of perturbations in their material realizations. These effects are still largely unexplored, so that new insight into static and dynamic magnetism, in particular by sensitive local probes, is highly desired. Here we present a comprehensive O-17 nuclear magnetic resonance study of beta-TeVO4, where the anisotropy of the main exchange interactions and additional weak interchain exchange interactions complement the theoretical phase diagram. Our results confirm the dynamical nature of the intriguing spin-stripe phase that has been reported in previous studies. In addition, we find that the magnetic order in the high-field phase, which develops just below the magnetization saturation, is consistent with an unusual type of spin-density-wave (SDW) order with different alignments of the magnetic moments on the neighboring chains. This is reminiscent of the ordering in the SDW phase, realized in the absence of the magnetic field, and is thus most likely stabilized by magnetic anisotropy.

A family of layered manganese-pnictide antiferromagnets ${\mathrm{BaMn}}_{2}{Pn}_{2}$ ($\mathit{Pn}$ stands for P, As, Sb, and Bi) has been recently shown to host anomalously large magnetoresistance (MR) with both positive and negative MR components. In search for the microscopic picture of MR in this family, we here report a local-probe $^{55}\mathrm{Mn}$ nuclear magnetic resonance (NMR) study. The zero-field NMR spectra and the temperature dependence of the spin-lattice relaxation rates are fully consistent with the proposed G-type antiferromagnetic order. However, a close inspection of the $^{55}\mathrm{Mn}$ NMR spectra reveals a fine structure, which is due to the weakly localized charge carriers. As these carriers localize and segregate in the presence of electron correlations, they also undergo collective spin fluctuations which freeze-out at low temperatures and thus contribute to the $^{55}\mathrm{Mn}$ spin-lattice relaxation. The characteristic temperatures of the appearance of these additional features in the magnetic response probed by $^{55}\mathrm{Mn}$ NMR correlate well with the anomalies in the resistivity and anomalously large MR, which hints that the two phenomena are connected.

We combine the Ramsey interferometry protocol, the Stern-Gerlach detection scheme, and the use of elongated geometry of a cloud of fully polarized cold cesium atoms to measure the selected component of the magnetic-field gradient along the atomic cloud in a single shot. In contrast to the standard method where the precession of two spatially separated atomic clouds is simultaneously measured to extract their phase difference, which is proportional to the magnetic-field gradient, we here demonstrate a gradiometer using a single image of an expanding atomic cloud with the phase difference imprinted along the cloud. Using resonant radio-frequency pulses and Stern-Gerlach imaging, we first demonstrate nutation and Larmor precession of atomic magnetization in an applied magnetic field. Next, we let the cold atom cloud expand in one dimension and apply the protocol for measuring the magnetic-field gradient. The resolution of our single-shot gradiometer is not limited by thermal motion of atoms and has an estimated absolute accuracy below $\ifmmode\pm\else\textpm\fi{}0.2$ mG/cm ($\ifmmode\pm\else\textpm\fi{}20$ nT/cm).

Paradigmatic quantum spin liquid has been in the past closely linked to the high-temperature superconductivity. Here we focus on a layered 1T-TaS2, which has recently emerged as a surprising candidate for a quantum spin liquid on a triangular lattice. Upon doping 1T-TaS2 with Se, the Se-77 nuclear magnetic resonance and Ta-181 nuclear quadrupole resonance data show a remarkable robustness of the quantum spin liquid at low Se doping levels despite the growth of inhomogeneities in the electronic state. A dramatic change in the low-energy electronic excitations are observed in samples with a moderate Se content where the Mott insulating state gives way to a correlated metal and a low-temperature superconductivity. The effects of antiferromagnetic correlations can still be traced in the normal state above the superconducting critical temperature T-c = 3.5 K and may, together with the underlying disorder, account for the large superconducting gap-to-T-c ratio 2 Delta/k(B)T(c) approximate to 7 deduced from the scanning tunneling microscopy.

We demonstrate that the metallic nature of rubidium clusters confined and arrayed in the framework of insulating low-silica X zeolite is preserved. The $^{87}$Rb NMR spin-lattice relaxation assigned to rubidium clusters shows a Korringa behavior from 190~K down to 10~K, which is compatible with a macroscopic observation of low electrical resistivity. The density of states at the Fermi level is found to be enhanced compared to the sodium case.

While the vast majority of known physical realizations of the Tomonaga-Luttinger liquid (TLL) have repulsive interactions defined with the dimensionless interaction parameter K-c < 1, we here report that Rb2Mo3As3 is in the opposite TLL regime of attractive interactions. This is concluded from a TLL-characteristic power-law temperature dependence of the Rb-87 spin-lattice relaxation rates over a broad temperature range yielding the TLL interaction parameter for charge collective modes K-c = 1.4. The TLL of the one-dimensional band can be traced almost down to T-c = 10.4 K, where the bulk superconducting state is stabilized by the presence of a three-dimensional band and characterized by the Rb-87 temperature-independent Knight shift and the absence of the Hebel-Slichter coherence peak in the relaxation rates. The small superconducting gap measured in high magnetic fields reflects either the importance of the vortex core relaxation or the uniqueness of the superconducting state stemming from the attractive interactions defining the precursor TLL.

A comprehensive study of the molecular mixed-valence compound Rb${}_{4}$O${}_{6}$ led the authors to the discovery of a peculiar $\ensuremath{\pi}*$ orbital ordering transition of magnetic O${}_{2}^{\ensuremath{-}}$ anions within the charge ordered state, which promotes the formation of an orbital order-driven quantum spin state, composed of spin dimers. The experiments suggest that a delicate interplay between an electron-lattice coupling and Kugel-Khomskii-type superexchange in $\ensuremath{\pi}$-electron systems determines the magnetostructural properties. These results establish a fruitful analogy between $\ensuremath{\pi}$- and more conventional $3d$-mixed-valence systems and push the research of such systems into new directions to tackle the intertwining of various active degrees of freedom.

We demonstrate the emission of correlated atom jets from a matter-wave soliton in a quasi-one-dimensional optical trap. We characterize the dependence of jet properties on the frequency, amplitude, and length of the modulation, and qualitatively reproduce the trends in the mean-field picture with a one-dimensional time-dependent Gross-Pitaevskii equation simulation. High-order jets are observed for sufficiently long pulses. A double-pulse modulation sequence produces consecutive jets, and a multipulse sequence may lead to irregular three-dimensional jets at a finite angle to the direction of the channel. In the limit of vanishing high-order jets beyond-mean-field number correlations of jet pairs are demonstrated, implying possible number squeezing.

A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi-one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described.

Copper carbodiimide, CuNCN, is a geometrically frustrated nitrogen-based analog of cupric oxide, whose magnetism remains ambiguous. Here, we employ a combination of local-probe techniques, including (CU)-C-63,65 nuclear quadrupole resonance, C-13 nuclear magnetic resonance, and muon spin rotation to show that the magnetic ground state of the Cu2+ (S = 1/2) spins is frozen and disordered. Moreover, these complementary experiments unequivocally establish the onset of an intrinsically inhomogeneous magnetic state at T-h = 80 K. Below T-h, the low-temperature frozen component coexists with the remnant high-temperature dynamical component down to T-1 = 20 K, where the latter finally ceases to exist. Based on a scaling of internal magnetic fields of both components, we conclude that the two components coexist on a microscopic level.