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Bose-Einstein condensates (BECs) have been proposed for many applications in atom interferometry, as their coherence over long evolution times promises unprecedented sensitivity. To date, BECs can be efficiently created in devices using atom chips, but these are still complex and place high demands on size, weight and power. To further simplify these setups, we equipped an atom chip with a nano-structured diffraction-grating to derive all beams for the magneto-optical trap (MOT) from a single laser beam. Moreover, using a 2D$^+$-MOT as an atomic source and a beam with uniform intensity for the grating illumination, we capture $1\times10^9$ atoms in one second, cool them to $14\,\mu$K, and demonstrate magnetic trapping using the atom chip. This is a major step towards the simplification of portable BEC devices for quantum sensing on earth and in space., Comment: 12 pages, 3 figures

Ultracold atoms are crucial for unlocking truly precise and accurate quantum metrology, and provide an essential platform for quantum computing, communication and memories. One of the largest ongoing challenges is the miniaturization of these quantum devices. Here, we show that the typically macroscopic optical lattice architecture at the heart of many ultra-precise quantum technologies can be realized with a single input laser beam on the same diffractive chip already used to create the ultracold atoms. Moreover, this inherently ultra-stable platform enables access to a plethora of new lattice dimensionalities and geometries, ideally suited for the design of high-accuracy, portable quantum devices., Comment: 7 pages, 2 figures

In a wide range of quantum technology applications, ranging from atomic clocks to the creation of ultracold or quantum degenerate samples for atom interferometry, optimal laser sources are critical. In particular, two phase-locked laser sources with a precise difference frequency are needed for efficient coherent population trapping (CPT) clocks, gray molasses laser cooling, or driving Raman transitions. Here we show how a simple cost-effective laser diode can selectively amplify only one sideband of a fiber-electrooptically-modulated seed laser to produce moderate-power phase-locked light with sub-Hz relative linewidth and tunable difference frequencies up to $\approx 15\,$GHz. The architecture is readily scalable to multiple phase-locked lasers and could conceivably be used for future on-chip compact phase-locked laser systems for quantum technologies., Comment: 4 pages, 5 figures

It has long been understood that dilute samples of chiral molecules such as rarefied gases should exhibit Rayleigh optical activity. We extend the existing theory by accounting for molecular dynamics and correlations, thus obtaining a more general theory of Rayleigh-Brillouin optical activity applicable to dense samples such as neat liquids.

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., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

We report initial research to develop a compact and practical primary thermometer based on Doppler broadening thermometry (DBT). The DBT sensor uses an intrinsic property of thermalized atoms, namely, the Doppler width of a spectral line characteristic of the atoms being probed. The DBT sensor, being founded on a primary thermometry approach, requires no calibration or reference, and so in principle could achieve reliable long-term in-situ thermodynamic temperature measurement. Here we describe our approach and report on initial proof-of-concept investigations with alkali metal vapour cells. Our focus is to develop long-term stable thermometers based on DBT that can be used to reliably measure temperatures for long periods and in environments where sensor retrieval for re-calibration is impractical such as in nuclear waste storage facilities., Comment: 7 pages, 4 figures, referees' comments incorporated

Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for laser cooling in two stages at two distinct wavelengths - as commonly used for loading e.g. Sr or Yb atoms into optical lattice or tweezer clocks. Here, we optically characterize a wide variety of binary gratings at different wavelengths to find a simple empirical fit to experimental grating diffraction efficiency data in terms of dimensionless etch depth and period for various duty cycles. The model avoids complex 3D light-grating surface calculations, yet still yields results accurate to a few percent across a broad range of parameters. Gratings optimized for two (or more) wavelengths can now be designed in an informed manner suitable for a wide class of atomic species enabling advanced quantum technologies., Comment: 11 pages, 3 figures, 2 tables. See also 4-page supplementary document

Cold atom fountain clocks provide exceptional long term stability as they increase interrogation time at the expense of a larger size. We present a compact cold atom fountain using a grating magneto-optical trap (GMOT) to laser cool and launch the atoms in a simplified optical setup. The fountain is evaluated using coherent population trapping and demonstrates improved single-shot stability from the launch. Ramsey times up to 100 ms were measured with a corresponding fringe linewidth of 5 Hz. This technique could improve both short- and long-term stability of cold atom clocks whilst remaining compact for portable applications., Comment: 5 pages, 4 figures

External-cavity diode lasers are ubiquitous in atomic physics and a wide variety of other scientific disciplines, due to their excellent affordability, coherence length and versatility. However, for higher power applications, the combination of seed lasers, injection-locking and amplifiers can rapidly become expensive and complex. Here we present a useful, high-power, single-diode laser design with specifications: $>210\,$mW, $100\,$ms-linewidth ($427 \pm 7$) kHz, $>99\%$ mode purity, $10\,$GHz mode-hop-free tuning range and $12\,$nm coarse tuning. Simple methods are outlined to determine the spectral purity and linewidth with minimal additional infrastructure. The laser has sufficient power to collect $10^{10}$ $^{87}$Rb atoms in a single-chamber vapour-loaded magneto-optical trap. With appropriate diodes and feedback, the system could be easily adapted to other atomic species and laser formats., Comment: 4 pages, 3 figures

Compact vacuum systems are key enabling components for cold atom technologies, facilitating extremely accurate sensing applications. There has been important progress towards a truly portable compact vacuum system, however size, weight and power consumption can be prohibitively large, optical access may be limited, and active pumping is often required. Here, we present a centilitre-scale ceramic vacuum chamber with He-impermeable viewports and an integrated diffractive optic, enabling robust laser cooling with light from a single polarization-maintaining fibre. A cold atom demonstrator based on the vacuum cell delivers $10^7$ laser-cooled $^{87}$Rb atoms per second, using minimal electrical power. With continuous Rb gas emission active pumping yields a $10^{-7}\,$mbar equilibrium pressure, and passive pumping stabilises to $3\times 10^{-6}\,$mbar, with a $17\,$day time constant. A vacuum cell, with no Rb dispensing and only passive pumping, has currently kept a similar pressure for more than \ch{500 days}. The passive-pumping vacuum lifetime is several years, estimated from short-term He throughput, with many foreseeable improvements. This technology enables wide-ranging mobilization of ultracold quantum metrology., Comment: 6 pages, 2 figures, to appear in Applied Physics Letters

Studying the conversion between transverse light modes via four-wave mixing in a heated rubidium vapour, we demonstrate and explain a transfer between azimuthal and radial mode numbers. These relate to orthogonal modal dimensions, which one would not normally expect to interact. While angular momentum conservation in this nonlinear process dictates the selection rules for the angular mode number, the role of the radial mode number is more esoteric. We demonstrate systematically that the Gouy phase is the key to understanding this conversion, leading to strikingly different conversion behaviour in the thick and thin medium regime. Our experimental investigation of the transition between these regimes bridges the gap between previous experiments in atomic thick media and work in nonlinear crystals. Our work sets a clear starting point to explore new territory in the thick medium regime, allowing efficient radial-to-azimuthal and radial-to-radial mode conversion., Comment: 6 pages, 5 figures, Supplementary Material - 4 pages. Thanks to the referees for their comments

We optically assess Fresnel zone plates (FZPs) that are designed to guide cold atoms. Imaging of various ring patterns produced by the FZPs gives an average RMS error in the brightest part of the ring of 3% with respect to trap depth. This residue will be due to the imaging system, incident beam shape and FZP manufacturing tolerances. Axial propagation of the potentials is presented experimentally and through numerical simulations, illustrating prospects for atom guiding without requiring light sheets., Comment: 10 pages, 5 figures

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects $10^7$ $^{87}$Rb atoms, which are subsequently cooled to $20\,\mu$K in optical molasses. We optically probe the microwave atomic ground-state splitting using lin$\perp$lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only $0.5\,$mm, the measured short-term fractional frequency stability is $2 \times 10 ^{-11} /\sqrt{\tau}$., Comment: 8 pages, 4 figures

Laguerre-Gauss beams, and more generally the orbital angular momentum of light (OAM) provide valuable research tools for optical manipulation, processing, imaging and communication. Here we explore the high-efficiency frequency conversion of OAM in a four-wave mixing process in rubidium vapour. Conservation of the OAM in the two pump beams determines the total OAM shared by the generated light fields at 420 nm and 5.2 um - but not its distribution between them. We experimentally investigate the spiral bandwidth of the generated light modes as a function of pump OAM. A small pump OAM is transferred almost completely to the 420 nm beam. Increasing the total pump OAM broadens the OAM spectrum of the generated light, indicating OAM entanglement between the generated light fields. This clears the path to high-efficiency OAM entanglement between widely disparate wavelengths., Comment: Fully revised to include referees' improvements and journal requirements. Supplementary material is included as an ancillary file

The interaction of spatially structured light fields with atomic media can generate spatial structures inscribed in the atomic populations and coherences, allowing for example the storage of optical images in atomic vapours. Typically, this involves coherent optical processes based on Raman or EIT transitions. Here we study the simpler situation of shaping atomic populations via spatially dependent optical depletion. Using a near resonant laser beam with a holographically controlled 3D intensity profile, we imprint 3D population structures into a thermal rubidium vapour. This 3D population structure is simultaneously read out by recording the spatially resolved fluorescence of an unshaped probe laser. We find that the reconstructed atomic population structure is largely complementary to the intensity structure of the control beam, however appears blurred due to global repopulation processes. We identify and model these mechanisms which limit the achievable resolution of the 3D atomic population. We expect this work to set design criteria for future 2D and 3D atomic memories.

Double-resonance optically pumped magnetometers are an attractive instrument for unshielded magnetic field measurements due to their wide dynamic range and high sensitivity. Use of linearly polarised pump light creates alignment in the atomic sample, which evolves in the local static magnetic field, and is driven by a resonant applied field perturbation, modulating the polarisation of transmitted light. We show for the first time that the amplitude and phase of observed first- and second-harmonic components in the transmitted polarisation signal contain sufficient information to measure static magnetic field magnitude and orientation. We describe a laboratory system for experimental measurements of these effects and verify a theoretical derivation of the observed signal. We demonstrate vector field tracking under varying static field orientations and show that the static field magnitude and orientation may be observed simultaneously, with experimentally realised resolution of 1.7 pT and 0.63 mrad in the most sensitive field orientation., Comment: 8 pages, 7 figures

Optically pumped atomic magnetometers (OPMs) offer highly sensitive magnetic measurements using compact hardware, offering new possibilities for practical precision sensors. Double-resonance OPM operation is well suited to unshielded magnetometry, due to high sensor dynamic range. However, sensor response is highly anisotropic with variation in the orientation of the magnetic field. We present data quantifying these effects and discuss implications for the design of practical sensors., Comment: IEEE Sensors 2017 paper preprint

An atom interferometer using a Bose-Einstein condensate of $^{87}$Rb atoms is utilized for the measurement of magnetic field gradients. Composite optical pulses are used to construct a spatially symmetric Mach-Zehnder geometry. Using a biased interferometer we demonstrate the ability to measure small residual forces in our system at the position of the atoms. These are a residual magnetic field gradient of 15$\pm$2 mG/cm and and an inertial acceleration of 0.08$\pm$0.02 m/s$^2$. Our method has important applications in the calibration of precision measurement devices and the reduction of systematic errors., Comment: 7 pages, 6 figures

Double resonance optically pumped magnetometry can be used to measure static magnetic fields with high sensitivity by detecting a resonant atomic spin response to a small oscillating field perturbation. Determination of the resonant frequency yields a scalar measurement of static field ($B_0$) magnitude. We present calculations and experimental data showing that the on-resonance polarimeter signal of light transmitted through an atomic vapour in arbitrarily oriented $B_0$ may be modelled by considering the evolution of alignment terms in atomic polarisation. We observe that the amplitude and phase of the magnetometer signal are highly dependent upon $B_0$ orientation, and present precise measurements of the distribution of these parameters over the full 4{\pi} solid angle.

We have laser cooled 3$\times10^6$ $^{87}$Rb atoms to 3$\mu$K in a micro-fabricated grating magneto-optical trap (GMOT), enabling future mass-deployment in highly accurate compact quantum sensors. We magnetically trap the atoms, and use Larmor spin precession for magnetic sensing in the vicinity of the atomic sample. Finally, we demonstrate an array of magneto-optical traps with a single laser beam, which will be utilised for future cold atom gradiometry., Comment: 8 pages, 6 figures

We report the first use of a ring cavity to both enhance the output power and dramatically narrow the linewidth ($<1\,$MHz) of blue light generated by four wave mixing in a rubidium vapour cell. We find that the high output power available in our cavity-free system leads to power broadening of the generated blue light linewidth. Our ring cavity removes this limitation, allowing high output power and narrow linewidth to be achieved concurrently. As the cavity blue light is widely tunable over the $^{85}$Rb 5S$_{1/2} \,\,F=3$ $\rightarrow$ 6P$_{3/2}$ transition, this narrow linewidth light would be suitable for second-stage laser cooling, which could be valuable for efficient $^{85}$Rb BEC production., Comment: 5 pages, 3 figures

We have studied the optical properties of gratings micro-fabricated into semiconductor wafers, which can be used for simplifying cold-atom experiments. The study entailed characterisation of diffraction efficiency as a function of coating, periodicity, duty cycle and geometry using over 100 distinct gratings. The critical parameters of experimental use, such as diffraction angle and wavelength are also discussed, with an outlook to achieving optimal ultracold experimental conditions., Comment: 8 pages

We have simulated the optical properties of micro-fabricated Fresnel zone plates (FZPs) as an alternative to spatial light modulators (SLMs) for producing non-trivial light potentials to trap atoms within a lensless Fresnel arrangement. We show that binary (1-bit) FZPs with wavelength (1 \mu m) spatial resolution consistently outperform kinoforms of spatial and phase resolution comparable to commercial SLMs in root mean square error comparisons, with FZP kinoforms demonstrating increasing improvement for complex target intensity distributions. Moreover, as sub-wavelength resolution microfabrication is possible, FZPs provide an exciting possibility for the creation of static cold-atom trapping potentials useful to atomtronics, interferometry, and the study of fundamental physics., Comment: 14 pages, to appear in New Journal of Physics Atomtronics special issue

We have used diffraction gratings to simplify the fabrication, and dramatically increase the atomic collection efficiency, of magneto-optical traps using micro-fabricated optics. The atom number enhancement was mainly due to the increased beam capture volume, afforded by the large area (4cm^2) shallow etch (200nm) binary grating chips. Here we provide a detailed theoretical and experimental investigation of the on-chip magneto-optical trap temperature and density in four different chip geometries using 87Rb, whilst studying effects due to MOT radiation pressure imbalance. With optimal initial MOTs on two of the chips we obtain both large atom number (2x10^7) _and_ sub-Doppler temperatures (50uK) after optical molasses., Comment: 12 pages, 6 figures, 2 linked supplementary figures

We propose a flexible and robust scheme to create closed quasi-one dimensional guides for ultra-cold atoms through the dressing of hyperfine sub-levels of the atomic ground state. The dressing field is spatially modulated by inductive effects over a micro-engineered conducting loop, freeing the trapping region from leading wires in its proximity. We show that arrays of connected ring traps can also be created by carefully designing the shape of the conducting loop. We report on characteristics of the trap and mechanisms that limit the range of parameters available for experimental implementation, including non-adiabatic losses and heat dissipation by induced currents. We outline conditions to select appropriate parameters for operation of the trap with atom-chip technology., Comment: 7 pages, 7 pdf figures

We present two novel dressed inductive ring trap geometries, ideal for atom interferometry or studies of superfluidity and well-suited to utilisation in atom chip architectures. The design permits ring radii currently only accessible via near-diffraction-limited optical traps, whilst retaining the ultra-smooth magnetic potential afforded by inductive traps. One geometry offers simple parallel implementation of multiple rings, whereas the other geometry permits axial beam-splitting of the torus suitable for whole-ring atom interferometry., Comment: 9 pages, 3 figures, linked movies

The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the pump axis - are spontaneously broken. We observe the simultaneous spatial structuring of the density of a cold atomic cloud and an optical pump beam. The resulting patterns have hexagonal symmetry. The experiment demonstrates the manipulation of matter by opto-mechanical self-assembly with adjustable length scales and can be potentially extended to quantum degenerate gases., Comment: 20 pages, 6 figures

New counter-propagating geometries are presented for localising ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an 'optical revolver,' axial lattices of rings and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase-stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts., Comment: 3 pages, 6 figures Modified to include referees' improvements

A planar triplet of diffraction gratings is used to transform a single laser beam into a four-beam tetrahedral magneto-optical trap. This `flat' pyramid diffractor geometry is ideal for future microfabrication. We demonstrate the technique by trapping and subsequently sub-Doppler cooling 87Rb atoms to 30microKelvin., Comment: 3 pages, 4 figures

We have realised a 4-beam pyramidal magneto-optical trap ideally suited for future microfabrication. Three mirrors split and steer a single incoming beam into a tripod of reflected beams, allowing trapping in the four-beam overlap volume. We discuss the influence of mirror angle on cooling and trapping, finding optimum efficiency in a tetrahedral configuration. We demonstrate the technique using an ex-vacuo mirror system to illustrate the previously inaccessible supra-plane pyramid MOT configuration. Unlike standard pyramidal MOTs both the pyramid apex and its mirror angle are non-critical and our MOT offers improved molasses free from atomic shadows in the laser beams. The MOT scheme naturally extends to a 2-beam refractive version with high optical access. For quantum gas experiments, the mirror system could also be used for a stable 3D tetrahedral optical lattice., Comment: 8 pages, 6 figures, 2 movies

Single-impulse three-dimensional magnetic focusing of vertically launched cold atoms has been observed. Four different configurations of the lens were used to vary the relative radial and axial focusing properties. Compact focused clouds of 85Rb were seen for all four configurations. It is shown that an atom-optical ray matrix approach for describing the lensing action is insufficient. Numerical simulation using a full approximation to the lens's magnetic field shows very good agreement with the radial focusing properties of the lens. However, the axial (vertical direction) focusing properties are less well described and the reasons for this are discussed., Comment: Revised to incorporate referee suggestions, final version

We propose the novel combination of a laser guide and magnetic lens to transport a cold atomic cloud. We have modelled the loading and guiding of a launched cloud of cold atoms with the optical dipole force. We discuss the optimum strategy for loading typically 30% of the atoms from a MOT and guiding them vertically through 22cm. However, although the atoms are tightly confined transversely, thermal expansion in the propagation direction still results in a density loss of two orders of magnitude. By combining the laser guide with a single impulse from a magnetic lens we show one can actually increase the density of the guided atoms by a factor of 10., Comment: 18 pages 11 figures. To appear in New J. Phys. Original version modified to include referee's improvements

We have theoretically investigated 3D focusing of a launched cloud of cold atoms using a pair of magnetic lens pulses (the alternate-gradient method). Individual lenses focus radially and defocus axially or vice-versa. The performance of the two possible pulse sequences are compared and found to be ideal for loading both 'pancake' and 'sausage' shaped magnetic/optical microtraps. It is shown that focusing aberrations are considerably smaller for double-impulse magnetic lenses compared to single-impulse magnetic lenses. An analysis of the clouds focused by double-impulse technique is presented., Comment: 14 pages, 6 figures. Accepted for publication in New Journal of Physics

We have theoretically investigated the focusing of a launched cloud of cold atoms. Time-dependent spatially-varying magnetic fields are used to impart impulses leading to a three-dimensional focus of the launched cloud. We discuss possible coil arrangements for a new focusing regime: isotropic 3D focusing of atoms with a single-impulse magnetic lens. We investigate focusing aberrations and find that, for typical experimental parameters, the widely used assumption of a purely harmonic lens is often inaccurate. The baseball lens offers the best possibility for isotropically focusing a cloud of weak-field-seeking atoms in 3D., Comment: 16 pages, 7 figures