Here we review the field of atom chips in the context of Bose–Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and all the way to novel probing of surfaces and new forces. In addition, technological applications are also being intensively pursued. This review will describe these developments and more, including new ideas which have not yet been realized.

We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers which make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.

The Stern-Gerlach effect, found a century ago, has become a paradigm of quantum mechanics. Unexpectedly, until recently, there has been little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Several theoretical studies have explained why a Stern-Gerlach interferometer is a formidable challenge. Here, we provide a detailed account of the realization of a full-loop Stern-Gerlach interferometer for single atoms and use the acquired understanding to show how this setup may be used to realize an interferometer for macroscopic objects doped with a single spin. Such a realization would open the door to a new era of fundamental probes, including the realization of previously inaccessible tests at the interface of quantum mechanics and gravity.

In this invited review in honor of 100 years since the Stern-Gerlach (SG) experiments, we describe a decade of SG interferometry on the atom chip. The SG effect has been a paradigm of quantum mechanics throughout the last century, but there has been surprisingly little evidence that the original scheme, with freely propagating atoms exposed to gradients from macroscopic magnets, is a fully coherent quantum process. Specifically, no full-loop SG interferometer (SGI) has been realized with the scheme as envisioned decades ago. Furthermore, several theoretical studies have explained why it is a formidable challenge. Here we provide a review of our SG experiments over the last decade. We describe several novel configurations such as that giving rise to the first SG spatial interference fringes, and the first full-loop SGI realization. These devices are based on highly accurate magnetic fields, originating from an atom chip, that ensure coherent operation within strict constraints described by previous theoretical analyses. Achieving this high level of control over magnetic gradients is expected to facilitate technological applications such as probing of surfaces and currents, as well as metrology. Fundamental applications include the probing of the foundations of quantum theory, gravity, and the interface of quantum mechanics and gravity. We end with an outlook describing possible future experiments.

We investigate both theoretically and experimentally the effect of thermal motion of laser cooled atoms on the coherence of Rabi oscillations induced by an inhomogeneous driving field. The experimental results are in excellent agreement with the derived analytical expressions. For freely falling atoms with negligible collisions, as those used in our experiment, we find that the amplitude of the Rabi oscillations decays with time t as exp[−(t/τ ) 4 ] , where the coherence time τ drops with increasing temperature and field gradient. We discuss the consequences of these results regarding the fidelity of Rabi rotations of atomic qubits. We also show that the process is equivalent to the loss of coherence of atoms undergoing a Ramsey sequence in the presence of static magnetic field gradients -a common situation in many applications. In addition, our results are relevant for determining the resolution when utilizing atoms as field probes. Using numerical calculations, our model can be easily extended to situations in which the atoms are confined by a potential or to situations where collisions are important.

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Interference between overlapping periodic patterns gives rise to important phenomena, such as moiré fringes, appearing when the patterns have different periods or orientations. Here we present a novel phenomenon, applicable to both the classical and quantum regimes, where two one-dimensional localized periodic patterns with the same period interfere to create fringes with anomalous periodicity. We analyze the effect theoretically and demonstrate it with atomic matter waves. When a central parameter of the system is scanned continuously, we observe a discontinuous but piecewise-rigid periodicity of the resulting fringes. We show that this is a universal phenomenon that emerges from a superposition of two spatially shifted localized periodic patterns of any source or nature when they interfere with a global phase difference. The rigidity of the spectrum becomes even more robust for a coherent superposition of non-overlapping wavepackets, although the conventional interferometric visibility drops to zero. The effect is expected to appear in space and time, as well as in the momentum distribution of quantum particles.

Moiré patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms, that for one-dimensional finitesize periodic systems, moiré patterns give rise to anomalous features in both classical and quantum systems. In contrast to the standard moiré phenomenon, in which the pattern periodicity is a result of a beat-note between its constituents, we demonstrate moiré patterns formed from constituents with the same periodicity. Surprisingly, we observe, in addition, rigidity and singularities. We furthermore uncover universal properties in the frequency domain, which might serve as a novel probe of emitters. These one-dimensional effects could be relevant to a wide range of periodic phenomena.Moiré patterns are an omnipresent phenomenon [1]. They appear when two periodic structures or fields are overlaid. Such patterns may have implications for any overlapping periodic phenomenon. Specifically, in condensed matter, recent years have witnessed the emergence of moiré engineering -the tailoring of electronic, and magnetic properties of van der Waals heterostructures [2] or correlated oxides [3]. Such moiré materials have also been associated with quantum information and simulation [4,5]. Inspired by the subtle role moiré patterns may play, we set out to study the formation of these patterns in one-dimensional finite-size periodic systems, and found that such moiré patterns give rise to anomalous features in both the classical and quantum domains. In contrast to the standard moiré phenomenon, in which the moiré-pattern periodicity is a result of a beat-note between the different constituents forming it, we demonstrate moiré patterns formed from constituents with the same periodicity. In addition, we observe rigidity and singularities, when varying both the periodicity of the constituents and the relative phase (relative translation). We furthermore uncover universal properties in the frequency domain, which might serve as a novel probe of emitting sources. We simulate such a system with ultracold atoms, precisely controlled by an atom chip [6], where we make use of a conservation law imposed by the invariance of phase-space distributions under unitary * equal contribution † corresponding author