In the Stern-Gerlach effect, a magnetic field gradient splits particles into spatially separated paths according to their spin projection. The idea of exploiting this effect for creating coherent momentum superpositions for matter-wave interferometry appeared shortly after its discovery, almost a century ago, but was judged to be far beyond practical reach. Here we demonstrate a viable version of this idea. Our scheme uses pulsed magnetic field gradients, generated by currents in an atom chip wire, and radio-frequency Rabi transitions between Zeeman sublevels. We transform an atomic Bose-Einstein condensate into a superposition of spatially separated propagating wavepackets and observe spatial interference fringes with a measurable phase repeatability. The method is versatile in its range of momentum transfer and the different available splitting geometries. These features make our method a good candidate for supporting a variety of future applications and fundamental studies.

We experimentally demonstrate a new interferometry paradigm: a self-interfering clock. We split a clock into two spatially separated wave packets, and observe an interference pattern with a stable phase showing that the splitting was coherent, i.e., the clock was in two places simultaneously. We then make the clock wave packets "tick" at different rates to simulate a proper time lag. The entanglement between the clock's time and its path yields "which path" information, which affects the visibility of the clock's self-interference. By contrast, in standard interferometry, time cannot yield "which path" information. As a clock we use an atom prepared in a superposition of two spin states. This first proof-of-principle experiment may have far-reaching implications for the study of time and general relativity and their impact on fundamental quantum effects such as decoherence and wave packet collapse. Two-slit interferometry of quanta, such as photons and electrons, figured prominently in the Bohr-Einstein debates on the consistency of quantum theory [1, 2]. A fundamental principle emerging from those debates-intimately related to the uncertainty principle-is that "which path" information about the quanta passing through slits blocks their interference. At the climax of the debates, Einstein claimed that a clock, emitting a photon at a precise time while being weighed on a spring scale to measure the change in its massenergy, could evade the uncertainty principle. Yet Bohr showed that the clock's gravitational redshift introduced enough uncertainty in the emission time to satisfy the uncertainty principle. Inspired by the subtle role time may play in quantum mechanics, we have now sent a clock through a spatial interferometer. The proof-of-principle experiment described below presents clock interferometry as a new tool for studying the interplay of general relativity[3] and quantum mechanics [4].Quantum mechanics cannot fully describe a self-interfering clock in a gravitational field.If the paths of a clock through an interferometer have different heights, then general relativity predicts that the clock must "tick" slower along the lower path. However, time in quantum mechanics is a global parameter, which cannot differ between paths. In standard interferometry (e.g.[5]), a difference in height between two paths affects their relative phase and shifts their interference pattern; but in clock interferometry, a time differential between paths yields "which path" information, degrading the visibility of the interference pattern [6]. It follows that, while standard interferometry may probe general relativity [7][8][9] In principle, any system evolving with a well defined period can be a clock. In our experiment, we utilize a quantum two-level system. Specifically, each clock is a 87 Rb atom in a superposition of two Zeeman sublevels, the m F = 1 and m F = 2 sublevels of the F = 2 hyperfine state.The general scheme of the clock interferometer is shown in Fig. 1 atoms 90 µm below the chip surface). Initially, af...

Work is an essential concept in classical thermodynamics, and in the quantum regime, where the notion of a trajectory is not available, its definition is not trivial. For driven (but otherwise isolated) quantum systems, work can be defined as a random variable, associated with the change in the internal energy. The probability for the different values of work captures essential information describing the behaviour of the system, both in and out of thermal equilibrium. In fact, the work probability distribution is at the core of “fluctuation theorems” in quantum thermodynamics. Here we present the design and implementation of a quantum work meter operating on an ensemble of cold atoms, which are controlled by an atom chip. Our device not only directly measures work but also directly samples its probability distribution. We demonstrate the operation of this new tool and use it to verify the validity of the quantum Jarzynksi identity.

The discovery of the Stern-Gerlach (SG) effect almost a century ago was followed by suggestions to use the effect as a basis for matter-wave interferometry. However, the coherence of splitting particles with spin by a magnetic gradient to a distance exceeding the position uncertainty in each of the arms was not demonstrated until recently, where spatial interference fringes were observed in a proof-ofprinciple experiment. Here we present and analyze the performance of an improved high-stability SG spatial fringe interferometer based on two spatially separate wave packets with a maximal distance that is more than an order of magnitude larger than their minimal widths. The improved performance is enabled by accurate magnetic field gradient pulses, originating from a novel atom chip configuration, which ensures high stability of the interferometer operation. We analyze the achieved stability using several models, discuss sources of noise, and detail interferometer optimization procedures. We also present a simple analytical phase-space description of the interferometer sequence that demonstrates quantitatively the complete separation of the superposed wave packets 2 .indistinguishable spin state. This was made possible by the long experimental times available due to the slow velocity of the atoms, initially trapped and prepared in a Bose-Einstein condensation (BEC) state, as well as the inherent nonlinearity of the applied magnetic gradients giving rise to a focusing (lensing) effect. Due to the large splitting (relative to the wave packet width), spatial interference fringes could be observed from the SG effect for the first time, turning this experiment into an analog of the double-slit experiment.The interferometric scheme based on spatial interference fringes has an advantage over the closed-loop fourmagnetic-gradients interferometer originally envisioned, in that it does not require very accurate recombination of two wave packets with different spins, as we demonstrate in this paper. Specifically, it is insensitive to imperfections of the wave packet shape, and to magnetic gradient imperfections giving rise to the Humpty-Dumpty effect. On the other hand, it requires high resolution imaging of the fringe patterns and therefore limits the final separations in position or momentum between the two wave packets. This limitation can be overcome by additional accelerating and stopping stages, as demonstrated with Bragg splitting [21]. Such robustness may eventually lead to advantageous technological applications.Here we present an analysis of the performance of a high stability SG spatial fringe longitudinal interferometer, based on an atom chip [22], over a range of momentum splitting and separation distances allowed by the resolution of our imaging system (up to a differential velocity of ∼10 mm s −1 after splitting and separation of ∼4 μm). For this range we show a multi-shot visibility (a measure of stability) larger than 90%, corresponding to a phase instability smaller than 0.45 radians. We analyze the sources o...

We present a feasibility study for loading cold atomic clouds into magnetic traps created by singlewall carbon nanotubes grown directly onto dielectric surfaces. We show that atoms may be captured for experimentally sustainable nanotube currents, generating trapped clouds whose densities and lifetimes are sufficient to enable detection by simple imaging methods. This opens the way for a novel type of conductor to be used in atomchips, enabling atom trapping at sub-micron distances, with implications for both fundamental studies and for technological applications.

Trapping a Rydberg atom close to a surface is an important step towards the realisation of many proposals of quantum information or hybrid quantum systems. One of the challenges in these experiments is to overcome the electric field emanating from contaminations on the surface. Here we report on measurements of an electric field created by 87 Rb atoms absorbed on a 25 nm thick layer of SiO 2 , covering a 90 nm layer of Au. The electric field is measured using a two-photon transition to the 23D 5/2 and 25S 1/2 state. The electric field value that we measure is higher than typical values measured above metal surfaces, but is consistent with other measurements above SiO 2 surfaces. In addition, we measure the temporal behaviour of the field and observe that we can reduce it in a single experimental cycle, using UV light or by mildly heating the surface, whereas the buildup of the field takes thousands of cycles. We explain these results by a change in the ad-atoms distribution on the surface. These results indicate that the stray electric field can be reduced, opening new possibilities for experiments with trapped Rydberg atoms near surfaces. † Present address: CQ Center for Collective Quantum Phenomena and Their Applications,

We observe a density-dependent collective suppression of optical pumping between the hyperfine ground states in an array of submicrometer-sized clouds of dense and cold rubidium atoms. The suppressed Raman transition rate can be explained by strong resonant dipole-dipole interactions that are enhanced by increasing atom density, and are already significant at densities of 0.1k 3 , where k denotes the resonance wavenumber. The observations are consistent with stochastic electrodynamics simulations that incorporate the effects of population transfer via internal atomic levels embedded in a coupled-dipole model.

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.