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...

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.

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...

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.

Clocks play a special role at the interface of general relativity and quantum mechanics. We analyze a clock-interferometry thought experiment and go on to theoretically derive and experimentally test a complementarity relation for quantum clocks in the context of the gravitational time lag. We study this relation in detail and discuss its application to various types of quantum clocks. * Electronic address: rohrlich@bgu.ac.il; corresponding author 1 arXiv:1802.09235v1 [quant-ph]

The geometric phase due to the evolution of the Hamiltonian is a central concept in quantum physics, and may become advantageous for quantum technology. In non-cyclic evolutions, a proposition relates the geometric phase to the area bounded by the phase-space trajectory and the shortest geodesic connecting its end points. The experimental verification of this geodesic rule proposition has remained elusive for more than three decades. Here, we report an unambiguous experimental confirmation of the geodesic rule for a non-cyclic geometric phase by means of a spatial SU(2) matter-wave interferometer, demonstrating, with high precision, the predicted phase sign change and π jumps. We show the connection between our results and the Pancharatnam phase. Finally, we point out that the geodesic rule can be applied to obtain the red-shift in general relativity, enabling a completely new quantum tool to measure gravity.The geometric phase (GP), the phase acquired over the course of an evolution of the Hamiltonian in parameter space, is a central concept in classical and in quantum physics (1-9). Originally, the GP was defined only for an evolution of a system in a closed trajectory in phase space, 1 arXiv:1908.03008v1 [cond-mat.quant-gas]

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.