We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.

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.

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 study the storage and retrieval of images in a hot atomic vapor using the gradient echo memory protocol. We demonstrate that this technique allows for the storage of multiple spatial modes. We study both spatial and temporal multiplexing by storing a sequence of two different images in the atomic vapor. The effect of atomic diffusion on the spatial resolution is discussed and characterized experimentally. For short storage time a normalized spatial cross-correlation between a retrieved image and its input of 88 % is reported.

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 paper, we present a simple yet efficient and effective multi-resolution approach to gray-scale and rotation invariant texture classification. Given a texture image, we at first convolve it with J Gabor filters sharing the same parameters except the parameter of orientation. Then by binarizing the obtained responses, we can get J bits at each location. Then, each location can be assigned a unique integer, namely "rotation invariant binary Gabor pattern (BGP ri )", formed from J bits associated with it using some rule. The classification is based on the image's histogram of its BGP ri s at multiple scales. Using BGP ri , there is no need for a pre-training step to learn a texton dictionary, as required in methods based on clustering such as MR8. Extensive experiments conducted on the CUReT database demonstrate the overall superiority of BGP ri over the other state-of-the-art texture representation methods evaluated. The Matlab source codes are publicly available at

Using a nondegenerate four-wave mixing process in hot rubidium vapor, we demonstrate a compact diode-laser-pumped system for the generation of intensity-difference squeezing down to 8 kHz with a maximum squeezing of -7 dB. To the best of our knowledge, this is the first demonstration of kilohertz-level intensity-difference squeezing using a semiconductor laser as the pump source. This scheme is of interest for experiments involving atomic ensembles, quantum communications, and precision measurements. The diode-laser-pumped system would extend the range of possible applications for squeezing due to its low cost, ease of operation, and ease of integration.