In 1958, P.W. Anderson predicted the exponential localization 1 of electronic wave functions in disordered crystals and the resulting absence of diffusion. It has been realized later that Anderson localization (AL) is ubiquitous in wave physics 2 as it originates from the interference between multiple scattering paths, and this has prompted an intense activity. Experimentally, localization has been reported in light waves 3,4,5,6,7 , microwaves 8,9 , sound waves 10 , and electron 11 gases but to our knowledge there is no direct observation of exponential spatial localization of matter-waves (electrons or others). Here, we report the observation of exponential localization of a Bose-Einstein condensate (BEC) released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle 12 . We operate in a regime allowing AL: i) weak disorder such that localization results from many quantum reflections of small amplitude; ii) atomic density small enough that interactions are negligible. We image directly the atomic density profiles vs time, and find that weak disorder can lead to the stopping of the expansion and to the formation of a stationary exponentially localized wave function, a direct signature of AL. Fitting the exponential wings, we extract the localization length, and compare it to theoretical calculations. Moreover we show that, in our one-dimensional speckle potentials whose noise spectrum has a high spatial frequency cut-off, exponential localization occurs only when the de Broglie wavelengths of the atoms in the expanding BEC are larger than an effective mobility edge corresponding to that cut-off. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

We report the demonstration of a Sagnac-effect atom interferometer gyroscope which uses stimulated Raman transitions to coherently manipulate atomic wave packets. We have measured the Earth's rotation rate, and demonstrated a short-term sensitivity to rotations of 2 3 10 28 ͑rad͞s͒͞ p Hz.

We report a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part.Our observations are compatible with the self-consistent theory of Anderson localization, taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold. 1Anderson localization (AL) was proposed more than 50 years ago [1] to understand how disorder can lead to the total cancellation of conduction in certain materials. It is a purely quantum, one-particle effect, which can be interpreted as due to interference between the various amplitudes associated with the scattering paths of a matter wave propagating among impurities [2]. Anderson localization is predicted to strongly depend on the dimension [3]. In the three-dimensional (3D) case, a mobility edge is predicted, which corresponds to an energy threshold separating localized from extended states. Determining the precise behavior of the mobility edge remains a challenge for numerical simulations, microscopic theory and experiments [2]. The quest for AL has been pursued not only in condensed matter physics [4], but also in wave physics [5]: for instance with light waves [6][7][8][9], microwaves [10,11] and acoustic waves [12]. Following theoretical proposals [13][14][15][16][17][18], recent experiments [19,20] have shown that ultracold atoms in optical disorder constitute a remarkable system to study 1D localization [21][22][23]. Here, we report a study of 3D localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part. Our observations are compatible with the self-consistent theory of AL [24], taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold.Our scheme (Fig. 1a) is a generalization of the one that allowed us to demonstrate AL in 1D [15,19]. It involves a dilute Bose-Einstein condensate (BEC) with several 10 4 atoms of 87 Rb, initially in a shallow quasi-isotropic Gaussian optical trap, released and suddenly submitted to an optical disordered potential generated by a laser speckle [25]. The atoms, in the |F = 2, m F = −2 hyperfine state of the ground electronic state, are suspended by a magnetic gradient that compensates gravity (the residual component of the magnetic potential is isotropic and repulsive, of the form −mω 2 r 2 /2, with ω = ...

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We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions.

We propose in this White Paper a concept for a space experiment using cold atoms to search for ultra-light dark matter, and to detect gravitational waves in the frequency range between the most sensitive ranges of LISA and the terrestrial LIGO/Virgo/KAGRA/INDIGO experiments. This interdisciplinary experiment, called Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE), will also complement other planned searches for dark matter, and exploit synergies with other gravitational wave detectors. We give examples of the extended range of sensitivity to ultra-light dark matter offered by AEDGE, and how its gravitational-wave measurements could explore the assembly of super-massive black holes, first-order phase transitions in the early universe and cosmic strings. AEDGE will be based upon technologies now being developed for terrestrial experiments using cold atoms, and will benefit from the space experience obtained with, e.g., LISA and cold atom experiments in microgravity.KCL-PH-TH/2019-65, CERN-TH-2019-126

Inertial sensors relying on atom interferometry offer a breakthrough advance in a variety of applications, such as inertial navigation, gravimetry or ground- and space-based tests of fundamental physics. These instruments require a quiet environment to reach their performance and using them outside the laboratory remains a challenge. Here we report the first operation of an airborne matter-wave accelerometer set up aboard a 0g plane and operating during the standard gravity (1g) and microgravity (0g) phases of the flight. At 1g, the sensor can detect inertial effects more than 300 times weaker than the typical acceleration fluctuations of the aircraft. We describe the improvement of the interferometer sensitivity in 0g, which reaches 2 x 10-4 ms-2 / √Hz with our current setup. We finally discuss the extension of our method to airborne and spaceborne tests of the Universality of free fall with matter waves.

We report the demonstration of an atom interferometer-based gravity gradiometer. The gradiometer uses stimulated two-photon Raman transitions to measure the relative accelerations of two ensembles of laser cooled atoms. We have used this instrument to measure the gradient of the Earth's gravitational field. [S0031-9007(98)06679-4]