Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical diffraction. In an experiment of light storage in a gas of diffusing atoms, a complex initial condition is imprinted, and its diffusion dynamics is monitored.The self-similarity of both the amplitude and the phase pattern is demonstrated, and an algebraic decay associated with the mode order is measured. Notably, as opposed to a regular diffusion spreading, a self-similar contraction of a special subset of the solutions is predicted and observed.Typeset by REVT E X 1

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We present new techniques for inertial-sensing atom interferometers which produce multiple phase measurements per experimental cycle. With these techniques, we realize two types of multiport measurements, namely quadrature phase detection and real-time systematic phase cancellation, which address challenges in operating high-sensitivity cold-atom sensors in mobile and field applications. We confirm experimentally the increase in sensitivity due to quadrature phase detection in the presence of large phase uncertainty, and demonstrate suppression of systematic phases on a single shot basis.Cold atom interferometers have demonstrated extremely high sensitivity as inertial sensors measuring gravity [1][2][3], gravity gradients [4][5][6][7][8], accelerations and rotations [9][10][11][12][13][14][15][16][17]. In addition to precision measurements of physical constants [18][19][20][21][22], tests of general relativity [23][24][25][26][27][28], searches for dark energy [29,30], and gravitational wave detection [31,32], they are promising candidates as on-board inertial measurement units [10,[33][34][35] and as mobile gravimeters for geodesic studies or subterranean exploration [36][37][38][39][40][41]. These prospects provide strong motivation for improving the robustness of atom interferometers while maintaining high phase sensitivity and accuracy under field conditions, such as strong vibrations and drifts in the thermal and magnetic environment.Atom interferometers typically yield a single phase measurement per shot. This may limit their performance in challenging conditions: first, phase sensitivity is maximal in the linear regime near mid-fringe, which requires locking the phase from shot to shot [40]. This is difficult to maintain when the inertial signal changes on short timescales, such as in mobile applications, or when vibrations introduce large uncontrolled phase variation. Realtime correction using classical sensors can be applied to return the interferometer to mid-fringe [40,42], but effects such as delay in their response [43] ultimately limit their effectiveness for strong vibrations. Second, many systematic phase shifts are typically canceled with the "kreversal" technique, using sequential measurements with opposite wave vectors [5,44]. However, it is not effective against fast variations in systematic effects, which may arise in field applications, and it inherently reduces the bandwidth and sensitivity per √ Hz of the interferometer. In this Letter, we introduce two new schemes which extend inertial-sensing atom interferometers to yield multiple phase signals in each experiment, increasing its information bandwidth and improving its performance. One scheme utilizes a composite beam-splitter, which replaces the final beam-splitter in typical atom interferometers, and the other is based on operating dual concurrent interferometers on a single atomic ensemble, with independent control of their phases. Using these schemes, we demonstrate two measurement approaches which address chal-lenges of deployable a...

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