Abstract:
The unprecedented precision of atom interferometry will soon lead to laboratory tests of general relativity to levels that will rival or exceed those reached by astrophysical observations. We propose such an experiment that will initially test the equivalence principle to 1 part in 10^15 (300 times better than the current limit), and 1 part in 10^17 in the future. It will also probe general relativistic effects--such as the non-linear three-graviton coupling, the gravity of an atom's kinetic energy, and the falling of light--to several decimals. Further, in contrast to astrophysical observations, laboratory tests can isolate these effects via their different functional dependence on experimental variables.

Abstract:
Chameleons are a well motivated scalar field that might explain the observed late time accelerated expansion of the universe. Chameleons possess the interesting property that their mass, and hence interaction range, is dependent on the density of their environment. One very appealing feature of chameleons is the potential to test a model of dark energy in a laboratory setting. Here we briefly review two proposed experiments to search for chameleons using neutron interferometry techniques for the Snowmass 2013 Community Summer Study.

Abstract:
In recent years there has been an enormous progress in matter wave interferometry. The Colella- Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer, are the prototype of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question of to what extent the gravitational red shift, and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the non-vanishing, non-relativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.

Abstract:
The general relativistic gravitomagnetic clock effect consists in the fact that two point particles orbiting a central spinning object along identical, circular equatorial geodesic paths, but in opposite directions, exhibit a time difference in describing a full revolution. It turns out that the particle rotating in the same sense of the central body is slower than the particle rotating in the opposite sense. In this paper it is proposed to measure such effect in an Earth laboratory experiment involving interferometry of slow neutrons. With a sphere of 2.5 cm radius and spinning at 4.3 x 10^4 rad/s as central source, and using neutrons with wavelength of 1 Angstrom it should be possible to obtain, for a given sense of rotation of the central source, a phase shift of 0.18 rad, well within the experimental sensitivity. By reversing the sense of rotation of the central body it should be possible to obtain a 0.06 fringe shift.

Abstract:
In this paper, we present a brief overview of atom interferometry. This field of research has developed very rapidly since 1991. Atom and light wave interferometers present some similarities but there are very important differences in the tools used to manipulate these two types of waves. Moreover, the sensitivity of atomic waves and light waves to their environment is very different. Atom interferometry has already been used for a large variety of studies: measurements of atomic properties and of inertial effects (accelerations and rotations), new access to some fundamental constants, observation of quantum decoherence, etc. We review the techniques used for a coherent manipulation of atomic waves and the main applications of atom interferometers.

Abstract:
In this paper we discuss in detail an experimental scheme to test the universality of free fall (UFF) with a differential $^{87}$Rb / $^{85}$Rb atom interferometer applicable for extended free fall of several seconds in the frame of the STE-QUEST mission. This analysis focuses on suppression of noise and error sources which would limit the accuracy of a violation measurement. We show that the choice of atomic species and the correctly matched parameters of the interferometer sequence are of utmost importance to suppress leading order phase shifts. In conclusion we will show the expected performance of $2$ parts in $10^{15}$ of such an interferometer for a test of the UFF.

Abstract:
The light-pulse atom interferometry method is reviewed. Applications of the method to inertial navigation and tests of the Equivalence Principle are discussed.

Abstract:
We analyze the dynamics of neutron beams in interferometry experiments using quantum dynamical semigroups. We show that these experiments could provide stringent limits on the non-standard, dissipative terms appearing in the extended evolution equations.

Abstract:
We propose and demonstrate a new scheme for atom interferometry, using light pulses inside an optical cavity as matter wave beamsplitters. The cavity provides power enhancement, spatial filtering, and a precise beam geometry, enabling new techniques such as low power beamsplitters ($<100 \mathrm{\mu W}$), large momentum transfer beamsplitters with modest power, or new self-aligned interferometer geometries utilizing the transverse modes of the optical cavity. As a first demonstration, we obtain Ramsey-Raman fringes with $>75\%$ contrast and measure the acceleration due to gravity, $\mathit{g}$, to $60 \mathrm{\mu \mathit{g} / \sqrt{Hz}}$ resolution in a Mach-Zehnder geometry. We use $>10^7$ cesium atoms in the compact mode volume ($600 \mathrm{\mu m}$ $1/e^2$ waist) of the cavity and show trapping of atoms in higher transverse modes. This work paves the way toward compact, high sensitivity, multi-axis interferometry.

Abstract:
Neutron spin can be coupled to the Earth's rotating frequency. Once if the Earth's rotating frequency is time-dependent, then the neutron will acquire a Berry's topological phase (cyclic adiabatic geometric phase). So, a potential method to investigate the Earth's time-varying rotating frequency by measuring the phase difference between geometric phases of neutron spin polarized vertically down and up is proposed.