Microgravity Gradiometry Measurement Schemes with Multiple-Pathway Atom Interferometers

We propose a new atom-interferometry scheme for measuring the value and derivatives of the gravitational field in the microgravity environment found in the Cold-Atom Laboratory to be deployed by the US National Aeronautics and Space Administration to the International Space Station. The operation of the proposed atom interferometer consists of splitting a Bose-Einstein condensate, confined by harmonic (spring-like) forces, into multiple pieces using a sequence of laser pulses by a method known as momentum-space engineering [1]. In a perfect harmonic oscillator potential the oscillation period is independent of the oscillation amplitude. Thus all of the condensate pieces will come to rest at the same time. At this point, the harmonic confinement is turned off. The nearly motionless condensate clouds now experience only tidal forces which effectively act like negative springs and the clouds are accelerated away from each other. The various clouds thus accumulate different phases due to their respective accelerations at different points in space. After a sufficient delay period, the confinement is then turned back on bringing all of the clouds together at the same time. At this point the same sequence of laser pulses is used to again split the reassembled condensate, producing multiple clouds each having a different velocity. These clouds again separate and some of them will have interference patterns imprinted on them. These patterns contain information about the value and derivatives of the gravitational field in the microgravity environment. We have simulated some of these interferometric schemes using both a one-dimensional time-dependent Gross-Pitaevskii equation and a Lagrangian variational Method (LVM) to the 3D time–dependent, Gross–Pitaevskii equation. We have used the LVM method to facilitate rapid interferometer design and to understand how these interference patterns can be used to measure the gravitational field and its derivatives. We also compare the sensitivity of the different interferometric schemes. These types of interferometers have the potential to make precision measurements of Newton\u27s universal gravitational constant. [1] Edwards, M. et al., Physical Review A vol. 82, 063613 (2010)