Critical Time and Length Scales and New Procedures for Performing ``Squeezed State Atom Interferometry,'' Using BEC's in Finite Optical Lattices

Kasevich has suggested\footnote{M. Kasevich, Compte Rendus, Serie IV, 2,, \#3 : 497-507} that ``squeezed state interferometry,'' using Bose Einstein Condensates (BEC’s) in Optical Lattices, may be useful for developing new, potentially revolutionary procedures for measuring gravity, acceleration and$/$or values of $\hbar$$/m$$_a$$_t$$_o$$_m$. The essential physics associated with his argument involves being able to address and manipulate, many atoms, in a BEC, at many locations, simultaneously, coherently (using an Optical Lattice), beginning from a non-BEC, many-body Fock state (for example, initialized from a Mott insulating state). A variant of his idea includes an additional procedure in which the Optical Lattice is accelerated coherently for discrete intervals of time in such a way that the BEC effectively ``sees'' an Umklapp transition in the direction of gravity and then (using a rotated lattice) perpendicular to it. A complication, associated with the new procedure, involves identifying the effects of boundaries and limitations associated with the finiteness of the lattice. Using a generalization of band theory to finite lattices\footnote{Scott R Chubb, Bull of the APS, v 49,\#1, part 2, 549 (2004.)}, estimates of critical time and length scales, based on simulations of the propagation of representative wave-packets, are used to quantify the effects of these limiting factors.