Abstract
We theoretically analyse a multi-modes atomic interferometer consisting of a sequence of Kapitza-Dirac pulses (KD) applied to cold atoms trapped in a harmonic trap. The pulses spatially split the atomic wave-functions while the harmonic trap coherently recombines all modes by acting as a coherent spatial mirror. The phase shifts accumulated among different KD pulses are estimated by measuring the number of atoms in each output mode or by fitting the density profile. The sensitivity is rigorously calculated by the Fisher information and the Cramér-Rao lower bound. We predict, with typical experimental parameters, a temperature independent sensitivity which, in the case of the measurement of the gravitational constant g can significantly exceed the sensitivity of current atomic interferometers.
Highlights
The goal of interferometry is to estimate the unknown value of a phase shift
We theoretically analyse a multi-modes atomic interferometer consisting of a sequence of Kapitza-Dirac pulses (KD) applied to cold atoms trapped in a harmonic trap
Most current interferometric protocols for the measurement of gravity or inertial forces are based on the manipulation of free falling atoms realizing Mach-Zehnder like configurations
Summary
The goal of interferometry is to estimate the unknown value of a phase shift. The phase shift can arise because of a difference in length among two interferometric arms, as in the first optical Michelson-Morley probing the existence of aether or in LIGO and VIRGO gravitational wave detectors [1]. Relative to the 2-photon processes used in the current most sensitive light-pulse atom interferometers, LMT beam splitters in atomic fountains can provide a 44-fold increased phase shift sensitivity [16]. With KD pulses applied to atoms in a harmonic trap, it is possible to reach large spatial separations between the interferometric modes by avoiding, at the same time, atom losses and defocusing occurring in Bragg processes (mostly due to the constraint of narrow momentum widths). The number of beams is proportional to the strength of the applied KD pulse while their distance is proportional to the ratio between the harmonic trap length and the wave-length of the optical wave In this manuscript we discuss in detail the theory of the multi-modes KD interferometer which was introduced in [23]
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