Abstract
Long-time atom interferometry is instrumental to various high-precision measurements of fundamental physical properties, including tests of the equivalence principle. Due to rotations and gravity gradients, the classical trajectories characterizing the motion of the wave packets for the two branches of the interferometer do not close in phase space, an effect which increases significantly with the interferometer time. The relative displacement between the interfering wave packets in such open interferometers leads to a fringe pattern in the density profile at each exit port and a loss of contrast in the oscillations of the integrated particle number as a function of the phase shift. Paying particular attention to gravity gradients, we present a simple mitigation strategy involving small changes in the timing of the laser pulses which is very easy to implement. A useful representation-free description of the state evolution in an atom interferometer is introduced and employed to analyze the loss of contrast and mitigation strategy in the general case. (As a by-product, a remarkably compact derivation of the phase-shift in a general light-pulse atom interferometer is provided.) Furthermore, exact results are obtained for (pure and mixed) Gaussian states which allow a simple interpretation in terms of the alignment of Wigner functions in phase-space. Analytical results are also obtained for expanding Bose–Einstein condensates within the time-dependent Thomas–Fermi approximation. Finally, a combined strategy for rotations and nonaligned gravity gradients is considered as well.
Highlights
In this article we analyze in detail the loss of integrated contrast in open atom interferometers, where classical phase-space trajectories do not close, with particular emphasis on the effects of gravity gradients
The potential of light-pulse atom interferometry [1, 2] for high-precision measurements has been amply demonstrated with its successful implementation in extremely sensitive inertial sensors, including gyroscopes [3,4,5], gradiometers [6] and the currently most precise absolute gravimeters [7,8,9]
It has already found applications in accurate measurements of fundamental constants [10,11,12,13,14,15] and tests of fundamental properties [16,17,18], and it is a key ingredient in plans for future tests of the equivalence principle in space [19, 20], next-generation satellite geodesy missions [25] or even alternative proposals for gravitational-wave detection [26]
Summary
In this article we analyze in detail the loss of integrated contrast in open atom interferometers, where classical phase-space trajectories do not close, with particular emphasis on the effects of gravity gradients. Plans for the European Space Agency’s STE-QUEST mission [19] have estimated a 40% loss of contrast due to gravity gradients despite a required effective temperature for the atom cloud below 70 pK, and this is the main driver behind the need for such a narrow momentum distribution ( it has other added benefits on diffraction efficiencies or systematics associated with the Rabi frequency) Such a loss of contrast is, a generic feature of open interferometers, where the classical trajectories characterizing the motion of the wave packets do not close in phase space and the resulting relative displacements in position and momentum, δR and δP, cause a reduction of the quantum overlap between the interfering states in each exit port. The Gross-Pitaevskii equation and its solution for expanding BECs within the framework of the scaling approach and the time-dependent Thomas-Fermi approximation are briefly reviewed in Appendix D and its connection with free evolution at late times is discussed in some detail
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