Overcoming loss of contrast in atom interferometry due to gravity gradients

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 phaseshift 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.

Representation-free description of atom interferometers in time-dependent linear potentials

“…In the case that the two interferometer branches cross in space, it is the signed area which is relevant. Needless to say that the general result derived in appendix C agrees with the considerations presented in [81,82] which are valid for both Raman and Bragg diffraction. In the special case of a closed interferometer, equation (37) coincides with the result obtained within the semi-classical description [67].…”

“…In contrast to the average functionsF for the MZ interferometer, equation (59), and the T 3 -interferometer, equation (77), which are constant in the interval 0<t<T, due to the time-dependence of F 1 (t), also the average¯( ) t F is now time-dependent during the interferometer sequence. However, as shown in appendix D, due to the symmetries of δr(t), equation (89), and¯( ) t F , only the constant term F 0 in F 2 , equation (81), and F 1 (t), equation (82), will contribute to the phase shift δf 1 arising from the linear potentials. According to equation (39) we thus obtain the second contribution 10 Here we use…”

“…In this article we develop a novel formalism based on the ideas and results presented in [80][81][82], valid for atoms moving in any time-and state-dependent linear potential. In order to determine the phase and contrast of an atom interferometer, the complete time evolution is usually split into pieces describing the time-evolution resulting from its basic building blocks: beam splitters, mirrors, and free propagation.…”

T 3-Interferometer for atoms

“…However, an interferometric measurement of the difference of two different global phase factors of two systems is possible. In such an interferometer the cubic phase is independent [36] of the initial wave function.…”

“…This deficiency leads to a loss of contrast [36] and a dependence of the phase shift on the initial state.…”