Theoretical Comparison of Stern-Gerlach Interferometer Sequences in Cylindrically Symmetric Fields*

Recent work has demonstrated practical coherent recombination of the arms of a magnetic Stern-Gerlach matter-wave interferometer [1], an act once compared to putting Humpty-Dumpty back together again [2]. These devices use inhomogeneous electric and/or magnetic fields to send two states with different dipole moments down separate arms of an interferometer. Using laser-cooled atoms, it is possible to achieve a spatial separation in excess of the thermal de Broglie wavelength of the atoms within the arms before spatially recombining them. As shown by Comparat [3], in a cylindrically symmetric geometry, a significant limitation to the visibility of Stern-Gerlach interferometers comes from the transverse off-axis components of the accelerating field, as these remain unchanged when the gradient of the field is reversed. Thus, off-axis atoms experience a net displacement in both position and momentum that limits coherent recombination.

We provide theoretical modeling of one such interferometer using rubidium Rydberg atoms in a cylindrically symmetric DC electric field.  We show that the visibility limitations imposed by off-axis atoms depend on the sequence being examined, and further that many superficially similar sequences are significantly different in this regard, with some demonstrating robust visibility in experimentally relevant regimes.

[1] Y. Margalit, O. Dobkowski, Z. Zhou, O. Amit, Y. Japha, S. Moukouri, D. Rohrlich, A. Mazumdar, S. Bose, C. Henkel, and R. Folman, “Realization of a complete Stern-Gerlach interferometer: Toward a test of quantum gravity”, Science Advances 7, Publisher: American Association for the Advancement of Science, eabg2879 (2021).

[2] B.-G. Englert, J. Schwinger, and M. O. Scully, “Is spin coherence like Humpty-Dumpty? I. Simplified treatment”, en, Foundations of Physics 18, 1045–1056 (1988).

[3] D. Comparat, “Limitations for field-enhanced atom interferometry”, Physical Review A 101, Publisher: American Physical Society, 023606 (2020).