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New Journal of Physics

Analysis of a high-stability Stern–Gerlach spatial fringe interferometer

Yair Margalit, Zhifan Zhou, Shimon Machluf, Yonathan Japha, S. Moukouri, R. Folman

Published Jul 8, 2019• 27 citations
Publisher

Abstract

The discovery of the Stern–Gerlach (SG) effect almost a century ago was followed by suggestions to use the effect as a basis for matter-wave interferometry. However, the coherence of splitting particles with spin by a magnetic gradient to a distance exceeding the position uncertainty in each of the arms was not demonstrated until recently, where spatial interference fringes were observed in a proof-of-principle experiment. Here we present and analyze the performance of an improved high-stability SG spatial fringe interferometer based on two spatially separate wave packets with a maximal distance that is more than an order of magnitude larger than their minimal widths. The improved performance is enabled by accurate magnetic field gradient pulses, originating from a novel atom chip configuration, which ensures high stability of the interferometer operation. We analyze the achieved stability using several models, discuss sources of noise, and detail interferometer optimization procedures. We also present a simple analytical phase-space description of the interferometer sequence that demonstrates quantitatively the complete separation of the superposed wave packets 2 .

DOI
10.1088/1367-2630/ab2fdc

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The discovery of the Stern–Gerlach (SG) effect almost a century ago was followed by suggestions to use the effect as a basis for matter-wave interferometry. However, the coherence of splitting particles with spin by a magnetic gradient to a distance exceeding the position uncertainty in each of the arms was not demonstrated until recently, where spatial interference fringes were observed in a proof-of-principle experiment. Here we present and analyze the performance of an improved high-stability SG spatial fringe interferometer based on two spatially separate wave packets with a maximal distance that is more than an order of magnitude larger than their minimal widths. The improved performance is enabled by accurate magnetic field gradient pulses, originating from a novel atom chip configuration, which ensures high stability of the interferometer operation. We analyze the achieved stability using several models, discuss sources of noise, and detail interferometer optimization procedures. We also present a simple analytical phase-space description of the interferometer sequence that demonstrates quantitatively the complete separation of the superposed wave packets 2 .
The Stern-Gerlach (SG) effect, discovered almost a century ago, has become a paradigm of quantum mechanics. Surprisingly there is little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Specifically, no high-visibility spatial interference pattern has been observed with such a scheme, and furthermore no full-loop SG interferometer has been realized with the scheme as envisioned decades ago. On the contrary, numerous theoretical studies explained why it is a near impossible endeavor. Here we demonstrate for the first time both a high-visibility spatial SG interference pattern and a full-loop SG interferometer, based on an accurate magnetic field, originating from an atom chip, that ensures coherent operation within strict constraints described by previous theoretical analyses. This also allows us to observe the gradual emergence of time-irreversibility as the splitting is increased. Finally, achieving this high level of control over magnetic gradients may facilitate technological applications such as large-momentum-transfer beam splitting for metrology with atom interferometry, ultra-sensitive probing of electron transport down to shot-noise and squeezed currents, as well as nuclear magnetic resonance and compact accelerators.
Abstract In this invited review in honor of 100 years since the Stern-Gerlach (SG) experiments, we describe a decade of SG interferometry on the atom chip. The SG effect has been a paradigm of quantum mechanics throughout the last century, but there has been surprisingly little evidence that the original scheme, with freely propagating atoms exposed to gradients from macroscopic magnets, is a fully coherent quantum process. Specifically, no full-loop SG interferometer (SGI) has been realized with the scheme as envisioned decades ago. Furthermore, several theoretical studies have explained why it is a formidable challenge. Here we provide a review of our SG experiments over the last decade. We describe several novel configurations such as that giving rise to the first SG spatial interference fringes, and the first full-loop SGI realization. These devices are based on highly accurate magnetic fields, originating from an atom chip, that ensure coherent operation within strict constraints described by previous theoretical analyses. Achieving this high level of control over magnetic gradients is expected to facilitate technological applications such as probing of surfaces and currents, as well as metrology. Fundamental applications include the probing of the foundations of quantum theory, gravity, and the interface of quantum mechanics and gravity. We end with an outlook describing possible future experiments.
Here we propose and demonstrate a new way of using SG type methods in order to split and recombine matter waves. We use Rabi oscillations and magnetic field gradients in order to split87Rb atoms into two momentum components while keeping the two outputs of the beam splitter (BS) in the same spin state (Zeeman sublevels). After recombining the two outputs of the BS a spatial fringe pattern is observed. The new BS may enable a wide range of applications, such as, fundamental studies of many-body entanglement and dephasing processes, probing classical and quantum properties of nearby solids, and metrology of rotation, acceleration and gravity on a chip scale.
We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers that make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.
An atom interferometer using two Stern-Gerlach magnets as polariser and analyser is described. The interferometer was first operated with a thermal beam of ground state potassium atoms. In that case the beam splitters are two radio-frequency zones within a transverse homogeneous magnetic field building a coherent superposition of Zeeman states. Ramsey fringes are obtained by scanning the RF-frequency through the resonance profile. Pulsing the RF power allows to get the time-of-flight distribution of the beam. Atomic interference fringes (``Stern-Gerlach fringes'') are observed when the magnitude of an inhomogeneous magnetic field located in between the beam splitters is scanned. When the inhomogeneous field is also pulsed, the scalar Bohm-Aharonov effect is observed. The use of metastable helium atoms (He*23S) in place of potassium atoms is proposed. In addition to the usual advantages provided by metastable atoms of high internal energy, this atom offers the specific advantage to behave as an ideal spin-one particle. This allows us to greatly simplify the polarisation scheme of the interferometer. Possible applications involving transversally inhomogeneous magnetic fields are given and limitations due to the finite source size and angular aperture are discussed.
We show that superficially similar implementations of Stern-Gerlach Interferometers (SGIs) are expected to differ dramatically in their sensitivity to fields transverse to the primary acceleration direction. These transverse fields unavoidably accompany any static magnetic or electric field gradients, and have been shown by Comparat [Phys. Rev. A 101, 023606 (2020)] to limit the precision application of SGIs. As a concrete example, we consider SGIs with ultracold Rb Rydberg atoms accelerated by spatially-varying electric fields. We find that the deleterious effect of transverse fields imply that only some implementations (sequences of field gradients, internal state swaps, and so-on) may exhibit fringes with high visibility.