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.
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.
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.
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.
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 .
Realizing a spatial superposition with massive objects is one of the most fundamental challenges, as it will test quantum theory in new regimes, probe quantum-gravity, and enable to test exotic theories like gravitationally induced collapse. A natural extension of the successful implementation of an atomic Stern-Gerlach interferometer (SGI), is a SGI with a nano-diamond (ND) in which a single spin is embedded in the form of a nitrogen-vacancy center (NV). As the ND rotation, and with it the rotation of the NV spin direction, may inhibit such a realization, both in terms of Newtonian trajectories and quantum phases, we analyze here the role of rotations in the SGI. We take into account fundamental limits, such as those imposed by the quantum angular uncertainty relation and thermal fluctuations. We provide a detailed recipe for which a superposition of massive objects is enabled. This may open the door not only to fundamental tests, but also to new forms of quantum technology.
Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. We introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman transitions can be understood as a special case. We also show that the SG interferometer can keep high contrast against a misalignment in position and momentum caused by the field gradient.
A coherent electric analogue of the Stern-Gerlach experiment has been performed with helium atoms in Rydberg states. The atoms, travelling in pulsed supersonic beams, were prepared in superpositions of Rydberg states with different static electric dipole polarisabilities using pulses of microwave radiation. State-dependent forces were then exerted on them, transverse to their direction of propagation, using inhomogeneous electric fields. These fields were generated between a pair of electrodes in a wedge configuration. The forces applied resulted in the coherent evolution of each atomic wavepacket into a superposition of spatially separated momentum states. The classical paths of least action associated with these momentum states evolved over time up to a separation of ∼2 nm. The coherent evolution of the atoms, and hence the superposition of atomic wavepackets in this ‘half-loop’ electric Rydberg-atom interferometer, was monitored by measuring the internal Rydberg state populations at the end of each measurement cycle. The experimental data are in good quantitative agreement with the results of semiclassical calculations of the phase evolution of the atomic superposition states which account for contributions from Stark shifts, the momentum differences between the classical paths of least action through the apparatus, and the spatial separation of the atomic wavepackets.