Experimental proof of coherent spatial interference from the logitudinal (1D) Stern-Gerlach (SG) interferometer. (a) A single-shot interference pattern of a thermal cloud with a negligible BEC fraction, with a visibility of 𝑉 = 0.65, clearly showing that a BEC is not needed for the interferometer to work. (b) A multishot image made by averaging 40 consecutive interference images using a BEC (no correction or postselection) with a normalized visibility of 𝑉 = 0.99, proving that the interferometer is phase stable and that no BEC interference (with random fringe position) was involved. (c) Spin oscillations observed at the output of the full-loop SG. The data agrees almost perfectly with the theory developed for a spatial interferometer by the group of Wolfgang Schleich. The excellent agreement again proves that coherent spatial splitting has been achieved. Additional experimental results include clock interferometry and geometrical phase, results which all fit nicely with the theory of a spatial SG interferometer. For a detailed review of the experiments see: Keil, M. et al. (2021). Stern-Gerlach Interferometry with the Atom Chip. In: Friedrich, B., Schmidt-Böcking, H. (eds) Molecular Beams in Physics and Chemistry. Springer, Cham. https://doi.org/10.1007/978-3-030-63963-1_14 I believe I have never before addressed a scientific paper with nonacademic language, but for reasons which I hope I can make clear below, I allow myself in this Commentary to go beyond scientific language. Prof. Devereux has been attempting for quite a number of years to claim that coherent Stern-Gerlach (SG) splitting is impossible. For example, he claimed that "Einsteinian relativity, and the understanding of Schrödinger evolution applicability through a static potential, forbid continuation of a spin superposition through the Stern–Gerlach field."1 While I am convinced that trying to oppose the mainstream paradigm is an essential part of doing science and therefore welcome such attempts, I am weary of attempts that are made without proper arguments. Prof. Devereux tried to present his arguments in person in a workshop in Frankfurt in 2019 when the SG lab was declared an EPS Historic Site, and once again was unable to make any proper argument to support his point of view. Now, he is publishing rather bizarre theoretical arguments stating "Thus, wavefunction development in the Stern-Gerlach magnet is discontinuous when the atom absorbs real energy from the magnet. Discontinuity in wavefunction evolution implies a loss of interference downstream of the S-G magnet." I will let the community judge the veracity of his theoretical arguments.2 I decided to write this commentary not because of all of the above, but because this time Prof. Devereux has also wandered into the experimental realm, explaining why previous SG interferometry experiments, and specifically my group's experiments, are in fact not proving that coherent SG splitting is possible. Doing so without a proper understanding of these decade-long experiments is regrettable. To begin with, Prof. Devereux tries to explain the numerous different experiments that we have conducted over the last 10 years3 and sums them up in three short paragraphs. Such a short account immediately excludes any possibility of a serious in-detail discussion. In addition, some important references from our work are missing, and there are unfortunate significant typos in the references that were included. But to all of these defects, one could turn a blind eye. However, the complete misunderstanding of the physics behind our experiments, which Prof. Devereux exhibits in the short text he wrote, leaves me with no option but to react. He writes: "The researchers have not demonstrated that each Rb atom's wavefunction is split into two coherent wave-packets, analogous to individual photons passing a double-slit screen, yielding interference." Here, he seems to be talking about our experiments in which the signal was a spatial interference fringe pattern.4, 5 He seems to think that it is possible that half of the atoms went one way and half the other way. His claim is wrong because if two halves of the BEC were to go along a different path, we would get BEC interference, and BEC interference was shown a long time ago to give rise to an interference pattern with a random fringe position. As in our experiment we have averaged over many experimental cycles (to prove the phase stability of the interferometer), these random BEC fringes would have been averaged to zero visibility, whereas we observed very high visibility. Furthermore, we even saw the spatial interference pattern with a thermal cloud (!) which clearly has no collective coherence, see Fig. 1a,b. (For interferometry with a BEC, see;6-9 see also our theoretical work.10) He writes: "But, instead of checking whether every atom has retained its original spin direction, with an additional S-G apparatus, they employ Ramsey's oscillating fields method [17], which is sometimes mistaken for an interferometer." Here, he seems to be talking about our experiments in which the signal was a spin population oscillation.11, 12 His claim is again false. Indeed, we apply a Ramsey sequence, but this in no way contradicts spatial splitting and interferometry. In fact, most spatial interferometers currently in use utilize Ramsey sequences. It is important to note that in this experiment a unique phase accumulation relation was observed (T3, where T is the interferometer time), and theoretical calculations done by the Ulm group of Wolfgang Schleich confirmed that this is a unique signal of a spatial interferometer where the two wave-packets were separated in real space and took different space-time paths until they recombined, see Fig. 1c.11 For the sake of completeness, I add two technical points: First, Devereux's suggestion to do a measurement with "an additional S-G apparatus" is in fact exactly what we do, since we apply in these experiments a fifth magnetic gradient pulse to separate the spins spatially according to their spin before we take a picture with a CCD.11 Second, to make sure there is no error in our interpretation of the experiment, we conducted this experiment in two ways. Specifically, we change the sign of the forces on each of the wave-packets (in order to achieve recombination) once by flipping the spins with a π pulse, and also by flipping the direction of the magnetic gradient. Both experiments give the same result, thus showing that the results and their interpretation are robust. Finally, he suggests a new experiment with slits (Figure 1 of his paper), unaware that such an experiment was indeed already realized by us. In his suggestion for a new experiment, he describes the idea of expanding the two wave-packets after the SG splitting by diffracting them via narrow slits so that they would overlap and interfere. Indeed, this is exactly what was done in our experiment utilizing a spatial-interference-fringe-pattern signal4, 5. The only difference was that instead of the diffraction in the slits, we found that we can allow for enough time-of-flight so that the wave-packets expand on their own sufficiently in order to overlap and create an interference pattern. This was done both with a dilute BEC and a thermal cloud. An important point of fundamental physics: There is one difference, however, which I would like to emphasize between the experiment we did and the experiment suggested by Prof. Devereux in Figure 1 of his paper. The suggested experiment as is would simply not work. Since the two wave-packets are distinguishable (due to their orthogonal spin) there will be no interference. In the original proposal decades ago, the spins up and down were defined along some quantization axis (let us call it z) and the eventual measurement was along x, and this choice erased the which-path-information. But in Prof. Devereux's suggestion, there seems to be no such erasing operation. In our experiment, we erased this spin orthogonality with a final π/2 pulse. Let me end by stating that I do agree that there is still a lot of room for additional experimental investigations of the SG apparatus, as it is not at all the simple apparatus as the textbooks portray it to be. For example, the role of spin precession and constraints due to Maxwell's equations are interesting questions.13-17 To conclude, the SG effect and SG spatial interferometry have a long experimental and theoretical history which I have not reviewed here.18 The experimental realization of SG spatial interferometry has already given rise to quite a few applications.19-22 I am sincerely satisfied to see that numerous experimental and theoretical groups are starting to utilize the technique, especially since it may offer a way to achieve the long-sought-after spatial superposition of a macroscopic object.12, 23-28 Prof. Devereux would have saved himself and everyone else a lot of time if he would just have taken the time to understand in detail both the numerous theoretical studies and the experiments which have already been done. It is unfortunate that, apparently, the peer review process failed to identify such a manuscript as flawed. The author declares no conflict of interest. The peer review history for this article is available at https://www.webofscience.com/api/gateway/wos/peer-review/10.1002/ntls.20240025. Data available on request from the author.
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