Stern-Gerlach Research Articles

Application of the Continuous Stern-Gerlach Effect for Laser Spectroscopy of the ^{40}Ar^{13+} Fine Structure in a Penning Trap.

We report on the successful demonstration of a novel scheme for detecting optical transitions in highly charged ions. We applied it to determine the frequency of the dipole-forbidden 2p ^{2}P_{1/2}-^{2}P_{3/2} transition in the fine structure of ^{40}Ar^{13+} using a single ion stored in the harmonic potential of a Penning trap. Our measurement scheme does not require detection of fluorescence, instead it makes use of the continuous Stern-Gerlach effect. Our value of 679.216464(4)_{stat}(5)_{syst} THz is in reasonable agreement with the current best literature values and improves its uncertainty by a factor of 24.

Some comments on the historical paper by H. Schmidt-Böcking “The Stern-Gerlach experiment re-examined by an experimenter” (EPN 50/3 pp. 15-19)

Some comments on the historical paper by H. Schmidt-Böcking “The Stern-Gerlach experiment re-examined by an experimenter” (EPN 50/3 pp. 15-19)

Relativistic Quantum Reference Frames: The Operational Meaning of Spin.

The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach setup in the nonrelativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The origin of this difficulty lies in the fact that, on the one hand, the spin gets entangled with the momentum in Lorentz-boosted reference frames, and on the other hand, for a particle moving in a superposition of velocities, it is impossible to "jump" to its rest frame, where spin is unambiguously defined. Here, we find a quantum reference frame transformation corresponding to a "superposition of Lorentz boosts," allowing us to transform to the rest frame of a particle that is in a superposition of relativistic momenta with respect to the laboratory frame. This enables us to first move to the particle's rest frame, define the spin measurements there (via the Stern-Gerlach experimental procedure), and then move back to the laboratory frame. In this way, we find a set of "relativistic Stern-Gerlach measurements" in the laboratory frame, and a set of observables satisfying the spin su(2) algebra. This operational procedure offers a concrete way of testing the relativistic features of the spin, and opens up the possibility of devising quantum information protocols for spin in the special-relativistic regime.

Quantum coherence recovery through Stern–Gerlach erasure

Quantum erasure probes the dynamic nature of quantum coherence. It allows quantum systems to exhibit interference effects by recovering coherence that was previously lost through entanglement with another system. In this paper we examine the concept of a quantum eraser which creates and then erases path information through repeated use of the Stern–Gerlach effect. We explore the degree to which this eraser can recover quantum coherence. We find that the recovered coherence depends on the spin of the objects passing through the eraser and on the relative angle between the orientations of the eraser’s two magnets. We determine that full coherence can always be recovered for spin-1/2 objects independent of the value of the spin projection but cannot always be recovered for objects with larger spin values. We then discuss how the quantum coherence could be experimentally measured in this setup. Finally, we comment on the limitations of this Stern–Gerlach eraser and similar erasure schemes.

Stern–Gerlach splitting of low-energy ion beams

We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern–Gerlach (SG) effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with sizes in the micron range, such as those recently used in a successful implementation of the SG effect with neutral atoms. All relevant forces (Lorentz force and image charges) are taken into account, and measurable splittings are found by analytical and numerical calculations.

Improving student understanding of quantum mechanics underlying the Stern–Gerlach experiment using a research-validated multiple-choice question sequence

Engaging students with well-designed multiple-choice questions during class and asking them to discuss their answers with their peers after each student has contemplated the response individually can be an effective evidence-based active-engagement pedagogy in physics courses. Moreover, validated sequences of multiple-choice questions are more likely to help students build a good knowledge structure of physics than individual multiple-choice questions on various topics. Here we discuss a framework to develop robust sequences of multiple-choice questions and then use the framework for the development, validation and implementation of a sequence of multiple-choice questions focusing on helping students learn quantum mechanics via the Stern–Gerlach experiment (SGE) that takes advantage of the guided inquiry-based learning sequences in an interactive tutorial on the same topic. The extensive research in developing and validating the multiple-choice question sequence (MQS) strives to make it effective for students with diverse prior preparation in upper-level undergraduate quantum physics courses. We discuss student performance on assessment task focusing on the SGE after traditional lecture-based instruction versus after engaging with the research-validated MQS administered as clicker questions in which students had the opportunity to discuss their responses with their peers.

Effect of vibrational excitation and spin-rotation coupling on Stern-Gerlach experiments: A detailed case study on GdSn15 as an asymmetric rotor

Magnetic moments of clusters have been measured for about 30 years by Stern-Gerlach experiments, but the interpretation of the results on small clusters at low temperatures is still under debate. In this study, the authors develop a microscopic model reproducing their experimental results, thereby providing a tool to further study the magnetism of free nanoparticles.

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

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.

Observation of a quasi-one-dimensional variation of the Stern-Gerlach effect

Observation of a quasi-one-dimensional variation of the Stern-Gerlach effect

Propose a Non-Destructive Stern-Gerlach Apparatus for Measuring the Spin Polarization of Electron Beam

Propose a Non-Destructive Stern-Gerlach Apparatus for Measuring the Spin Polarization of Electron Beam

The Stern-Gerlach experiment re-examined by an experimenter

The historic Stern-Gerlach experiment (SGE), which was performed in 1922 in Frankfurt, is reviewed from an experimental point of view. It is shown that the SGE apparatus is a purely classical momentum spectrometer, in which the trajectories of particles are measured. With modern detection devices the passage of each single atom can be identified and its trajectory in the magnetic field precisely determined. At the time of their experiment Stern and Gerlach achieved a hitherto unprecedented momentum resolution corresponding to an energy resolution of one μeV.

Stern–Gerlach detection of neutral-atom qubits in a state-dependent optical lattice

We demonstrate qubit state measurement for ~160 Cesium atoms in a 3D optical lattice based on coherent spatial splitting of the atoms' wavefunctions. The measurement fidelity is 0.9994, essentially independent of the number of qubits measured. The detection scheme is reminiscent of the Stern-Gerlach experiment, but carried out in light traps. The measurement causes no loss, which allows us to demonstrate re-initialization of the 3D qubit array after state measurement, including the replacement of an atom lost to a background gas collision.

Stern-Gerlach experiment with light: separating photons by spin with the method of A. Fresnel.

In 1822 A. Fresnel described an experiment to separate a beam of light into its right- and left-circular polarization components using chiral interfaces. Fresnel's experiment combined three crystalline quartz prisms of alternating handedness to achieve a visible macroscopic separation between the two circular components. Such quartz polyprisms were rather popular optical components in XIXth century but today remain as very little known optical devices. This work shows the analogy between Fresnel's experiment and Stern-Gerlach experiment from quantum mechanics since both experiments produce selective deflection of particles (photons in case of Fresnel's method) according to their spin angular momentum. We have studied a historical quartz polyprism with eight chiral interfaces producing a large spatial separation of light by spin. We have also constructed a modified Fresnel biprism to produce smaller separations and we have examined the analogy with Stern-Gerlach apparatus for both strong and weak measurements. The polarimetric analysis of a Fresnel polyprism reveals that it acts as a spin angular momentum analyzer.

N-Doping at the Sub-Nanoscale: Dielectric and Magnetic Response of Neutral Phosphorus-Doped Tin Clusters.

Doped semiconductors play a prevalent role in all aspects of modern technology. Because of the trend for smaller and smaller devices, we have investigated N-doping at the sub-nanoscale. For that purpose, we present molecular beam electric and magnetic deflection experiments on Sn NP ( N = 6-12) and Sn NP2 ( N = 7-12) clusters combined with quantum chemical calculations and classical beam deflection simulations. The theoretically identified and experimentally confirmed global minima structures resemble the valence-isoelectronic pure tin anions/dianions very closely, while each phosphorus dopant occupies the site of a tin atom. In Stern-Gerlach experiments, the single-doped clusters show a partial atom-like deflection behavior with total electronicangular momentum J = 1/2 whereas the results for the double-doped species suggest singlet states. This is in full agreement with quantum chemical results. The effect of vibrational excitation on magnetic and electric deflection experiments is examined. Our results provide insight into how the electric, magnetic, and structure properties are affected by n-doping at the sub-nanoscale.

Stern-Gerlach experiment with arbitrary spin: Temporal evolution and entanglement

Because it has disclosed basic quantum properties and concepts, the Stern-Gerlach experiment (SGE) has been fundamental for the development of quantum mechanics; for example, it was particularly used to model the measurement problem on the quantum world. Despite being almost one hundred years old, the SGE is still providing new valuable insights in the development and understanding of quantum mechanics. In this paper, by using the evolution operator method, we derive the equations that provide the time evolution of the quantum state of a particle with arbitrary spin s in the Stern-Gerlach apparatus. Such temporal evolution shows quantum entanglement between the degrees of freedom of the particle. We theoretically study, through the von Neumann entropy, the entanglement that arose between the degrees of freedom of the system for the case when the particle is polarized with an arbitrary angle $ \theta$ , analyzing how the entanglement depends on this angle $ \theta$ .

The ALPHATRAP experiment

The ALPHATRAP experiment at the Max-Planck Institute for Nuclear Physics in Heidelberg aims at probing the validity of quantum electrodynamics in extremely strong electromagnetic fields. To this end, ALPHATRAP will determine the value of the magnetic moment, or the g-factor, of the electron bound in highly charged ions. Quantum electrodynamics predicts this value with extraordinary precision. As the bound electron in highly charged ions is exposed to the strongest fields available for high-precision spectroscopy in the laboratory, reaching up to 1016 V/cm in hydrogenlike lead 208Pb81+, a comparison of the theoretical prediction with a measured value can yield the most stringent test of the Standard Model in strong fields. The targeted precision of eleven digits or more can be achieved by storing single highly charged ions in a cryogenic Penning trap, where its eigenfrequencies can be determined with ultra-sensitive electronics to highest precision. Additionally, the spin state can be non-destructively determined using the continuous Stern–Gerlach effect, allowing spectroscopy of the Larmor precession. ALPHATRAP is constructed to enable the injection and the storage of externally produced ions. The coupling to the Heidelberg EBIT gives access to even the heaviest highly charged ions and thus extends the available field strength by more than two orders of magnitude compared to previous experiments. This article describes the technical architecture and the performance of ALPHATRAP and summarises the experimental measurement possibilities.

Measurement of Ultralow Heating Rates of a Single Antiproton in a Cryogenic Penning Trap.

We report on the first detailed study of motional heating in a cryogenic Penning trap using a single antiproton. Employing the continuous Stern-Gerlach effect we observe cyclotron quantum transition rates of 6(1) quanta/h and an electric-field noise spectral density below 7.5(3.4)×10^{-20} V^{2} m^{-2} Hz^{-1}, which corresponds to a scaled noise spectral density below 8.8(4.0)×10^{-12} V^{2} m^{-2}, results which are more than 2 orders of magnitude smaller than those reported by other ion-trap experiments.

Chiral Optical Stern-Gerlach Newtonian Experiment

We report on a chiral optical Stern-Gerlach experiment where chiral liquid crystal microspheres are selectively displaced by means of optical forces arising from optical helicity gradients. The present Newtonian experimental demonstration of an effect predicted at molecular scale [New J. Phys. 16, 013020 (2014)NJOPFM1367-263010.1088/1367-2630/16/1/013020] is a first instrumental step in an area restricted so far to theoretical discussions. Extending the Stern-Gerlach experiment legacy to chiral light-matter interactions should foster further studies, for instance towards the elaboration of chirality-enabled quantum technologies or spin-based optoelectronics.

Uncertainty relations for time-averaged weak values

Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a weak value analog of the Heisenberg-Robertson strong value uncertainty principle. It leads to the conclusion that it is possible to determine with high accuracy the simultaneous mean weak values of non-commuting operators by judicious choice of the pre- and post-selected states. Generally, when the time fluctuations of the two weak values are proportional to each other there is no uncertainty limitation on their variances and, in principle, their means can be determined with arbitrary precision even though their corresponding operators do not commute. To exemplify these properties we consider specific weak value uncertainty relations for the time-energy, coordinate-momentum and coordinate-kinetic energy pairs. In addition we analyze spin operators and the Stern-Gerlach experiment in weak and strong inhomogeneous magnetic fields. This classic case leads to anomalous spin values when the field is weak. However, anomalous spin values are also associated with large variances implying that their measurement demands increased signal averaging. These examples establish the importance of considering the time dependence of weak values in time of flight scattering experiments.

Beyond antihydrogen: testing CPT with the molecular antihydrogen ion

Measurements of Zeeman, Zeeman-hyperfine and ro-vibrational transitions in $\bar {H}_{2}^{-}(\bar {p}e^{+}\bar {p})$ compared to $H_{2}^{+}$ have the potential for more precise tests of CPT than can be obtained from antiprotons and antihydrogen. In particular, measurements of ro-vibrational transitions have a potential sensitivity to a difference between antiproton and proton mass three orders of magnitude higher than antihydrogen/hydrogen. Methods are outlined for precision measurements on a single $\bar {H}_{2}^{-}$ or ${H}_{2}^{+}$ ion in a cryogenic Penning trap, with non-destructive state identification using the continuous Stern-Gerlach effect or changes in mass. $\bar {H}_{2}^{-}$ can be produced using the $\bar {H}^{+}+\bar {p} \rightarrow \bar {H}_{2}^{-} + e^{+}$ reaction.