Grating Diffraction of Molecular Beams: Present Day Implementations of Otto Stern’s Concept

When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.

Precision Physics in Penning Traps Using the Continuous Stern-Gerlach Effect

Abstract“A single atomic particle forever floating at rest in free space” (H. Dehmelt) would be the ideal object for precision measurements of atomic properties and for tests of fundamental theories. Such an ideal, of course, can ultimately never be achieved. A very close approximation to this ideal is made possible by ion traps, where electromagnetic forces are used to confine charged particles under well-controlled conditions for practically unlimited time. Concurrently, sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to bring the trapped ion nearly to rest. Among different realisations of ion traps we consider in this chapter the so-called Penning traps which use static electric and magnetic fields for ion confinement. After a brief discussion of Penning-trap properties, we consider various experiments including the application of the “continuous Stern-Gerlach effect”, which have led recently to precise determinations of the masses and magnetic moments of particles and antiparticles. These serve as input for testing fundamental theories and symmetries.

Quantum or Classical Perception of Atomic Motion

An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to perceive quantum dynamics as classical. This has implications for the interpretation of quantum wavefunctions as a characteristic of ensembles or of single particles and the related question of wavefunction “collapse”. A brief historical overview is presented as well as recent emphasis on the role of the semi-classical “imaging theorem” in describing quantum to classical unitary evolution.

High-Resolution Momentum Imaging—From Stern’s Molecular Beam Method to the COLTRIMS Reaction Microscope

Multi-particle momentum imaging experiments are now capable of providing detailed information on the properties and the dynamics of quantum systems in Atomic, Molecular and Photon (AMO) physics. Historically, Otto Stern can be considered the pioneer of high-resolution momentum measurements of particles moving in a vacuum and he was the first to obtain sub-atomic unit (a.u.) momentum resolution (Schmidt-Böcking et al. in The precision limits in a single-event quantum measurement of electron momentum and position, these proceedings [1]). A major contribution to modern experimental atomic and molecular physics was his so-called molecular beam method [2], which Stern developed and employed in his experiments. With this method he discovered several fundamental properties of atoms, molecules and nuclei [2, 3]. As corresponding particle detection techniques were lacking during his time, he was only able to observe the averaged footprints of large particle ensembles. Today it is routinely possible to measure the momenta of single particles, because of the tremendous progress in single particle detection and data acquisition electronics. A “state-of-the-art” COLTRIMS reaction microscope [4–11] can measure, for example, the momenta of several particles ejected in the same quantum process in coincidence with sub-a.u. momentum resolution. Such setups can be used to visualize the dynamics of quantum reactions and image the entangled motion of electrons inside atoms and molecules. This review will briefly summarize Stern’s work and then present in longer detail the historic steps of the development of the COLTRIMS reaction microscope. Furthermore, some benchmark results are shown which initially paved the way for a broad acceptance of the COLTRIMS approach. Finally, a small selection of milestone work is presented which has been performed during the last two decades.

Otto Stern’s Legacy in Quantum Optics: Matter Waves and Deflectometry

Otto Stern became famous for molecular beam physics, matter-wave research and the discovery of the electron spin, with his work guiding several generations of physicists and chemists. Here we discuss how his legacy has inspired the realization of universal interferometers, which prepare matter waves from atomic, molecular, cluster or eventually nanoparticle beams. Such universal interferometers have proven to be sensitive tools for quantum-assisted force measurements, building on Stern’s pioneering work on electric and magnetic deflectometry. The controlled shift and dephasing of interference fringes by external electric, magnetic or optical fields have been used to determine internal properties of a vast class of particles in a unified experimental framework.

100 Years Molecular Beam Method Reproduction of Otto Stern’s Atomic Beam Velocity Measurement

The history of Otto Stern’s pioneering measurement of the Maxwell-Boltzmann velocity distribution of a Silver atomic beam performed 1919 in Frankfurt is described. It is shown how Albert Einstein influenced Stern in his research. This experimental apparatus is not any more existing; therefore it was reconstructed in the workshops of the Physics faculty of the Goethe University in Frankfurt. The experimental verification of Stern’s results was finally achieved by a team of Frankfurt high school students (Gymnasium Riedberg) under the supervision of their teachers Axel Gruppe and Simon Cerny. By fighting against a number of difficulties, they succeeded to get the reconstructed apparatus started and were able to reproduce the results from the early experiments of Stern.

Our Enduring Legacy from Otto Stern

Otto Stern’s scientific legacy continues to animate discoveries on a rapidly advancing research frontier.

Manipulation and Control of Molecular Beams: The Development of the Stark-Decelerator

State-selective manipulation of beams of atoms and molecules with electric and magnetic fields has been crucial for the success of the field of molecular beams. Originally, this manipulation only involved the transverse motion. In this Chapter, the development of the Stark-decelerator, that allows to also manipulate and control the longitudinal motion of molecules in a beam, is presented.

The Precision Limits in a Single-Event Quantum Measurement of Electron Momentum and Position

A modern state-of-the-art “quantum measurement” [The term “quantum measurement” as used here implies that parameters of atomic particles are measured that emerge from a single scattering process of quantum particles.] of momentum and position of a single electron at a given time [“at a given time” means directly after the scattering process. (It should be noticed that the duration of the reaction process is typically extremely short => attoseconds).] and the precision limits for their experimental determination are discussed from an experimentalists point of view. We show—by giving examples of actually performed experiments—that in a single reaction between quantum particles at a given time only the momenta of the emitted particles but not their positions can be measured with sub-atomic resolution. This fundamental disparity between the conjugate variables of momentum and position is due to the fact that during a single-event measurement only the total momentum but not position is conserved as function of time. We highlight, that (other than prevalently perceived) Heisenberg’s “Uncertainty Relation” UR [1] does not limit the achievable resolution of momentum in a single-event measurement. Thus, Heisenberg’s statement that in a single-event measurement only either the position or the momentum (velocity) of a quantum particle can be measured with high precision contradicts a real experiment. The UR states only a correlation between the mean statistical fluctuations of a large number of repeated single-event measurements of two conjugate variables. A detailed discussion of the real measurement process and its precision with respect to momentum and position is presented.

Wilhelm Heinrich Heraeus—Doctoral Student at the University Frankfurt

Wilhelm Heinrich Heraeus (*1900 – †1985), the founder of the Wilhelm and Else Heraeus Foundation, wrote his doctoral thesis at the University of Frankfurt in 1922–23 under the supervision of Richard Wachsmuth and Walther Gerlach. Thereby, he became a witness of the Stern-Gerlach experiment, completed in Frankfurt in 1922. In his thesis, Heraeus investigated “The dependence of the thermoelectrical force of iron on its structure” and was able to show that earlier measurements by G. Borelius were incorrect and irreproducible. On 23 July 1923, Heraeus passed his doctoral examination in Frankfurt under Wachsmuth’s auspices.