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Physical Review A

Double Stern-Gerlach experiments on Mn@Sn12 : Refocusing of a paramagnetic superatom

Thomas M. Fuchs, Rolf Schäfer

Published Dec 11, 2018• 21 citations
Publisher

Abstract

We report magnetic double deflection experiments on cryogenically cooled $\mathrm{Mn}@{\mathrm{Sn}}_{12}$ clusters. Refocusing efficiencies of up to 90% are achieved by keeping the magnetic-flux density virtually constant between the two Stern-Gerlach magnets. The spin dynamics are probed by introducing magnetic-flux density variations along the molecular-beam path. We apply a microscopic model for the interpretation of our results taking the coupling of electronic spin and rotational degrees of freedom into account. The combination of our experimental and theoretical results reveals unexpected insights into the interplay between rotation and spin dynamics of small metal clusters depending on magnetic-field modulations.

DOI
10.1103/physreva.98.063411

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We report magnetic double deflection experiments on cryogenically cooled Mn@Sn12\mathrm{Mn}@{\mathrm{Sn}}_{12}Mn@Sn12​ clusters. Refocusing efficiencies of up to 90% are achieved by keeping the magnetic-flux density virtually constant between the two Stern-Gerlach magnets. The spin dynamics are probed by introducing magnetic-flux density variations along the molecular-beam path. We apply a microscopic model for the interpretation of our results taking the coupling of electronic spin and rotational degrees of freedom into account. The combination of our experimental and theoretical results reveals unexpected insights into the interplay between rotation and spin dynamics of small metal clusters depending on magnetic-field modulations.
The Stern-Gerlach experiment has played an important role in our understanding of quantum behavior. We propose and analyze a modified version of this experiment where the magnetic field of the detector is in a quantum superposition, which may be experimentally realized using a superconducting flux qubit. We show that if incident spin-1/2 particles couple with the two-state magnetic field, a discrete target distribution results that resembles the distribution in the classical Stern-Gerlach experiment. As an application of the general result, we compute the distribution for a Gaussian waveform of the incident fermion. This analysis allows us to demonstrate theoretically: (1) the quantization of the intrinsic angular momentum of a spin-1/2 particle, and (2) a correlation between EPR pairs leading to nonlocality, without necessarily collapsing the particle’s spin wavefunction.
We report a different type of optical Stern-Gerlach effect, where a magnetic-field gradient is replaced with a light-intensity gradient and a paramagnetic atom is deflected according to its magnetic quantum number. The laser light is detuned between the D1D1D1 and D2D2D2 frequencies, with the size of the detuning from the D2D2D2 resonance being twice that from the D1D1D1 resonance, and it is circularly polarized to produce an ac Stark shift that takes the form of a pure Zeeman shift. Slow rubidium atoms are extracted from a magneto-optical trap and then spin polarized. The atoms traversing the laser-intensity gradient on one side of the Gaussian beam profile show deflections that depend on the atomic spin state and the laser polarization. When the laser-beam axis is aligned with the slit that defines the atomic beam, we observe focusing and defocusing of the atomic beam.
The classical Stern-Gerlach experiment is analyzed with an emphasis on the spin dynamics. The central question asked is whether there occurs a relaxation of the spin angular momentum during the time the particle passes through the Stern-Gerlach magnet. We examine in particular the transverse relaxation, involving angular momentum exchange between the spin of the particles and the spins of the magnet. A method is presented describing relaxation effects at an individual particle level. This leads to a stochastic equation of motion for the spins. This is coupled to a classical equation of motion for the particle translation. The experimental situation is then modeled through simulations of individual trajectories using two sets of parameter choices and three different sets of initial conditions. The two main conclusions are: (A) if the coupling between the magnet and the spin is solely described by the Zeeman interaction with the average magnetic field the simulations show a clear disagreement with the experimental observation of Stern and Gerlach. (B) If one, on the other hand, also allows for a T(2) relaxation time shorter than the passage time one can obtain a practically quantitative agreement with the experimental observations. These conclusions are at variance with the standard textbook explanation of the Stern-Gerlach experiment.
A successful transverse Stern–Gerlach experiment has been performed, using a beam of neutral potassium atoms and an inhomogeneous time-dependent magnetic field of the form[Formula: see text]A classical analysis of the Stern–Gerlach experiment is given for a rotating inhomogeneous magnetic field. In general, when space quantization is achieved, the spins are quantized along the effective magnetic field in the reference frame rotating with angular velocity ω about the z axis. For ω = 0, the direction of quantization is the z axis (conventional Stern–Gerlach experiment), while at resonance (ω = −γH 0 ) the direction of quantization is the x axis in the rotating reference frame (transverse Stern–Gerlach experiment). The experiment, which was performed at 7.2 Mc, is described in detail.
The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684] claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are required to reproduce the qualitative experimental behaviour. We also present simulations of quantum dynamics in the Rabi experiment, in which an applied radiofrequency field induces spin transitions in the particle wave.