Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Utz, Marcel; Levitt, Malcolm H.; Cooper, Nathan

doi:10.1039/c4cp05606j

Cited by 23 publications

(38 citation statements)

References 12 publications

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“…The beam, which is now no longer equally populated in all nine states, exits the hexapole field adiabatically into a dipole field along the Z direction (Dip1). The strength of the magnetic field gradients within the hexapole lens (>T mm −1 ) results in initially pure m I , m J states in the Z frame of reference 32 . The beam then enters non-adiabatically (i.e., the direction of the magnetic dipole does not follow the change in the direction of the local magnetic field) into the first solenoid (Solenoid1) which generates an electromagnetic field, B1, oriented along the -X axis (antiparallel to the beam axis).…”

Section: Resultsmentioning

confidence: 99%

Setting benchmarks for modelling gas–surface interactions using coherent control of rotational orientation states

et al. 2020

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The coherent evolution of a molecular quantum state during a molecule-surface collision is a detailed descriptor of the interaction potential which was so far inaccessible to measurements. Here we use a magnetically controlled molecular beam technique to study the collision of rotationally oriented ground state hydrogen molecules with a lithium fluoride surface. The coherent control nature of the technique allows us to measure the changes in the complex amplitudes of the rotational projection quantum states, and express them using a scattering matrix formalism. The quantum state-to-state transition probabilities we extract reveal a strong dependency of the molecule-surface interaction on the rotational orientation of the molecules, and a remarkably high probability of the collision flipping the rotational orientation. The scattering matrix we obtain from the experimental data delivers an ultrasensitive benchmark for theory to reproduce, guiding the development of accurate theoretical models for the interaction of H 2 with a solid surface.

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Section: Resultsmentioning

confidence: 99%

Setting benchmarks for modelling gas–surface interactions using coherent control of rotational orientation states

et al. 2020

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“…It is a hexapole magnetic lens17 within which different quantum states experience different (quantized) forces depending on their total magnetic moment13 (see ref. 18 for a contemporary interpretation of beam deflection experiments). The schematic drawing in Fig.…”

Section: Resultsmentioning

confidence: 99%

A general method for controlling and resolving rotational orientation of molecules in molecule-surface collisions

et al. 2017

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The outcome of molecule–surface collisions can be modified by pre-aligning the molecule; however, experiments accomplishing this are rare because of the difficulty of preparing molecules in aligned quantum states. Here we present a general solution to this problem based on magnetic manipulation of the rotational magnetic moment of the incident molecule. We apply the technique to the scattering of H2 from flat and stepped copper surfaces. We demonstrate control of the molecule's initial quantum state, allowing a direct comparison of differences in the stereodynamic scattering from the two surfaces. Our results show that a stepped surface exhibits a much larger dependence of the corrugation of the interaction on the alignment of the molecule than the low-index surface. We also demonstrate an extension of the technique that transforms the set-up into an interferometer, which is sensitive to molecular quantum states both before and after the scattering event.

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“…That such a form of the wavepacket is valid follows from the work by Utz et al [86]. The authors show that the two wavepackets arising from a spin- 1 2 particle passing through a Stern-Gerlach apparatus are quickly decohered with respect to one another, even before they separate spatially.…”

Section: Impact Of the Magnetic Lens On The Molecular Statesmentioning

confidence: 89%

Transfer-matrix theory of surface spin-echo experiments with molecules

2020

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3 He beam spin-echo experiments have been used to study surface morphology, molecular and atomic surface diffusion, phonon dispersions, phason dispersions and phase transitions of ionic liquids. However, the interactions between 3 He atoms and surfaces or their adsorbates are typically isotropic and weak. To overcome these limitations, one can use molecules instead of 3 He in surface spin-echo experiments. The molecular degrees of freedom, such as rotation, may be exploited to provide additional insight into surfaces and the behaviour of their adsorbates. Indeed, a recent experiment has shown that ortho-hydrogen can be used as a probe that is sensitive to the orientation of a Cu(115) surface [Godsi et al., Nat. Comm. 8, 15357 (2017)]. However, the additional degrees of freedom offered by molecules also pose a theoretical challenge: a large manifold of molecular states and magnetic field-induced couplings between internal states. Here, we present a fully quantum mechanical approach to model molecular surface spin-echo experiments and connect the experimental signal to the elements of the time-independent molecule-surface scattering matrix. We present a one-dimensional transfer matrix method that includes the molecular hyperfine degrees of freedom and accounts for the spatial separation of the molecular wavepackets due to the magnetic control fields. We apply the method to the case of ortho-hydrogen, show that the calculated experimental signal is sensitive to the scattering matrix elements, and perform a preliminary comparison to experiment. This work sets the stage for Bayesian optimization to determine the scattering matrix elements from experimental measurements and for a framework that describes molecular surface spin-echo experiments to study dynamic surfaces.

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Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Cited by 23 publications

References 12 publications

Setting benchmarks for modelling gas–surface interactions using coherent control of rotational orientation states

Setting benchmarks for modelling gas–surface interactions using coherent control of rotational orientation states

A general method for controlling and resolving rotational orientation of molecules in molecule-surface collisions

Transfer-matrix theory of surface spin-echo experiments with molecules

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