Coulomb Crystallization in Free Electron Beams
Authors: Valerio Di Giulio, Rudolf Haindl, Armin Feist, Claus Ropers
Abstract
Classical Coulomb crystals and quantum Wigner crystals typically arise when repulsive interactions order like-charged particles in spatially confined environments. Here, we show that transient crystallization can also emerge in freely propagating electron pulses without external trapping. Experimentally, we use a transmission electron microscope to measure number-resolved energy correlations in photoemitted pulses containing up to nine electrons, revealing strong correlations at small particle numbers that progressively disappear in the pulse interior as the number increases. To explain these observations, we combine many-body simulations with a one-dimensional statistical-mechanical model, showing that the leading and trailing electrons generate a self-induced longitudinal potential that transiently confines the inner particles, enabling the formation of an ordered chain during propagation. The resulting crystallization phase diagram reveals how many-body ordering dynamics can be understood in terms of evolving macroscopic beam properties, namely its geometry and the ratio of the mean Coulomb interaction energy to the longitudinal thermal energy. Extending this framework, we theoretically demonstrate that weak transverse guiding through electrostatic or optical ponderomotive forces can sustain crystallization at larger particle numbers and predict spontaneous longitudinal periodic bunching in continuous electron beams. Our results identify conditions under which stochastic Coulomb interactions can be harnessed to generate self-structured, strongly correlated electron beams in both pulsed and continuous regimes.
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Abstract
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Abstract
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Abstract
The behavior of two-dimensional electron gas (2DEG) in extreme coupling limits are reasonably well-understood, but our understanding of intermediate region remains limited. Strongly interacting electrons crystalize into a solid phase known as the Wigner crystal at very low densities, and these evolve to a Fermi liquid at high densities. At intermediate densities, however, where the Wigner crystal melts into a strongly correlated electron fluid that is poorly understood partly due to a lack of microscopic probes for delicate quantum phases. Here we report the first imaging of a disordered Wigner solid and its quantum densification and quantum melting behavior in a bilayer MoSe2 using a non-in…
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Abstract
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Abstract
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In short
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Abstract
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Prior work it builds on
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Solid State PhysicsC. Nayak · 2000 · cited 10,873 times · Not summarized yet
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Multiple-shell structures of laser-cooled 24Mg+ ions in a quadrupole storage ringG. Birkl, S. Kassner, H. Walther · 1992 · Nature · cited 193 times · Not summarized yet
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Liquid State Physics: A Statistical Mechanical IntroductionClive A. Croxton, D. Chandler · 1974 · cited 220 times · Not summarized yet
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Introduction to lattice dynamicsH. Schober · 1995 · cited 501 times · Not summarized yet
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Ion TrapsM. Kajita · 2022 · cited 46 times · Not summarized yet
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