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Kapitza-Dirac Effect: Electron Diffraction from a Standing Light Wave Physics 138 SP’05 (Prof. D. Budker) Victor Acosta

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Contents •History •Introduction •Basic Setup/Results •Theory –Multi-Slit Analogy –Particle Interaction Picture –QM Treatment •U. Nebraska 2001 Results •Applications

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History •1804 –Young Proposes Double Slit Experiment •Wave nature of Light •1905 –Einstein Photoelectric Effect •Particle nature of Light •1927 –Davisson and Germer Electron Diffraction (crystalline metal) •Wave nature of matter •1930 –Kapitza and Dirac propose KDE •Light Intensity of mercury lamp only allows 10 -14 electrons to diffract •1960 –Invention of Laser •First Real Attempts at KDE –All 4 were unsuccessful (poor beam quality? Undeveloped Theory?) •2001 –KDE seen by U. Nebraska group

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Introduction to Kapitza-Dirac Effect (KDE) Figure 1. Adapted from Kapitza and Dirac's original paper. Electrons diffract from a standing wave of light (laser bouncing off mirror). Figure from Bataleen group (U. Nebraska). Analogy) KDE : Multi-Slit Diffraction Electron Beam : incident wave Light Source: grating

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Basic Setup/Results Data for atom diffraction from a grating of ’light’ taken at the University of Innsbruck. Diffraction peak separation = 2 photon recoil momenta. Figure from Bataleen group (U. Nebraska).

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Analogy: Multiple-Slit Diffraction θ Assume outgoing waves propagate at θ w.r.t grating axis (z>>d). d z Path Length Difference (PLD) = dSin[θ] Bragg Condition satisfied iff PLD = nλ → dSin[θ] = nλ Detector d

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Figure from Bataleen group (U. Nebraska).

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Quantum Mechanical Theory •Need full QM treatment to understand nature of diffraction peaks •First find H using Classical E+M •Then solve Time-Dependent Schroedinger Equation

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Figure from Bataleen group (U. Nebraska).

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Legend: Bragg Regime (Top) Raman-Nath (Bottom): n=0 (red) n=1 (blue) n=2 (green)

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Figure from Bataleen group (U. Nebraska).

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U. Nebraska 2001 Results: Raman-Nath Regime Laser off (Top) and Laser on (bottom) P laser= 10 W I laser= 271 GW/cm 2 V p= 7.18 meV. E o = 5.31 µeV V e =.0367c

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U. Nebraska 2001 Results: Bragg Regime Laser off (Top) and Laser on (bottom) P laser= 1.4 W I laser= 0.29 GW/cm 2 V p= 7.66 µeV. E o = 5.31 µeV V e =.0367c

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Applications •Coherent Electron Beam Splitter •Electron Interferometry –Greater Sensitivity than Atomic Version •λ electron ~ 10 -11 >.1λ atom –Low electron energies possible •Microscopic Stern-Gerlach Magnet? –Would separate Electron’s by spin •Need light grating that isn’t standing wave

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