# Atom Interferometry.

Series: International School of Physics “Enrico Fermi”Publisher: Burke : IOS Press, 2014Copyright date: ©2014Description: 1 online resource (807 pages)Content type:- text

- computer

- online resource

- 9781614994480

- 535.4

- QC410.9 -- .P763 2014eb

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Title Page -- Contents -- Preface -- Course group shot -- Interferometry with atoms -- Optics and interferometry with atoms: an introduction -- Basics of matter wave optics -- The wave equations -- Dispersion relations -- Phase and group velocity -- Path integral formulation -- JWKB approximation -- Eikonal approximation -- Coherence -- Spatial coherence -- Coherence in momentum space -- Higher-order coherence -- Index of refraction for matter waves -- Index of refraction caused by a classical potential -- Index of refraction from scattering -- Optics and interferometry using gratings -- Diffraction -- Diffraction in space -- Diffraction from nano-fabricated structures -- Light gratings from standing waves -- Diffraction in time -- Interferometers -- Three-grating Mach-Zehnder interferometer -- Selected experiments with beam interferometers -- Einstein's recoiling slit: a single photon as a coherent beamsplitter -- Interferometry with Bose-Einstein condensates in double-well potentials -- A Bose-Einstein condensate in a double-well potential: a simple model -- Single-particle approach -- Two-mode approximation -- Rabi dynamics -- Splitting -- Time-of-flight recombination -- In-trap recombination -- Phase shifts -- Effect of interactions: Josephson dynamics, squeezing, and dephasing -- Bose-Hubbard model with two sites -- Mean-field treatment -- Fluctuations and interferometry -- Squeezing during splitting -- Phase diffusion -- Effective single-particle Hamiltonian -- Probing many-body physics by interference -- Interference of 1D Bose gases -- The 1D Bose gas -- Multi-mode interference -- Pairs of 1D Bose gases in equilibrium -- Theoretical description -- Measurement of the matter wave interference contrast -- Probing relaxation in non-equilibrium 1D Bose gases -- Coherent splitting of a 1D Bose gas.

Dynamics of the matter wave interference contrast -- Prethermalization -- Light-cone-like emergence of thermal correlations -- Matter wave interferometry with composite quantum objects -- Introduction and outline -- Concepts and tools of coherent nanoparticle manipulation -- Coherence preparation -- Far-field diffraction at a nanomechanical grating -- Optical gratings -- Measurement-induced absorptive gratings -- Optical phase gratings -- Matter wave interferometry in the time domain -- From far-field to near-field diffraction and near-field interferometry -- A unified phase-space description of three-grating matter wave interferometry -- The Wigner function representation -- Grating diffraction in phase space -- Thin stationary gratings for fast particles -- Short ionizing grating pulses -- Classical pendant of the grating transformation -- The Talbot self-imaging effect -- Talbot-Lau interference in phase space -- Coherent description -- The KDTLI setup -- The OTIMA setup -- The influence of environmental decoherence -- Spontaneous collapse models -- Talbot-Lau interferometry -- Protection from collisional and thermal decoherence -- Quantum-assisted deflectometry -- Kapitza-Dirac-Talbot-Lau (KDTL) interferometry -- Experimental results: high-mass quantum interference -- Experimental results: quantum-interference-assisted metrology -- Optical polarizability -- Static polarizability -- Vibration-induced electric dipole moments -- Permanent electric dipole moments -- OTIMA interferometry -- Experimental design and conditions -- Requirements on mirror flatness and spectral purity of the grating lasers -- Vacuum requirements -- Vibrational isolation -- Alignment to gravity and the rotation of the Earth -- Beam divergence -- Experimental results -- Quantum interference seen as a mass-dependent modulation of cluster transmission.

Interference resonance in the time domain -- Interference pattern in position-space -- Perspectives for quantum delocalization experiments at high masses -- Atom interferometry using internal excitation: Foundations and recent theory -- Introduction -- The status of mass in classical relativistic mechanics: From 4 to 5 dimensions -- Generalization in the presence of gravitational and electromagnetic interactions -- Hamiltonian and Lagrangian: Parabolic approximation -- Equations of motion -- Wave equations for atom waves and wave packet propagation -- 5D expression of the phase shift -- Conclusions -- The interface of gravity and quantum mechanics illuminated by Wigner phase space -- Introduction -- How to include weak gravity in quantum mechanics -- Outline of the lectures -- Introduction to Wigner functions -- Ensemble of particles: classical dynamics a la Liouville -- Definition of phase-space distribution -- Dynamics: classical Liouville equation -- Solution of the Liouville equation -- Definition of the Wigner function -- Properties -- Weyl-Wigner correspondence -- Quantum Liouville equation -- Energy eigenvalue equation in phase space -- Summary -- Equivalence of inertial and gravitational mass -- Single particle -- Ensemble of particles: classical dynamics a la Liouville -- Dynamics: classical Liouville equation -- Initial distribution -- Ensemble of particles: quantum dynamics and quantum kinematics a la Wigner -- Appearance of inertial and gravitational mass in energy eigenstates -- Linear potential -- Linear potential plus wall -- Gravitational Coulomb potential -- Representation-free description of the Kasevich-Chu interferometer -- Building blocks -- Raman pulses -- Beam splitter -- Mirror -- Time evolution between the laser pulses -- The interferometer as an operator sequence -- Order of events in the two paths.

Exit port probability and phase-shift operator -- Acceleration in phase-shift operator -- Application to special potentials -- Linear potential -- Gravity gradients -- Wigner phase-space description of the Kasevich-Chu interferometer -- Wigner function from state vector -- Translation into phase space -- Dynamics through the interferometer -- Upper path -- Lower path -- Interference term -- Specific example -- Phase shift and loss of contrast -- Integration over phase space -- Exit probability from phase space -- Schrodinger cat -- Summary and outlook -- Appendix A. Weyl-Wigner correspondence of the displacement operator -- Appendix B. Quantum mechanics in phase space -- Appendix C. Phase-shift operator in the presence of weak gradients -- Appendix D. Phase-space dynamics and phase shift -- General relativity, atom interferometry, and gravitational wave detection -- Introduction -- General relativistic effects in atom interferometry -- Introduction -- Atom interferometry -- Experimental setup -- Non-relativistic phase shift calculation -- Phase shift formulae -- Proof -- General relativistic description of atomic interferometry -- Dynamics of the interferometer -- Relativistic phase shift formulae -- GR effects in the Earth's gravitational field -- Interferometer calculation in the Schwarzschild metric -- General relativistic effects and interpretation -- Summary and comparison -- An atomic gravitational wave interferometric sensor (AGIS) -- Introduction -- Gravitational wave signal -- Phase shift calculation -- Results -- Terrestrial experiment -- Experimental setup -- Backgrounds -- Vibration noise -- Laser phase noise -- Newtonian gravity backgrounds -- Timing errors -- Effects of rotation -- Effects of magnetic fields -- Satellite-based experiment -- Experimental setup -- Baseline limit from atom optics.

Environmental constraints on the interferometer region -- Limit on data taking rate -- Backgrounds -- Vibrations and laser phase noise -- Newtonian gravity backgrounds -- Timing errors -- Effects of rotation -- Effects of magnetic fields -- The radius of curvature of the beam -- Blackbody clock shift -- Comparison with LISA -- Gravitational wave sources -- Compact object binaries -- Stochastic sources -- Sensitivities -- Binary sources -- Stochastic gravitational wave backgrounds -- New physics signals -- Conclusion -- Comparison with previous work -- Summary -- A new method for gravitational wave detection with atomic sensors: Bing-Bang -- A new type of atom interferometer -- A differential measurement -- Backgrounds -- Atomic implementation -- Discussion -- General conclusions -- Appendix A. Earth field calculation results -- Quantum mechanics, matter waves, and moving clocks -- Quantum mechanics as a theory of waves oscillating at the Compton frequency -- Notation -- de Broglie's relations -- Construction of a path integral -- Derivation of the Schrodinger equation -- Derivation of the Dirac equation without gravity -- Re-writing the proper time -- Derivation of the Dirac equation -- Interpretation -- Derivation of the matter-waves-as-clocks picture from the Dirac equation -- Derivation of a Dirac equation with electromagnetic potentials -- Derivation of the Dirac equation with gravity, in curved space-time -- Derivation -- A simple limiting case -- Comparison to the usual form -- Discussion -- Review of some counterarguments -- Conclusion -- Brief summary of basics of atom interferometers -- Mach-Zehnder atom interferometers as redshift measurements -- Conventional redshift measurements with clocks -- Correcting for time dilation -- Experiment with piecewise freely falling clocks -- Comparison to atom interferometer.

Examples where interpretations as force measurements fail.

Since atom interferometers were first realized about 20 years ago, atom interferometry has had many applications in basic and applied science, and has been used to measure gravity acceleration, rotations and fundamental physical quantities with unprecedented precision. Future applications range from tests of general relativity to the development of next-generation inertial navigation systems. This book presents the lectures and notes from the Enrico Fermi school "Atom Interferometry", held in Varenna, Italy, in July 2013. The aim of the school was to cover basic experimental and theoretical aspects and to provide an updated review of current activities in the field as well as main achievements, open issues and future prospects. Topics covered include theoretical background and experimental schemes for atom interferometry; ultracold atoms and atom optics; comparison of atom, light, electron and neutron interferometers and their applications; high precision measurements with atom interferometry and their application to tests of fundamental physics, gravitation, inertial measurements and geophysics; measurement of fundamental constants; interferometry with quantum degenerate gases; matter wave interferometry beyond classical limits; large area interferometers; atom interferometry on chips; and interferometry with molecules.The book will be a valuable source of reference for students, newcomers and experts in the field of atom interferometry.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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