Guided-wave Atom Interferometers with Bose-Einstein Condensate

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ISBN 13 :
Total Pages : 226 pages
Book Rating : 4.:/5 (828 download)

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Book Synopsis Guided-wave Atom Interferometers with Bose-Einstein Condensate by : Ebubechukwu Odidika Ilo-Okeke

Download or read book Guided-wave Atom Interferometers with Bose-Einstein Condensate written by Ebubechukwu Odidika Ilo-Okeke and published by . This book was released on 2012 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: An atom interferometer is a sensitive device that has potential for many useful applications. Atoms are sensitive to electromagnetic fields due to their electric and magnetic moments and their mass allows them to be deflected in a gravitational field, thereby making them attractive for measuring inertial forces. The narrow momentum distribution of Bose-Einstein condensate (BEC) is a great asset in realizing portable atom interferometers. An example is a guided-wave atom interferometer that uses a confining potential to guide the motion of the condensate. Despite the promise of guided-wave atom interferometry with BEC, spatial phase and phase diffusion limit the contrast of the interference fringes. The control of these phases is required for successful development of a BEC-based guided-wave atom interferometer. This thesis analyses the guided-wave atom interferometer, where an atomic BEC cloud at the center of a confining potential is split into two clouds that move along different arms of the interferometer. The clouds accumulate relative phase due to the environment, spatially inhomogeneous trapping potential and atom-atom interactions within the condensate. At the end of the interferometric cycle, the clouds are recombined producing a cloud at rest and moving clouds. The number of atoms in the clouds that emerge depends on the relative phase accumulated by the clouds during propagation. This is investigated by deriving an expression for the probability of finding any given number of atoms in the clouds that emerge after recombination. Characteristic features like mean, standard deviation and cross-correlation function of the probability density distribution are calculated and the contrast of the interference fringes is optimized. This thesis found that optimum contrast is achieved through the control of total population of atoms in the condensate, trap frequencies, s-wave scattering length, and the duration of the interferometric cycle.

Improvements and Applications of a Guided-wave Bose Einstein Condensate Interferometer

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ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.:/5 (78 download)

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Book Synopsis Improvements and Applications of a Guided-wave Bose Einstein Condensate Interferometer by : John Hughson Burke

Download or read book Improvements and Applications of a Guided-wave Bose Einstein Condensate Interferometer written by John Hughson Burke and published by . This book was released on 2010 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Interferometry with Interacting Bose-Einstein Condensates in a Double-Well Potential

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Publisher : Springer
ISBN 13 : 3319272330
Total Pages : 244 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Interferometry with Interacting Bose-Einstein Condensates in a Double-Well Potential by : Tarik Berrada

Download or read book Interferometry with Interacting Bose-Einstein Condensates in a Double-Well Potential written by Tarik Berrada and published by Springer. This book was released on 2015-12-17 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis demonstrates a full Mach–Zehnder interferometer with interacting Bose–Einstein condensates confined on an atom chip. It relies on the coherent manipulation of atoms trapped in a magnetic double-well potential, for which the author developed a novel type of beam splitter. Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices, both for technological applications and fundamental tests. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Particle interactions in the Bose–Einstein condensate lead to a nonlinearity, absent in photon optics. This is exploited to generate a non-classical state with reduced atom-number fluctuations inside the interferometer. This state is then used to study the interaction-induced dephasing of the quantum superposition. The resulting coherence times are found to be a factor of three longer than expected for coherent states, highlighting the potential of entanglement as a resource for quantum-enhanced metrology.

High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer by : Billy Ian Robertson

Download or read book High Contrast Measurements with a Bose-Einstein Condensate Atom Interferometer written by Billy Ian Robertson and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Atom interferometry is a next-generation technique of precision measurement that can vastly outperform its optical analogue. These devices utilise the wave nature of atoms to make interferometric measurements of, for example, gravitational and magnetic fields, inertial effects, and the fine-structure constant. The main focus of this thesis is the creation of a general purpose atom interferometer in free space.We create a Bose-Einstein condensate of ~105 87Rb atoms in a crossed-optical dipole trap. The atomic wave function is coherently manipulated using highly tuned pulses comprising off-resonant light that form our atom-optical elements. These atom optics are analogous to the beam splitters and mirrors in an optical interferometer. By controlling the timing and amplitude of the pulses we demonstrate the ability to excite specific momentum states with high efficiency. The tuned atom optics allows for the construction of an atom interferometer in free space. From this we can measure the recoil velocity of an 87Rb atom and calculate the value of the fine structure constant. We also demonstrate the measurement of magnetic field gradients using atom interferometry. A second method of data readout is also demonstrated, known as contrast interferometry.This increases the rate at which information is obtained and decreases the measurement duration from a few hours to a few minutes.Within the vacuum chamber we also have a copper ring which form the basis of an AC coupled ring trap for atoms. The long term goal is to use this as a waveguide for atom interferometry and, whilst not the main focus of this thesis, we present some proof-of-principle type data demonstrating the ring trap. In addition we show the first Kapitza-Dirac splitting of a BEC within the waveguide which forms the first part of a guided atom interferometer.

Bose-Einstein Condensates and Atom Lasers

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Publisher : Springer Science & Business Media
ISBN 13 : 0306471035
Total Pages : 322 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Bose-Einstein Condensates and Atom Lasers by : S. Martellucci

Download or read book Bose-Einstein Condensates and Atom Lasers written by S. Martellucci and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the International School of Quantum Electronics 27th course on Bose Einstein Condensates and Atom Lasers, October 19-24, 1999, Erice, Italy. Since the experimental demonstration of Bose Einstein Condensation in dilute atomic gases there has been an explosion of interest in the properties of this novel macroscopic quantum system. The book covers the methods used to produce these new samples of coherent atoms, their manipulation and the study of their properties. Emphasis is given to the anticipated development of new types of sources, which more and more resemble traditional types of lasers. Because of recent new applications and increasing demand for lasers, sensors and associated instrumentation, the chapters also cover current developments in the basic techniques, materials and applications in the field of the generation of coherent atoms.

Coherent atomic matter waves - Ondes de matiere coherentes

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Publisher : Springer Science & Business Media
ISBN 13 : 3540410473
Total Pages : 725 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Coherent atomic matter waves - Ondes de matiere coherentes by : R. Kaiser

Download or read book Coherent atomic matter waves - Ondes de matiere coherentes written by R. Kaiser and published by Springer Science & Business Media. This book was released on 2001-02-28 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, devoted to the study of quantum effects in atomic systems, reviews the state of the art in the fields of Bose--Einstein condensation, quantum information processing, and the problems of propagation of matter waves in complex media. The specific topics include: theory and experiments in Bose--Einstein condensation, theory and experiments on decoherence phenomena in simple quantum systems and the connection to quantum measurement, atom interferometry, quantum computing, multiple scattering problems in atomic physics, quantum and nonlinear optics in a photonic band gap and quantum chaos and atomic physics. Pedagogical in style, the articles address PhD students as well as researchers.

Atom Interferometry

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ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Atom Interferometry by : Boris Décamps

Download or read book Atom Interferometry written by Boris Décamps and published by . This book was released on 2016 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis's first part describes the realization of three experiments using an atom interferometer operated with a lithium supersonic beam. The second part presents the development of a new BEC interferometer designed to test matter neutrality. The first three experiments rely on the interactions of lithium atom with different electromagnetic fields. A time dependent electric potential difference was used to produce phase modulation of both interferometer arms at different frequencies, leading to homodyne and heterodyne detection of atom waves. A geometric phase of light (the Pancharatnam phase) was successfully transferred to our interferometer signal during Bragg diffraction, enlarging the atom optics toolbox for phase control in an atom interferometer. Finally, a focused laser beam was used to measure accurately the value of one lithium tune-out wavelength (for which its dynamic polarizability is zero). The new BEC interferometer was designed to measure a possible non-zero electric charge of rubidium isotopes 85Rb and 87Rb with enhanced sensitivity to the electron-proton charge difference and neutron neutrality. This setup relies on a large spatial separation between the two interferometer arms in a fountain configuration aiming at a cycle time of 5s. These features required particular design work both on the atomic source (atom-chip) and the diffraction process (Large Momentum Transfer). The technical choices on the vacuum chambers, laser system and magnetic sources are described and characterized. Finally, the up-to-date cold-atom source performances is shown and compared to our expectations.

Precision Interferometry with Bose-Einstein Condensates

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ISBN 13 :
Total Pages : 191 pages
Book Rating : 4.:/5 (9 download)

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Book Synopsis Precision Interferometry with Bose-Einstein Condensates by : Alan O. Jamison

Download or read book Precision Interferometry with Bose-Einstein Condensates written by Alan O. Jamison and published by . This book was released on 2014 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation describes the creation of the first matter-wave interferometer using ytterbium (Yb) atoms. Most of the experiments focus on a contrast interferometer geometry with a Bose-Einstein condensate (BEC) as source. The recoil frequency of the 174-Yb atom is measured with this interferometer. The recoil frequency of an atom is part of a set of precision measurements that together give a value for the fine structure constant. The experimental results of this dissertation lay the groundwork for a future sub part-per-billion (ppb) precision measurement of the Yb recoil frequency. The contrast interferometry technique is extended to substantially longer times scales than those achieved in previous experiments. A measurement at the ~10 parts-per-million level is made. Systematic effects and statistical scaling are studied and found to be compatible with the desired sub-ppb precision for a future measurement. Such a measurement requires a detailed theoretical study of possible systematic shifts to the measured value. A substantial portion of this dissertation consists of this analysis, carried out in sufficient generality as to guide future sub-ppb level measurements. In addition to a large number of possible systematic shifts due to well-understood physics, two more complex effects are identified and studied: Diffraction phases and atom-atom interactions.

Physics of Ultra-Cold Matter

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Publisher : Springer Science & Business Media
ISBN 13 : 1461454131
Total Pages : 411 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Physics of Ultra-Cold Matter by : J.T. Mendonça

Download or read book Physics of Ultra-Cold Matter written by J.T. Mendonça and published by Springer Science & Business Media. This book was released on 2012-11-28 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of laser cooling of atoms led to the discovery of ultra-cold matter, with temperatures below liquid Helium, which displays a variety of new physical phenomena. Physics of Ultra-Cold Matter gives an overview of this recent area of science, with a discussion of its main results and a description of its theoretical concepts and methods. Ultra-cold matter can be considered in three distinct phases: ultra-cold gas, Bose Einstein condensate, and Rydberg plasmas. This book gives an integrated view of this new area of science at the frontier between atomic physics, condensed matter, and plasma physics. It describes these three distinct phases while exploring the differences, as well as the sometimes unexpected similarities, of their respective theoretical methods. This book is an informative guide for researchers, and the benefits are a result from an integrated view of a very broad area of research, which is limited in previous books about this subject. The main unifying tool explored in this book is the wave kinetic theory based on Wigner functions. Other theoretical approaches, eventually more familiar to the reader, are also given for extension and comparison. The book considers laser cooling techniques, atom-atom interactions, and focuses on the elementary excitations and collective oscillations in atomic clouds, Bose-Einstein condensates, and Rydberg plasmas. Linear and nonlinear processes are considered, including Landau damping, soliton excitation and vortices. Atomic interferometers and quantum coherence are also included.

Atom Optics and Space Physics

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Publisher : IOS Press
ISBN 13 : 1607504197
Total Pages : 519 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Atom Optics and Space Physics by : Wolfgang Schleich

Download or read book Atom Optics and Space Physics written by Wolfgang Schleich and published by IOS Press. This book was released on 2009-07-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this volume is to discuss the rapidly moving field of atom optics and interferometry with all its intricate aspects ranging from fundamental physics to applications and the theory of relativity. The breathtaking success in manipulating atoms using lasers has encouraged these two so far disjunct communities to move closer together and begin collaborations. After an introduction to atom optics and Bose-Einstein condensation, the theoretical foundations of cold atom interferometers, their use to test gravity, and their implementation in laboratory measurements of the Earth rotation and of Newton's gravitational constant are discussed. Several papers discuss the characteristics of gyroscopes and interferometers as sensors for inertial forces, starting from gyroscopes based on light waves and comparing their sensitivity to those based on matter waves. The final topic is the variation of fundamental constants, a subject that during the last years has attracted a lot of attention from different communities of physics.

Bose-einstein Condensation - From Atomic Physics To Quantum Fluids, Procs Of The 13th Physics Summer Sch

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Publisher : World Scientific
ISBN 13 : 9814491985
Total Pages : 315 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Bose-einstein Condensation - From Atomic Physics To Quantum Fluids, Procs Of The 13th Physics Summer Sch by : Mukunda Prasad Das

Download or read book Bose-einstein Condensation - From Atomic Physics To Quantum Fluids, Procs Of The 13th Physics Summer Sch written by Mukunda Prasad Das and published by World Scientific. This book was released on 2000-12-28 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bose-Einstein condensation of dilute gases is an exciting new field of interdisciplinary physics. The eight chapters in this volume introduce its theoretical and experimental foundations. The authors are lucid expositors who have also made outstanding contributions to the field. They include theorists Tony Leggett, Allan Griffin and Keith Burnett, and Nobel-Prize-winning experimentalist Bill Phillips. In addition to the introductory material, there are articles treating topics at the forefront of research, such as experimental quantum phase engineering of condensates, the “superchemistry” of interacting atomic and molecular condensates, and atom laser theory.

Pushing the Frontiers of Atomic Physics

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Publisher : World Scientific
ISBN 13 : 9814273007
Total Pages : 372 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Pushing the Frontiers of Atomic Physics by : Robin Coté

Download or read book Pushing the Frontiers of Atomic Physics written by Robin Coté and published by World Scientific. This book was released on 2009 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: In memoriam. Herbert Walther, scientist extraordinaire / P. Meystre. Willis E. Lamb / P. Berman -- Nobel Laureate session. When is a quantum gas a quantum liquid? / E.A. Cornell. Cooperative emission of light quanta : a theory of coherent radiation damping / R.J. Glauber. Coherent control of ultracold matter : fractional quantum Hall physics and large-area atom interferometry / S. Chu -- Precision measurements. More accurate measurement of the electron magnetic moment and the fine structure constant / G. Gabrielse. Determination of the fine structure constant with atom interferometry and Bloch oscillations / F. Biraben. Precise measurements of s-wave scattering phase shifts with a juggling atomic clock / K. Gibble. Quantum control of spins and photons at nanoscales / M.D. Lukin -- Quantum information and quantum optics. Atomic ensemble quantum memories / A. Kuzmich. Quantum non-demolition photon counting and time-resolved reconstruction of non-classical field states in a cavity / S. Haroche. Spin squeezing on an atomic-clock transition / V. Vuletić. Quantum micro-mechanics with ultracold atoms / D. Stamper-Kurn. Improved "position squared" readout using degenerate cavity modes / J.G.E. Harris -- Quantum degenerate systems. Tunable interactions in a Bose-Einstein condensate of Lithium : photoassociation and disorder-induced localization / R.G. Hulet. A purely dipolar quantum gas / T. Pfau. Bose-Einstein condensation of exciton-polaritons / Y. Yamamoto. Anderson localization of matter waves / P. Bouyer. Anderson localization of a non-interacting Bose-Einstein condensate / M. Inguscio. Fermi gases with tunable interactions / J.E. Thomas. Photoemission spectroscopy for ultracold atoms / D.S. Jin. Universality in strongly interacting Fermi gases / P.D. Drummond. Mapping the phase diagram of a two-component Fermi gas with strong interactions / Y. Shin. Exploring universality of few-body physics based on ultracold atoms near Feshbach resonances / C. Chin -- Optical lattices and cold molecules. Atom interferometry with a weakly interacting Bose-Einstein condensate / G. Modugno. An optical plaquette : minimum expressions of topological matter / B. Paredes. Strongly correlated bosons and fermions in optical lattices / I. Bloch. Laser cooling of molecules / P. Pillet. A dissipative Tonks-Girardeau gas of molecules / S. Dürr. Spectroscopy of ultracold KRb molecules / W.C. Stwalley. Cold molecular ions : single molecule studies / M. Drewsen -- Ultrafast phenomena. The frontiers of attosecond physics / L.F. DiMauro. Strong-field control of X-ray processes / L. Young

High Contrast Interferometry and Finite Temperature Coherence of Bose-Einstein Condensates

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (141 download)

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Book Synopsis High Contrast Interferometry and Finite Temperature Coherence of Bose-Einstein Condensates by : Christopher Hugh Carson

Download or read book High Contrast Interferometry and Finite Temperature Coherence of Bose-Einstein Condensates written by Christopher Hugh Carson and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis outlines the main experimental results of a Bose-Einstein condensate(BEC) interferometer and the finite temperature coherence of elongated BECs. Cold atom and BEC-based interferometers take advantage of the wave nature of atoms as they are cooled and can be used for precision measurements of fundamental physics, fundamental constants, rotations and gravitational gradients. The coherence properties of atomic matter-waves are of great interest, in particular phase coherence, which has played an important role in fundamental research involving BEC interferometry. When subject to high cloud aspect ratios, BECs become elongated and exhibited phase fluctuations, which can have a dramatic affect on the performance of matter-wave interferometers. A brief overview of the history and basic theory of Bose-Einstein condensates is presented as well as introducing the various studies and applications in metrology involving BECs. The theory of the techniques used to create a BEC, such as laser cooling, trapping and evaporation, are discussed along with the dynamics of BECs, matter-wave interference and phase fluctuations. The experimental chapters describe the various concepts, techniques and mechanisms used to experimentally observe matter-wave interference fringes. The interference fringes are a result of realising two BECs from a double-well potential, which is created using a combination of magnetic and optical potentials, and allowing them to expand and overlap. The main interferometry results are then discussed, this includes the observation of single-shot interference fringes with contrast ≥95%, which has a strong dependence on the detuning of the imaging beam. Also, a strong dependence on fringe contrast with the focal location of the camera is observed, which can now be clearly attributed to the Talbot effect. This is the first reported observation of the spatial Talbot effect of light interacting with period BEC fringes, revealing the drastic effect it can have on the interference signal. The major results regarding phase fluctuations in elongated condensates are presented. These include the existence of large regular period phase fluctuations, which should normally be of random phase and size. By dynamically changing the aspect ratio of the condensate during an experimental sequence, a controlled generation and removal of phase fluctuations in a Bose-Einstein condensate is observed, indicating a phase revival. The thesis concludes by considering potential improvements and future experiments, which could be used towards the experimental implementation of a BEC interferometer.

Bose-Einstein Condensates and Atom Lasers

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Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Bose-Einstein Condensates and Atom Lasers by : S. Martellucci

Download or read book Bose-Einstein Condensates and Atom Lasers written by S. Martellucci and published by Springer. This book was released on 2000-10-31 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation Physics researchers survey the methods used to produce, manipulate, and study the condensate in dilute atomic gases, which have generated a lot of excitement since their experimental demonstration in 1995. They emphasize the anticipated development of new types of sources for the novel macroscopic quantum system of coherent atoms. Such sources are looking more and more similar to the various types of lasers--pulsed, CW, mode locked--and likely to produce a revolution similar to that sparked by lasers four decades previously. The 23 papers comprise the proceedings of an international school of quantum electronics held in Erice, Italy in October 1999. Annotation c. Book News, Inc., Portland, OR (booknews.com).

An On-chip Atom Interferometer Using a Bose-Einstein Condensate

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ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (624 download)

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Book Synopsis An On-chip Atom Interferometer Using a Bose-Einstein Condensate by : Ying-Ju Wang

Download or read book An On-chip Atom Interferometer Using a Bose-Einstein Condensate written by Ying-Ju Wang and published by . This book was released on 2005 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bose-Einstein-condensate Interferometer with Macroscopic Arm Separation

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Publisher :
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.X/5 (3 download)

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Book Synopsis Bose-Einstein-condensate Interferometer with Macroscopic Arm Separation by : Ofir Garcia-Salazar

Download or read book Bose-Einstein-condensate Interferometer with Macroscopic Arm Separation written by Ofir Garcia-Salazar and published by . This book was released on 2007 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Guide to Experiments in Quantum Optics

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Publisher : John Wiley & Sons
ISBN 13 : 3527683933
Total Pages : 743 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis A Guide to Experiments in Quantum Optics by : Hans-A. Bachor

Download or read book A Guide to Experiments in Quantum Optics written by Hans-A. Bachor and published by John Wiley & Sons. This book was released on 2019-07-10 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides fully updated coverage of new experiments in quantum optics This fully revised and expanded edition of a well-established textbook on experiments on quantum optics covers new concepts, results, procedures, and developments in state-of-the-art experiments. It starts with the basic building blocks and ideas of quantum optics, then moves on to detailed procedures and new techniques for each experiment. Focusing on metrology, communications, and quantum logic, this new edition also places more emphasis on single photon technology and hybrid detection. In addition, it offers end-of-chapter summaries and full problem sets throughout. Beginning with an introduction to the subject, A Guide to Experiments in Quantum Optics, 3rd Edition presents readers with chapters on classical models of light, photons, quantum models of light, as well as basic optical components. It goes on to give readers full coverage of lasers and amplifiers, and examines numerous photodetection techniques being used today. Other chapters examine quantum noise, squeezing experiments, the application of squeezed light, and fundamental tests of quantum mechanics. The book finishes with a section on quantum information before summarizing of the contents and offering an outlook on the future of the field. -Provides all new updates to the field of quantum optics, covering the building blocks, models and concepts, latest results, detailed procedures, and modern experiments -Places emphasis on three major goals: metrology, communications, and quantum logic -Presents fundamental tests of quantum mechanics (Schrodinger Kitten, multimode entanglement, photon systems as quantum emulators), and introduces the density function -Includes new trends and technologies in quantum optics and photodetection, new results in sensing and metrology, and more coverage of quantum gates and logic, cluster states, waveguides for multimodes, discord and other quantum measures, and quantum control -Offers end of chapter summaries and problem sets as new features A Guide to Experiments in Quantum Optics, 3rd Edition is an ideal book for professionals, and graduate and upper level students in physics and engineering science.