Spin Squeezing And Non Linear Atom Interferometry With Bose Einstein Condensates

Interferometry, the most precise measurement technique known today, exploits the wave-like nature of the atoms or photons in the interferometer. As expected from the laws of quantum mechanics, the granular, particle-like features of the individually independent atoms or photons are responsible for the precision limit, the shot noise limit. However this “classical” bound is not fundamental and it is the aim of quantum metrology to overcome it by employing entanglement among the particles. This work reports on the realization of spin-squeezed states suitable for atom interferometry. Spin squeezing was generated on the basis of motional and spin degrees of freedom, whereby the latter allowed the implementation of a full interferometer with quantum-enhanced precision.

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.

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.

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

This book, written by experts in the fields of atomic physics and nonlinear science, covers the important developments in a special aspect of Bose-Einstein condensation, namely nonlinear phenomena in condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; mathematical methods/rigorous results; and the beyond-the-mean-field approach.

Progress in atomic physics has been so vigorous during the past decade that one is hard pressed to follow all the new developments. In the early 1990s the first atom interferometers opened a new field in which we have been able to use the wave nature of atoms to probe fundamental quantum me chanics questions as well as to make precision measurements. Coming fast on the heels of this development was the demonstration of Bose Einstein condensation in dilute atomic vapors which intensified research interest in studying the wave nature of matter, especially in a domain in which "macro scopic" quantum effects (vortices, stimulated scattering of atomic beams) are visible. At the same time there has been much progress in our understanding of the behavior of waves (notably electromagnetic) in complex media, both periodic and disordered. An obvious topic of speculation and probably of future research is whether any new insight or applications will develop if one examines the behavior of de Broglie waves in analogous situations. Finally, our ability to manipulate atoms has allowed us not only to create macroscopically occupied quantum states but also to exercise fine control over the quantum states of a small number of atoms. This has advanced to the study of quantum entanglement and its relation to the theory of measurement and the theory of information. The 1990s have also seen an explosion of interest in an exciting potential application of this fine control: quantum computation and quantum cryptography.

This book presents theoretical methods and experimental results on the study of multipartite quantum correlations in spin-squeezed Bose–Einstein condensates. Nonclassical correlations in many-body system​s are particularly interesting for both fundamental research and practical applications. For their investigation, ultracold atomic ensembles offer an ideal platform, due to their high controllability and long coherence times. In particular, we introduce criteria for detecting and characterizing multipartite entanglement, Einstein–Podolsky–Rosen steering, and Bell correlations. Moreover, we present the experimental observation of such correlations in systems of about 600 atoms.