Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates

Abstract

Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual photons or atoms within the interferometer. Motivated by the potential impact on metrology as wells as by fundamental questions in the context of entanglement, a lot of theoretical and experimental effort has been made to study squeezed states. The first squeezed states useful for quantum enhanced metrology have been proposed and generated in quantum optics, where the squeezed variables are the coherences of the light field. In this tutorial we focus on spin squeezing in atomic systems. We give an introduction to its concepts and discuss its generation in Bose-Einstein condensates. We discuss in detail the experimental requirements necessary for the generation and direct detection of coherent spin squeezing. Two exemplary experiments demonstrating adiabatically prepared spin squeezing based on motional degrees of freedom and diabatically realized spin squeezing based on internal hyperfine degrees of freedom are discussed.

Phd tutorial, 23 pages, 17 figures

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• Theory of single-shot phase contrast imaging in spinor Bose-Einstein condensates
• Full Bloch sphere teleportation of spinor Bose-Einstein condensates and spin ensembles
• Shortcuts to adiabatic cat-state generation in bosonic Josephson junctions
• Heisenberg-limited Sagnac Interferometer with Multi-particle States
• Entanglement generation between two spinor Bose-Einstein condensates with cavity QED
• Squeezing Quantum Many-Body Scars
• NOON States via Quantum Walk of Bound Particles
• Practical Limits of Error Correction for Quantum Metrology
• Transport of the repulsive Bose-Einstein condensate in a double-well trap: interaction impact and relation to Josephson effect
• Diffraction of strongly interacting molecular Bose-Einstein condensate from standing wave light pulses
• Quantum feedback control of atomic ensembles and spinor Bose-Einstein condensates
• Simultaneous Quantum Squeezing of Light Polarizations and Atomic Spins in a Cold Atomic Gas
• Effect of Inter-Well Interactions on Non-Linear Beam Splitters for Matter-Wave Interferometers