## Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein CondensatesInterferometry, 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. |

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### Contents

1 Introduction | 1 |

2 Spin Squeezing Entanglement and Quantum Metrology | 5 |

3 Squeezing Two Mean Field Modes of a BoseEinstein Condensate | 24 |

4 Nonlinear Interferometry Beyond the Standard Quantum Limit | 59 |

5 Outlook | 93 |

Appendix A Precision Absorption Imaging of Ultracold Atoms | 95 |

Appendix B Particle Loss and Number Squeezing | 107 |

Appendix C Active Stabilization of Magnetic FieldsBelow the Milligauss Level | 110 |

### Other editions - View all

Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates Christian Groß No preview available - 2014 |

Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates Christian Groß No preview available - 2013 |

### Common terms and phrases

ˆJ2z ˆJx ˆJz 87 Rubidium adiabatic approximately atom interferometer axis twisting barrier height V0 beam beamsplitter Bloch sphere Bose–Einstein condensate calculate coherent spin squeezing collective spin coupling pulses density matrix detection dipole trap double-well dynamics elementary spins entropy equation evolution F ¼ Feshbach resonance Hamiltonian Heisenberg limit hyperfine imaging system interaction Josephson energy Josephson Hamiltonian Josephson junction linear longitudinal magnetic field many-body entanglement mean field mean spin length measured non-linear interferometer number of atoms number squeezing occupation number optical lattice parameters particle loss photon shot noise Phys Rev Lett pixel potential projection noise Qubits Rabi frequency ramp readout relative phase Rev Mod Phys Rubidium Sect shot noise shot noise limit single particle spin direction squeezing experiment standard quantum limit symmetric technical noise temperature thesis total atom number trap frequency ultracold uncertainty variance von Neumann entropy wavefunction