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4.3.2 Ground-State of a BEC in a 1D Lattice . . . . . . . . . . . . . . . 70

4.3.3 Phase Evolution of Decoupled BECs . . . . . . . . . . . . . . . . 72

4.4 Expansion of a BEC from the Lattice . . . . . . . . . . . . . . . . . . . . 73

4.4.1 Expansion of a Coherent Array of Condensates . . . . . . . . . . 73

4.4.2 Interference Measurements from Shallow and Deep Lattices . . . . 75

5 Stability of a Dipolar BEC in a 1D Optical Lattice 79

5.1 Excitations in a Dipolar BEC . . . . . . . . . . . . . . . . . . . . . . . . 79

5.1.1 Phonons in a 3D Homogeneous Dipolar BEC . . . . . . . . . . . . 79

5.1.2 Rotons in a 2D Homogeneous Dipolar BEC . . . . . . . . . . . . . 81

5.2 Stability of a Single Trapped dBEC . . . . . . . . . . . . . . . . . . . . . 83

5.3 Stability Diagram of a

Cr - BEC in a 1D Lattice . . . . . . . . . . . . . 87

5.3.1 Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.2 Stability Diagram in the 1D Lattice . . . . . . . . . . . . . . . . . 92

5.4 Eﬀects of Inter-site Interactions on the Stability of a dBEC . . . . . . . . 95

5.4.1 Analysis of Inter-site Eﬀects in the Lattice . . . . . . . . . . . . . 96

5.4.2 Inter-site Coupling of Excitations . . . . . . . . . . . . . . . . . . 97

6 Collapse of a Dipolar BEC in a 1D Optical Lattice 101

6.1 Interaction-Induced Collapse of a Single dBEC . . . . . . . . . . . . . . . . 101

6.2 Deconﬁnement-Induced Collapse in the 1D Lattice . . . . . . . . . . . . . 104

6.2.1 Experimental Sequence . . . . . . . . . . . . . . . . . . . . . . . . 104

6.2.2 Collapse of a Coherent Array of dBECs . . . . . . . . . . . . . . . 106

6.2.3 Numerical Simulations of the Collapse Dynamics . . . . . . . . . 109

6.3 Collapse in Deep Lattices - Techniques for Roton Measurements . . . . . 112

7 Summary and Outlook 117

A appendix 121

A.1 Scattering Properties of Bosonic Dipolar Gases . . . . . . . . . . . . . . . . 121

A.1.1 Elastic Dipolar Scattering . . . . . . . . . . . . . . . . . . . . . . . 121

A.1.2 Inelastic Dipolar Scattering . . . . . . . . . . . . . . . . . . . . . 124

A.2 GPE in Thomas-Fermi Approximation with Contact Interactions . . . . . 125

A.3 Calculations on the Ground State in a 1D Optical Lattice . . . . . . . . . 126

A.4 Variational Calculations with a Gaussian-Shaped Dipolar BEC . . . . . . 127

A.5 Dipolar Interaction Energy between Two Gaussian-Shaped Clouds . . . . 128

A.6 Excitation Spectrum of a 2D Homogeneous Dipolar BEC . . . . . . . . . . 131

A.7 Fitting Procedure in Calibration of the Scattering Length . . . . . . . . . 132

A.8 Magnetic Field Ramps at the Feshbach Resonance . . . . . . . . . . . . . 133

Bibliography 137

Danksagung 153

1 2 3 4 5 6 7 8 9 10 11 ... 154 155

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