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Sapina, Igor: Dynamics of a dipolar Bose-Einstein condensate interacting with a superconducting surface. 2015
Inhalt
Introduction
Basics
Trapping neutral atoms
Conventional magnetic microtraps
Superconducting magnetic microtraps
Bose-Einstein condensation
Stationary Gross-Pitaevskii equation for a dipolar BEC
The Thomas-Fermi approximation
Dynamics of a BEC
The superconductor as a magnetic mirror
Boundary condition for the magnetic field
The superconducting surface as a magnetic mirror
Numerics
The GPE of a dipolar BEC
Determining the ground state of the BEC
Normalized gradient flow
Ground state in a harmonic trap
Time dependent GPE
Operator splitting
Time splitting spectral method
Time evolution in a harmonic potential
Other numerical methods
Modeling the system
GPE of a BEC close to a superconductor
The mirror potential
Potential generated by a TF ellipsoid
The column density model
Numerical approach to solve the GPE
Center-of-mass frequency shift
Frequency shift within TF approximation
Frequency shift based on a Thomas-Fermi ellipsoid
Frequency shift based on the column density model
Numerical results for the frequency shift
Different polarizations of the BEC
Polarization in the y-direction
Polarization in the x-direction (perpendicular to the surface)
Arbitrary polarization
BEC shape fluctuations
Numerical results
Harmonic trap
Shape fluctuations due to the eddy current effect
Hydrodynamic equations
Conclusion
Dipolar BEC
TF self-consistency equations for a BEC
Monopole-quadrupole modes
The index integrals
Frequency shift for 3D TF ellipsoid
Time-dependent trap frequencies
Bibliography