What is an Optical Lattice?

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Geometric effects in Optical Lattices


Let me try to visualize the formal analogy between distorted optical lattices and curved differential geometry as we know it from General Relativity.

Lattice defect of a dislocation-type -- analogy of a quantum of torsion in discrete geometry:

Lattice defect of a disclination-type -- analogy of a quantum of curvature in discrete geometry:

Atomic visualization of the disclination defect and its influence on bending of the crystal lines around:
(configurations generated with software "Molecular Dynamics" written by P. Marecki)

Time-dependent (elastic) deformations

Time-dependent distorsion waves deforming local distances between the lattice nodes -- analogy of metric (gravitational) waves:

Screenshot of the above:

Shaken (driven) quadratic optical lattice:

(2D and 3D plots of the same)

(Elastic) deformations and their (continuous) geometric interpretation