Quantum Optics Group (LMU) - Quantum Many Body Systems Division (MPQ)

Introduction into optical lattices

The polarizability of neutral atoms allows them to interact with electromagnetic fields, i.e. with light. The energy levels of a simple "two level atom" are shifted in the presence of a light field ("AC stark shift") which is typically characterized by its detuning from the atomic transition and its rabi coupling proportional to the light intensity. If the light field is red-detuned (light frequency smaller than atomic transition frequency) the atoms will be drawn to the intensity maximum, provided they are in the ground state. A blue detuned light field repells the atoms to dark regions. The corresponding potential seen by the atoms is proportional to the ratio of rabi coupling (which might vary in space with the intensity) and detuning.

An optical lattice is typically formed by two interferring laser beams, giving rise to a periodic intensity pattern which is seen as a periodic potential by the atoms. This potential has perfect cosine shape and can be controlled in depth via the intensity of the laser beams. The angle between the beams determines the lattice spacing which is just half the laser wavelength for counterpropagating beams and larger for any other angle. Another approach is to image a certain intensity pattern onto the atoms which is again seen as a potential landscape.

One key motvation for the work with ultracold atoms in the optical lattices is the similarity to solid state systems. The appropriate choice of atomic species and lattice spacing and depth allows to enter the typical parameter regime for solids and to explore condensed matter phenomena in a controlled and almost pure environment. The general hope is to be able to simulate interesting many-body systems beyond the reach of state-of-the art numerical methods and to find answers to so far unsolved questions of the field. One highlight certainly is the search for the mechanism behind high-temperature superconductivity within the cuprate family by exploring the Fermi-Hubbard model and the mechnisms of superexchange interactions.

Another aspect of the work with optical lattices with atoms sitting one-by-one in an optical lattice (Mott insulator state) is the application for quantum information purpose. Several proposals have been made to use this system as a register of qubits to perform quantum computation or to use as quantum memories. Forthermore, these system might be valid starting points for the creation of large entangled cluster states for measurement-based quantum computation.