Atoms and Molecules in Optical Lattices

Sufficiently cold atoms can be trapped in optical lattices, formed by a three-dimensional overlap of standing laser waves in x-, y-, and z-directions. If the kinetic energy of the atoms is lower than the potential energy minima of such lattices they are trapped in these minima and cannot leave their fixed positions. Such a state is called a Mott insulator (in analogy to the situation in solid state physics explained by Sir Nevil Mott where a Mott insulator describes a situation where electrical conductivity should be possible according to the band structure but the repulsive interaction between the electrons prevents electron transport). The potential well depth can be tuned by changing the intensity of the three laser beams. 

The research group of Th.W. Hansch succeeded in 2002 to trap for the first time cold atoms in such an optical lattice. They cooled at first the atoms below the critical temperature fort BE condensation. Then the well depth of the optical lattice was increased. This transferred the coherent state of the atoms in the free BEC, where all atoms are in the same state i.e. described by the same wavefunction and are therefore not distinguishable, into the incoherent Mott state, where each atom sits on its separate location and can be therefore distinguished from the other atoms. Decreasing the well depth brings the atoms again back into the coherent BEC state. Just by changing the well depth of the optical lattice switches the atomic ensemble from a coherent into an incoherent state and back [1204]. 

Example 9.13 In a standing light wave with X = 600 nm and a mean intensity of 10 W cm the intensity gradient between maxima and nodes is grad / = 6 X 10 W/cm. For a detuning Aty = y = 6 x 10 Hz and a saturation parameter S = 10 the dipole force acting on an atom is Fb = 10 N. The well depth is about 10 eV corresponding to a temperature of 100 mK. 

By choosing a suitable atom density it is possible to place one atom on each potential minimum of the lattice. Such atoms isolated from their surrounding are excellent candidates for precise atomic clocks if one chooses a narrowband forbidden electronic transition to a metastable atomic state as clock transition. Since the atoms are (besides their zero-point motion) at rest no Doppler-effect contributes to line broadening or shift. There are intense investigations to realize an atomic clock 

If more than one atom is trapped in a potential minimum, molecule formation can be studied and its dependence on the barrier height. This gives a handle to control chemical reactions by optical means. 

---