International Workshop on Atomic Interactions in Laser Fields - Abstracts
Gerard Nienhuis
Huygens Laboratorium, Universiteit Leiden, The Netherlands
Optically cooled and trapped atoms commonly experience a radiation field with periodically varying polarization. This allows the creation of atoms in quantummechanical translational states, with long-range order imposed by an effective periodic potential. These optical lattices can be specified by the reciprocal lattice vectors, which are determined by the differences of the optical wave vectors of the composing travelling waves. An important ingredient in the description of this situation is the evolution of the internal state of atoms in a light field with arbitrary polarization. Earlier, we obtained analytical invariant expressions for the steady state of a cycling atomic transition, including spontaneous decay, for a transition J → J with half-integer J-values [1]. Remarkably, then the stationary excited-state density matrix is always fully isotropic. This also enables us to evaluate explicitly the force pattern of cold atoms in an optical lattice explicitly [2]. We obtained similar results for transitions J → J+1 [3].
For other types of transitions J → J-1, and J → J (integer), polarization-dependent dark states exist, that do not couple to the radiation field. The position-dependence of these states gives rise to weak effective potentials of a geometric nature, due to non-adiabatic coupling the steady state contains no excited atoms. For dark states, where the normal light shifts disappear, these weak forces are the only ones present. They can become sufficiently strong to support bound states [4].
Energy eigenstates of atoms in periodic potentials are also eigenstates of translation over a lattice vector. Fourier transforms of these Bloch waves are the Wannier states, which can be viewed as localized around a lattice site. We have analyzed an exactly solvable model for the transport properties of atoms through a lattice. This transport is described by a master equation for the density matrix, with optical pumping described as quantum jumps, and tunneling through the barriers as a Hamiltonian diffusion process. The time-dependent distribution function over the lattice sites can then be solved analytically, provided that the atoms are kept in the lowest Bloch band by efficient cooling at all times. In the presence of a dark state, there is one Bloch state in the Brillouin zone that is insensitive to optical pumping. Then the average waiting time for the next jump becomes infinite, even though there is always a next jump in the long run. This is characteristic of Lévy statistics [5].