  We consider a simple model of lossless interaction between a two-level single
atom and a standing-wave single-mode laser field which creates a
one-dimensional optical lattice. Internal dynamics of the atom is governed by
the laser field which is treated to be classical with a large number of
photons. Center-of-mass classical atomic motion is governed by the optical
potential and the internal atomic degree of freedom. The resulting
Hamilton-Schr\"odinger equations of motion are a five-dimensional nonlinear
dynamical system with two integrals of motion. The main focus of the paper is
chaotic atomic motion that may be quantified strictly by positive values of the
maximal Lyapunov exponent. It is shown that atom, depending on the value of its
total energy, can either oscillate chaotically in a well of the optical
potential or fly ballistically with weak chaotic oscillations of its momentum
or wander in the optical lattice changing the direction of motion in a chaotic
way. In the regime of chaotic wandering atomic motion is shown to have fractal
properties. We find a useful tool to visualize complicated atomic motion --
Poincar\'e mapping of atomic trajectories in an effective three-dimensional
phase space onto planes of atomic internal variables and momentum. We find
common features with typical non-hyperbolic Hamiltonian systems -- chains of
resonant islands of different sizes embedded in a stochastic sea, stochastic
layers, bifurcations, and so on. The phenomenon of sticking of atomic
trajectories to boundaries of regular islands, that should have a great
influence to atomic transport in optical lattices, is found and demonstrated
numerically.
