We calculate spectra and wave functions of Rydberg atoms in strong magnetic fields using adiabatic basis sets, which reflect the different time scales of the electronic motion parallel and transverse to the magnetic field. For large absolute values of the azimuthal quantum number m, nonadiabatic corrections are found to be negligible, and the adiabatic basis states and their energies are exact solutions. With decreasing value of
∣m∣, the system turns nonadiabatic, and the statistical behavior of the spectra changes from being consistent with classically regular to being consistent with classically chaotic motion. A relation describing the parameter region in which this transition occurs is obtained.
How does the existence of chaos in classical dynamics affect the quantum spectrum of the system? The atom in a magnetic field is a prototype of systems where complete classical and quantal calculations are possible. Transition from regular to chaotic trajectories are linked quantally to the progressive breaking of some peculiar symmetries of the system. We propose a method and its experimental realization on lithium atom to clearly see a transition between regularity and chaos on a quantum spectrum by selecting the starting state of the excitation. In addition, experimental and calculated spectra on hydrogen shows a remarkably good agreement.