Chaos in quantum wells and analogous optical systems

The quantized states of a 60 rim wide potential well in a large tilted magn etic field are investigated using scaled field resonant tunnelling spectros copy. In contrast to previous experiments on this type of system, the tunne lling characteristics are measured by changing both the magnetic field stre ngth B and the applied bias voltage V such that V/B-2 is approximately cons tant. This ensures that the classical phase space for electrons in the pote ntial well has the same mixed stable-chaotic character for all fields. As a consequence of this scaling, each closed orbit in the potential well produ ces many periodic resonant peaks in plots of d(2)I/dB(2) versus B. This typ e of scaled field experiment can be used to probe quantum states correspond ing to dynamical regimes which are inaccessible to fixed field resonant tun nelling studies. We also consider analogies between the electron orbits and light rays in gradient refractive index lenses. (C) 2001 Elsevier Science B.V. All rights reserved.