Chaos in quantum wells and analogous optical systems

The quantized states of a View the MathML source wide potential well in a large tilted magnetic field are investigated using scaled field resonant tunnelling spectroscopy. In contrast to previous experiments on this type of system, the tunnelling characteristics are measured by changing both the magnetic field strength B and the applied bias voltage V such that V/B2 is approximately constant. This ensures that the classical phase space for electrons in the potential well has the same mixed stable-chaotic character for all fields. As a consequence of this scaling, each closed orbit in the potential well produces many periodic resonant peaks in plots of d2I/dB2 versus B. This type of scaled field experiment can be used to probe quantum states corresponding to dynamical regimes which are inaccessible to fixed field resonant tunnelling studies. We also consider analogies between the electron orbits and light rays in gradient refractive index lenses.