Spontaneous emission from a quasi-two-dimensional Wigner crystal in a multilayer configuration - art. no. 033815

Spontaneous emission (SE) from electrons forming a quasi-two-dimensional Wi gner crystal in a dielectric cavity is discussed for a multilayer configura tion. All layers in the system are considered as dielectrics with real diel ectric constants. Within such a model, we treat SE completely from the quan tum-mechanical (QM) point of view, i.e., we use the quantized electromagnet ic field in dielectrics and calculate its interaction with electrons in the Wigner crystal. The full QM approach enables us to go beyond the standard dipole approximation and take into account, e.g., the vibration of electron s around their regular positions inside the crystal and the change of elect ron positions during the deexcitation process. We analyze only the perpendi cular transitions, which involve quantum states determined mainly by the im age potential. Since this potential is relatively weak for a typical config uration of a Wigner lattice, the corresponding electromagnetic lifetime tau is estimated to be very large (tau less than or similar to 10(-3) s). We d erive a simple expression for the angular distribution of the SE radiation and analyze its possible deviation from the dipole radiation (sin(2) theta) spectrum. For a typical Wigner crystal formed above a liquid He layer we h ave found no significant corrections to the spectrum obtained in the dipole approximation. We also consider the case of a Wigner crystal in a (micro)c avity between two metallic plates, discuss the effect of the cavity selecti on rules on the SE rate, and examine the corresponding discrete SE spectrum .