Photon generation by time-dependent dielectric: A soluble model

The notion of the photon is the most basic concept in quantum electrodynamics. However, the quantum nature of the electromagnetic field is well understood in the case of electromagnetic field in empty space only. In the case of fields interacting with external currents and other sources the notion of photons is not so clear. Of particular interest has become the case of electromagnetic field in cavities. If the cavity consists of perfect conductors proper boundary conditions for the field mimic the interaction of the field with charges in the mirrors. The case of field quantization in the presence of dielectrics without dispersion was studied in some detail @1#. Dispersion inevitably leads to damping, which makes the field quantization and hence the notion of photons rather complicated and not yet fully understood @2#. The even more complicated case of photons in a cavity with oscillating perfect mirrors has attracted a lot of interest recently. The corresponding classical problem of electromagnetic field in a cavity with oscillating mirrors does not have a solution in the closed form, but many approximate solutions have been found and discussed. Quantum effects in the electromagnetic field confined to a cavity with moving mirrors has attracted a lot of interest @3#. This problem is also interesting from the point of view of plasma physics @4#. The quantization of the field in such a situation with explicit time dependence does not follow in any natural way from the standard quantization procedures. Some purely quantum effects such as photon noise reduction have been discussed @5#. Yet another aspect of quantum electrodynamics in rapidly changing geometry was discussed recently in Ref. @6#. The fully inhibited spontaneous emission of the atom placed in a node of the resonant cavity mode is assumed. Then, suddenly one of the cavity mirrors is removed. Now the atom is free to emit a photon. The paper predicts an instantaneous response of the detector exposed by the removed mirror. Quantization of the electromagnetic field in the case of time-dependent boundaries is thus needed. Deeper under-