  The transfer Hamiltonian tunneling current is derived in a time-dependent
density matrix formulation and is used to examine photon-assisted tunneling.
Bardeen's tunneling expression arises as the result of first order perturbation
theory in a mean-field expansion of the density matrix. Photon-assisted
tunneling from confined electromagnetic fields in the forbidden barrier region
occurs due to time-varying polarization and wavefunction overlap in the gap,
which leads to a non-zero tunneling current in asymmetric device structures,
even in an unbiased state. The photon energy is seen to act as an effective
temperature dependent bias in a uniform barrier asymmetric tunneling example
problem. Higher order terms in the density matrix expansion give rise to
multi-photon enhanced tunneling currents that can be considered an extension of
non-linear optics where the non-linear conductance plays a similar role as the
non-linear susceptibilities in the continuity equations.
