Electric-field dependent quantum dynamics in a delta-function potential system

SC Althorpe, Pavel Soldán, Gabriel G. Balint‐Kurti

Benjamin Fain, Alex Boeglin, S. H. Lin

A general framework for description of quantum systems in strong external fields is established. The most important application of the theory is concerned with the multiphoton ionization of atoms and molecules. The adiabatic approximation is developed. The Hamiltonian of the system is diagonalized by a time-dependent unitary transformation, which generates an interaction energy vanishing for very slow fields. A general analysis of the photoionization rates is performed. A specific model is considered: one-dimensional motion in the δ-function potential and external harmonic electric field. This model allows the exact solution for time-dependent eigenvalues and eigenfunctions. These solutions are compared with the conventional free electron approach to the ionization states.

S. V. Mousavi

Eliade N. Stefanescu

Essentially, we solve the particle-field equations obtained in the matter distribution quantum mechanics. In the framework of this theory, a particle is described by a density amplitude function, we call wave function, as a packet of waves with the time dependent phases proportional to the relativistic Lagrangian. The mass quantization of such a particle, as a distribution of matter, is obtained from the equality of the spatial integral of the density with the mass as a characteristic of the relativistic dynamics of this matter. The particle dynamics, as a motion of a mass spatial distribution, is obtained from the equality of the wave propagation velocities with the distribution coordinate velocities. This description is a physical one, compared to the Schrödinger-Heisenberg description leading to unphysical results as a null velocity for the kinetic energy as a constant of motion, or Zitterbewegung. The description of a particle interaction with an electromagnetic field by additional Lagrangian terms, with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and an electric potential conjugated to time, leads to the Lorentz force, and the Maxwell equations. In the two conjugated spaces, of the coordinates and of the momentum, the dynamics of a quantum particle is described by propagation operators, depending on the coordinate-momentum product, applied to time dependent wave functions satisfying matter-field equations. Unlike the standard Schrödinger or Schrödinger-Dirac equations, depending only on the Hamiltonian operator, instead of the Hamiltonian these equations contain the Lagrangian, which, besides the Hamiltonian, include additional terms with an explicit dependence on velocity, as it is expected in a relativistic theory. We obtain the wave function of a particle-antiparticle system interacting with an electromagnetic field, as a wave packet of spinors propagating in space with finite dimensions, given by the finite definition domain of the density function, in the space of the matter-field momentum, as a constant of motion. We show that an electrically charged quantum particle, rotating in a central electric field, generates a vector potential with a magnetic field perpendicular to the rotational plane and an electric field in this plane. By a quantum transition, a photon is emitted in the particle rotational plane, with the magnetic field perpendicular to this plane, and the electric field contained in this plane. In this framework, the vector potential rotation is correlated to a particle momentum rotation, for the canonical matter-field momentum as a constant of motion, without any electromagnetic field radiated outside.

Donald Jack Kouri, David K. Hoffman

P. Schätz, Max Maier

The dependence of spectral holes of dye molecules in amorphous solids on the following parameters has been calculated: the electric field strength, the angles between the hole-burning and probing laser light fields and the external electric field, the electric dipole moment difference Δμm between the excited and ground state of the guest molecule, the contribution Δμ* of the host matrix to the electric dipole moment difference, and the angle γ, between Δμm and the transition dipole moment μge. When the molecular dipole moment difference Δμm dominates the spectral hole broadens or splits into two holes by the application of the electric field, depending on the angle γ and the directions of the laser light fields and the external field. With increasing values of the host-induced electric dipole moment difference Δμ* the spectral hole shape in the electric field changes significantly if appropriate directions of the light fields and the external field are chosen. The material parameters γ, Δμm, and Δμ* can be determined unequivocally by comparing the calculated holes both in the frequency dimension and the electric field dimension with experimental results.