Microscopic and Macroscopic Descriptions of Nonlinear Electromagnetic Interactions in Atomic Ensembles

V. L. Jacobs

Konstantin V. Krutitsky, Frank Burgbacher, Audretsch, J.

We present the rigorous microscopic quantum theory of the interaction of ultracold Bose and Fermi gases with the electromagnetic field of vacuum and laser photons. The main attention has been paid to the consistent consideration of dynamical dipole-dipole interactions. The theory developed is shown to be consistent with the general principles of the canonical quantization of electromagnetic field in a medium. Starting from the first principles of QED we have derived the general system of Maxwell-Bloch equations for atomic creation and annihilation operators and the propagation equation for the laser field which can be used for the self-consistent analysis of various linear and nonlinear phenomena in atom optics at high densities of the atomic system. All known equations which are used for the description of the behaviour of an ultracold atomic ensemble in a radiation field can be obtained from our general system of equations in a low-density limit.

V. L. Jacobs

Microscopic and macroscopic descriptions of electromagnetic-field propagation relevant to resonant pumpprobe optical phenomena, such as electromagnetically induced transparency, in quantized many-electron systems are formulated within the framework of a general reduced-density-matrix approach. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner. A semiclassical perturbation-theory treatment of the electromagnetic interaction is adopted, in which the electromagnetic field is described as a classical field satisfying either the microscopic form or the macroscopic form of the Maxwell equations. However, it is emphasized that a quantized-field approach is essential for a fully self-consistent quantummechanical formulation. Compact Liouville-space operator expressions are obtained for the linear and the general (n'th order) non-linear electromagnetic-response tensors for moving many-electron systems. These expressions can be evaluated for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space selfenergy operator in the Markov (short-memory-time) approximation. Environmental interactions can be treated in terms of the Liouville-space self-energy operator, and the influence of Zeeman coherences on electromagnetic-field propagation can be investigated by including an applied magnetic field together with the electromagnetic field.

C. Murray, T. Pohl

A.A. Varfolomeev

Mark S. Hillery, Leonard D. Mlodinow

Theories which have been used to describe the quantized electromagnetic field interacting with a nonlinear dielectric medium are either phenomenological or derived by quantizing the macroscopic Maxwell equations. Here we take a different approach and derive a Hamiltonian describing interacting fields from one which contains both field and matter degrees of freedom. The medium is modeled as a collection of two-level atoms, and these interact with the electromagnetic field. The atoms are grouped into effective spins and the the Holstein-Primakoff representation of the spin operators is used to expand them in inverse powers of the total spin. When the lowest order term of the interaction is combined with the free atomic and field Hamiltonians, a Hamiltonian describing a theory of noninteracting polaritons results. When higher order terms are expressed in terms of polariton operators standard nonlinear optical interactions emerge. These are then compared to the results of phenomenological and macroscopic theories. The theory is also used to derive an effective Hamiltonian describing counterpropagating modes in a nonlinear medium.