Eigenvalue distributions of large Euclidean random matrices for waves in random media

We study probability distributions of eigenvalues of Hermitian and non-Hermitian Euclidean random matrices that are typically encountered in the problems of wave propagation in random media.Comment: 29 pages, 10 figure

Transmission of quantum entanglement through a random medium

We study the high-dimensional entanglement of a photon pair transmitted through a random medium. We show that multiple scattering in combination with the subsequent selection of only a fraction of outgoing modes reduces the average entanglement of an initially maximally entangled two-photon state. Entanglement corresponding to a random pure state is obtained when the number of modes accessible in transmission is much less than the number of modes in the incident light. An amount of entanglement approaching that of the incident light can be recovered by accessing a larger number of transmitted modes. In contrast, a pair of photons in a separable state does not gain any entanglement when transmitted through a random medium.Comment: 6 pages, 2 figures. Text slightly revise

Non-Hermitian Euclidean random matrix theory

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave propagation in an ensemble of point-like scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.Comment: 11 pages, 9 figure

Euclidean matrix theory of random lasing in a cloud of cold atoms

We develop an ab initio analytic theory of random lasing in an ensemble of atoms that both scatter and amplify light. The theory applies all the way from low to high density of atoms. The properties of the random laser are controlled by an Euclidean matrix with elements equal to the Green's function of the Helmholtz equation between pairs of atoms in the system. Lasing threshold and the intensity of laser emission are calculated in the semiclassical approximation. The results are compared to the outcome of the diffusion theory of random lasing.Comment: 6 pages, 4 figure

Absorption imaging of a quasi 2D gas: a multiple scattering analysis

Absorption imaging with quasi-resonant laser light is a commonly used technique to probe ultra-cold atomic gases in various geometries. Here we investigate some non-trivial aspects of this method when it is applied to in situ diagnosis of a quasi two-dimensional gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known three-dimensional result (Beer-Lambert law) and outline the specific features of the two-dimensional case.Comment: 22 pages, 5 figure