Nonlinear spectroscopy with entangled photons; manipulating quantum pathways of matter.

Optical signals obtained by the material response to classical laser fields are given by nonlinear response functions which can be expressed by sums over various quantum pathways of matter. We show that some pathways can be selected by using nonclassical fields, through the entanglement of photon and material pathways, which results in a different-power law dependence on the incoming field intensity. Spectrally overlapping stimulated Raman scattering (SRS) and two-photon-absorption (TPA) pathways in a pump probe experiment are separated by controlling the degree of entanglement of pairs of incoming photons. Pathway-selectivity opens up new avenues for mapping photon into material entanglement. New material information, otherwise erased by interferences among pathways, is revealed.

Generalized Kramers-Heisenberg expressions for stimulated Raman scattering and two-photon absorption.

The frequency-domain pump-probe signal of a material system interacting with two quantum modes of the radiation field is recast in terms of products of scattering amplitudes (T matrix elements) rather than the third-order susceptibility Im chi((3)). The resulting expression offers a more intuitive physical picture for the optical process compared with the semiclassical approach which treats the radiation field as classical. It can be derived and interpreted using closed-time-path-loop diagrams which represent the joint state of the matter and the field for each contribution to the signal. The signal has two components representing stimulated Raman scattering omega(1) - omega(2) and two-photon absorption omega(1) + omega(2) two-photon resonances. Both are expressed as nonequi-librium steady-state photon and matter fluxes, as is common in the description of dissipative processes in open quantum systems.

Nonlinear optical spectroscopy of single, few, and many molecules; nonequilibrium Green's function QED approach.

Nonlinear optical signals from an assembly of N noninteracting particles consist of an incoherent and a coherent component, whose magnitudes scale ~ N and ~ N(N - 1), respectively. A unified microscopic description of both types of signals is developed using a quantum electrodynamical (QED) treatment of the optical fields. Closed nonequilibrium Green's function expressions are derived that incorporate both stimulated and spontaneous processes. General (n + 1)-wave mixing experiments are discussed as an example of spontaneously generated signals. When performed on a single particle, such signals cannot be expressed in terms of the nth order polarization, as predicted by the semiclassical theory. Stimulated processes are shown to be purely incoherent in nature. Within the QED framework, heterodyne-detected wave mixing signals are simply viewed as incoherent stimulated emission, whereas homodyne signals are generated by coherent spontaneous emission.

Emergence of order in selection-mutation dynamics.

We characterize the time evolution of a d -dimensional probability distribution by the value of its final entropy. If it is near the maximally possible value we call the evolution mixing, if it is near zero we say it is purifying. The evolution is determined by the simplest nonlinear equation and contains a d x d matrix as input. Since we are not interested in a particular evolution but in the general features of evolutions of this type, we take the matrix elements as uniformly distributed random numbers between zero and some specified upper bound. Computer simulations show how the final entropies are distributed over this field of random numbers. The result is that the distribution crowds at the maximum entropy, if the upper bound is unity. If we restrict the dynamical matrices to certain regions in matrix space, to diagonal or triangular matrices, for instance, then the entropy distribution is maximal near zero, and the dynamics typically becomes purifying.

Phase-sensitive stimulated Raman adiabatic passage in dipolar extended lambda systems.

The authors investigate the possible phase-sensitive behavior of (multiphoton) stimulated Raman adiabatic passage population transfer in extended lambda systems, if more than one state of an anharmonic progression of target levels is accessible in transitions of different photonicities. They use a minimal model four-level system (4LS) with one initial state separated from two target states by an apex state. The parameters of the 4LS are adapted from the bend states of the HCN-HNC system. Using a dressed-state analysis within the rotating wave approximation (RWA), the authors identify phase-dependent diabatic transitions between the two dressed states contributing to the state vector as the mechanism leading to phase-sensitive target populations. The essential features giving rise to the phase dependence are found to be different (non-zero-) diagonal elements of the dipole matrix, i.e., permanent dipole moments, and the presence of a direct two-photon overtone coupling between the apex state and the lower target state which formally enters the RWA Hamiltonian upon inclusion of permanent dipole moments. Among the parameters controlling the extent of the effect are the anharmonic properties of the target progression and the absolute values of the field frequencies, so that in view of the requirement to tune the driving fields into the vicinity of resonance, details of the level structure are of importance. A comparative numerical study executed without invoking RWA shows that qualitatively there are similar trends in the appearance of phase sensitivity, although the effects are considerably more pronounced in the full treatment. In the full treatment the authors also explore off-resonance conditions and discuss the signatures of phase sensitivity in the target populations.