Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin

Abstract

The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two seperate molecules give signals that appear on top of a genuine direct higher-order process with a single molecule. These many-body contributions are known as cascading and complicate the interpretation of multidimensional stimulated Raman and other nonlinear signals. In a quantum electrodynamic (QED) treatment, these cascading processes arise from second-order expansion in the molecular coupling to vacuum modes of the radiation field, i.e., single-photon exchange between molecules, which also gives rise to other collective effects. We predict the relative phase of the direct and cascading nonlinear signals and its dependence on the microsocopic dynamics as well as the sample geometry. This phase may be used to identify experimental conditions for distinguishing the direct and cascading signals by their phase. Higher order cascading processes involving the exchange of several photons between more than two molecules are

Theory of multiple quantum coherence signals in dilute thermal gases

“…Note that the near-field term in equation ( 17), scaling as ξ −3 (we drop for brevity the time argument), is the ξ 1 asymptote of the dipole-dipole coupling tensor (17) [43], and is associated with the electrostatic interaction. Because of its (slow) power-law decay with the distance, this interaction is considered to be pertinent at any interatomic separations [20], while the far-field contribution in equation ( 17) (see below) complicates the interpretation of nonlinear signals [44]. It is therefore the electrostatic interaction that was employed in all previous theoretical treatments dealing with MQC signals in dilute atomic gases [13,17,[36][37][38], where atomic angular momentum was also ignored.…”

“…where L γ = N α=1 L γ α , the action of R α j is defined by equation (37), and that of L γ α by (44). The superoperator R L j describes the coherent interaction of the individual atoms with the ultrashort incoming pulses, whereas exp(L γ t) governs their incoherent dynamics when the laser field is switched off.…”

Utilizing Microcavities To Suppress Third-Order Cascades in Fifth-Order Raman Spectra

“…1,[4][5][6][7] Recently a microscopic QED treatment of cascading was developed which connects it to virtual photon exchange between molecules and was applied to various sample geometries. 8,9 A host of other effects owe their origin to the quantum nature of the electric field. These include local-field effects, [9][10][11][12] dipole-dipole coupling, 13,14 the Lamb shift, 15 induced nonlinearities, 16,17 spontaneous quantum synchronization, 18 and superradiance.…”

“…Since the modes in perpendicular direction are not quantized, the conditions k ⊥ ≃ k ⊥ 2 and k ⊥ ≃ k ⊥ 3 can always be satisfied, which leads to the control of cascades by the longitudinal phase mismatch in the prefactor in Eq. (8). Thus, the photon frequencies are ω sq m = c k 2 2 sin 2 θ 2 + m 2 π 2 L 2 and ω pr m = c k 2 3 sin 2 θ 3 + m 2 π 2 L 2 , where θ 2 , θ 3 are the incident angles of k 2 , k 3 -pulses with respect to the longitudinal z-direction as illustrated in Fig.…”

“…According to the sincfunction sin 2 x x 2 in Eq. (8), the 50% suppression of the cascades results in k 2 |cosθ 2 | − mπ L 3 L , which gives rise to the range of the angle (4π−π) 2 × sin 2 π 2 (2π− π 2 ) 2 ≃ 0.005. In conclusion we demonstrated that the cascading processes can be considerably suppressed by controlling the size of microcavity and selecting the direction of the incoming pulses.…”