Interaction of Light with a Two-Energy-Level System

P. van der Straten, Harold J. Metcalf

Yehoshua Y. Kalisky

Light emission occurs as a result of interaction between light and matter. Let us assume a two-level atom with levels 1 (ground state) and 2 (excited state). The energies of the ground and excited states are E 1 and E 2 , respectively, and the energy difference is therefore given by the difference ΔE 12 =E 2 −E 1 . When light with photons of energy equal to this difference is absorbed by the atomic or molecular system, an electron will be excited from level 1 to level 2. The energy of the photons is given by ΔE 12 =E 12 =hν 12 (h is Planck's constant and 1→2 is the frequency of light resulting from the level 1→2 transition). This energy is absorbed by an atom or a molecule that has energy levels, separated by ΔE, where these energy levels are the ground and the excited states. This kind of “quantum jump” of an electron between two states occurs in atomic systems between electronic levels; it can be extended to molecular systems, where vibrational and translational energy levels participate in the quantum jump. The interaction between light and matter involves the transition of electrons between different states. This interaction results in the absorption of photons (stimulated absorption) as well as spontaneous and stimulated emission. These processes can be described using Einstein's A and B coefficients, as will be described in the next paragraphs.

Wangjun Lu, Cuilu Zhai, Shi-Qing Tang

In this paper, we present a method for measuring arbitrary-order correlation functions of the light field using a two-level atomic system. Theoretically, light field information should be mapped onto the atomic system after the light interacts with the atom. Therefore, we can measure the atomic system and thus obtain information about the light field. We study two typical models, the p-photon Jaynes–Cummings model, and the p-photon Tavis–Cummings model. In both models, we find that the pth-order correlation function of an unknown light field can be obtained by measuring the instantaneous change of energy of the two-level atoms with the aid of a known reference light field. Moreover, we find that the interactions other than the dipole interactions between light and atoms have no effect on the measurement results.

Philippe Lalanne

Reinhart Poprawe, Konstantin Boucke, Dieter Hoffman

Lukáš Novotný, Bert Hecht

The interaction of light with nanometer-sized structures is at the core of nano-optics. It is obvious that as the particles become smaller and smaller the laws of quantum mechanics will become apparent in their interaction with light. In this limit, continuous scattering and absorption of light will be supplemented or replaced by resonant interactions if the photon energy hits the energy difference of discrete internal (electronic) energy levels. In atoms, molecules and nanoparticles, like semiconductor nanocrystals and other “quantum confined” systems, these resonances are found at optical frequencies. Due to the resonant character, the light–matter interaction can often be approximated by treating the quantum system as an effective two-level system, i.e. by considering only those two (electronic) levels whose difference in energy is close to the interacting photon energy ħ ω 0 . In this chapter we consider single-quantum systems that are fixed in space, either by deposition to a surface or by being embedded into a solid matrix. The material to be covered should familiarize the reader with single-photon emitters and with concepts developed in the field of quantum optics. While various theoretical aspects related to the fields emitted by a quantum system have been discussed in Chapter 8, the current chapter focuses more on the nature of the quantum system itself. We adopt a rather practical perspective since more rigorous accounts can be found elsewhere (see e.g. [1–4]).