CHAPTER 2 The Driven Two-Level Atom

B. R. Mollow, Marvin M. Miller

R. Bonifacio, Brian W J McNeil, Gordon R. M. Robb

Z. Ficek, JOSIP SEKE, Andrey Vladimirovich Soldatov +2 more

Surendra Singh

In this chapter a quantum mechanical treatment of atomic response to the fields of an electromagnetic wave is presented. Absorption and emission of energy by atoms involves transition between their quantized energy levels driven by an interaction Hamiltonian. Schrodinger equation is used to derive the equations of motion for the density matrix of the atom, which is better suited to include the effects of mechanisms other than the interaction Hamiltonian – collisions, level decays, level shifts, etc. that also affect the state of the atom. Using the density matrix equation of motion and focusing on two atomic levels, induced dipole moment for a single two-level atom and polarization and susceptibility for a collection of two-level atoms, including the effects of level decays, and collisions, are calculated. Equations of motion for level populations are also derived. These expressions naturally predict stimulated emission as well as absorption. Expressed in terms of spontaneous emission rate they confirm the validity of equations derived in Chapter 5 using the dipole oscillator model of atomic response. The limit in which quantum mechanical equations for atomic response reduce to the classical dipole oscillator equations is also discussed.

Byron B. Taylor

This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.