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Additional Course Notes

Carl Wieman

Published Aug 17, 2009• 0 citations
OpenAlex

Abstract

Introduction, Photons - Light as a Particle, Photons - Light as a Particle, Photons - Light as a Particle, General, Photons - Light as a Particle, Emission and Absorption of Light, Emission and Absorption of Light, Electrons as Waves; Probability Waves, Electrons as Waves; Probability Waves, Electrons as Waves; Probability Waves, Electrons as Waves; Probability Waves, Schrodinger Eq and Potential Energy Wells, Schrodinger Eq and Potential Energy Wells, Schrodinger Eq and Potential Energy Wells, Schrodinger Eq and Potential Energy Wells, Atomic Structure, Solids and Conductivity, Solids and Conductivity, Special Relativity, Special Relativity, Special Relativity, Bose-Einstein Condensation, General, Photons - Light as a Particle, Emission and Absorption of Light, General, Electrons as Waves; Probability Waves, Schrodinger Eq and Potential Energy Wells, General, General

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Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
Electromagnetically induced transparency is an important tool for controlling light propagation and nonlinear wave mixing in atomic gases with potential applications ranging from quantum computing to table top tests of general relativity.Here we consider electromagnetically induced transparency in an atomic Bose-Einstein condensate trapped in a double well potential.One well is prepared as in standard electromagnetically induced transparency with a weak probe laser and control laser in a Λ configuration while tunneling between the wells provides a coherent coupling between identical electronic states in the two wells leading to the formation of spatially delocalized inter-well dressed states.The macroscopic inter-well coherence of the Bose-Einstein condensate wave function qualitatively modifies the normal electromagnetically induced transparency linear susceptibility and leads to the formation of additional absorption resonances and larger dispersion than electromagnetically induced transparency.We show that these new resonances can be interpreted in terms of the inter-well dressed states and the formation of a novel type of dark state involving the control laser and the inter-well tunneling.
The Schrödinger equation assumes that a particle behaves as a wave and yields a solution in terms of wave function and the energy of the particle under consideration. Once the wave function is known, then everything about the particle can be deduced from the wave function. This chapter covers the development of the Schrödinger wave equation and its applications to one-dimensional systems. Time-dependent and time-independent Schrödinger equations, bound and scattering states, probability density, probability current and expectation values, the solution of the time-independent 1D-Schrödinger equation for a free particle, infinite as well as finite potential wells, potential steps, and the finite potential barrier are discussed in detail in the chapter. The phenomenon of tunneling, relevance and the importance of the free particle, potential wells and potential barriers to contemporary fields of physics and chemistry, periodic solids and their band structures, the Kronig-Penney model, confined states in quantum wells, and wires and dots are other topics presented in innovative manners in the chapter. The importance of the topics presented here is demonstrated through carefully chosen solved examples and unsolved exercises from contemporary fields of sciences.