Program Overview

Selected Topics of Theoretical Atomic Physics

Course Description

The goal of this course is for students to acquire knowledge of elementary theoretical atomic physics, including light-matter interactions, operational knowledge in solving optical Bloch equations (OBEs), mechanical action of the light on atoms, and theoretical description of a cold atomic gas.

Learning Outcomes

Upon completing the degree, students will be able to:

• Demonstrate a thorough knowledge of advanced methods of theoretical physics, including classical mechanics, classical electrodynamics, statistical physics, and quantum physics
• Describe the state of the art in at least one of the presently active physics specialities
• Perform numerical calculations independently, even when a small personal computer or a large computer is needed, including the development of simple software programs
• Develop a personal sense of responsibility, given the free choice of elective/optional courses
• Develop the written and oral English language communication skills that are essential for pursuing a career in physics
• Search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development

Course Specific Learning Outcomes

Upon completing the course, students will be able to:

1. Solve the behavior of an atom interacting with electromagnetic waves (laser radiation) by employing OBEs (numerically and analytically)
2. Calculate the mechanical force arising from light on the atoms as a function of atomic velocity, detuning, intensity of radiation, and other relevant parameters
3. Quantitatively describe dipole matrix elements and associate them with Rabi frequencies
4. Provide a detailed description of laser cooling, evaporative cooling, the concepts of optical molasses, Magneto-Optical traps, and Bose-Einstein condensates
5. Quantitatively and qualitatively describe a cold atomic cloud with the Fokker-Planck equation
6. Quantitatively and qualitatively describe an ultra-cold atomic cloud with the Gross-Pitaevskii equation

Course Structure

The course is structured as follows:

1. Time-dependent perturbation theory in quantum mechanics; dipole approximation for the laser-atom interaction
2. Rabi problem, dressed states, Bloch vector, spontaneous decay from an excited state
3. Density matrix, spontaneous emission, OBEs, saturation intensity
4. Numerical solution of OBEs for N atomic states and multiple frequency excitation
5. Force on an atom, standing and moving atom, Doppler cooling
6. and 7. week: Project assignments for students
7. Temperature and thermodynamics of laser cooling kinetic theory, random motion
8. Fokker-Planck equation for cold gases
9. Magneto-optical trapping
10. Cooling below the Doppler limit, Sisyphus cooling
11. Evaporative cooling, Bose-Einstein condensate, Gross-Pitaevskii equation (GPE) 13.-15. week: Project assignments for students

Requirements for Students

Students are obliged to continuously perform tasks and project assignments week by week.

Grading and Assessing the Work of Students

Success in completing the project assignments, performing calculations, and exploring literature is graded during the semester. The final grade is concluded in the final oral exam.

Literature and Prerequisites

• Prerequisites: Passed Classical Electrodynamics and Quantum Physics
• The course is offered in the 9th semester of the regular study program in Physics.