Difference between revisions of "Photon-atom interactions"
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This chapter explores interactions between photons and atoms, starting from the QED Hamiltonian, using at first a perturbative approach which can be depicted diagramatically. Specifically, we discuss the van der Waals and Casimir interactions as an illustration of this approach. We then present an analysis of a two-level atom excited by light with a frequency nearly equal to that of the atomic transition, a scenario known as resonant scattering. In this scenario, ordinary perturbation theory fails because of the resonant behavior of the system. However, we show that the perturbative, diagramtic approach can be generalized by "factoring" out the physics of resonance. In this manner, we also obtain a description of the physics of an atom interacting with the vacuum, and thus undergoing spontaneous emission. The result shows both the exponential decay and the level shift expected from analysis of the same scenario using the optical Bloch equations. | This chapter explores interactions between photons and atoms, starting from the QED Hamiltonian, using at first a perturbative approach which can be depicted diagramatically. Specifically, we discuss the van der Waals and Casimir interactions as an illustration of this approach. We then present an analysis of a two-level atom excited by light with a frequency nearly equal to that of the atomic transition, a scenario known as resonant scattering. In this scenario, ordinary perturbation theory fails because of the resonant behavior of the system. However, we show that the perturbative, diagramtic approach can be generalized by "factoring" out the physics of resonance. In this manner, we also obtain a description of the physics of an atom interacting with the vacuum, and thus undergoing spontaneous emission. The result shows both the exponential decay and the level shift expected from analysis of the same scenario using the optical Bloch equations. | ||
| − | * [[Derivation of the QED Hamiltonian]] | + | * [[Derivation of the QED Hamiltonian]] ([https://cua-admin.mit.edu:8443/wiki/images/8/86/2009-03-16-QED_Hamiltonian.pdf 2009 Class notes]) |
| − | |||
| − | |||
* [[Feynman diagrams and perturbative expansion of the time evolution operator]] | * [[Feynman diagrams and perturbative expansion of the time evolution operator]] | ||
** [https://cua-admin.mit.edu:8443/wiki/images/9/9a/2009-03-20_Diagrams.pdf 2009 Class notes] | ** [https://cua-admin.mit.edu:8443/wiki/images/9/9a/2009-03-20_Diagrams.pdf 2009 Class notes] | ||
** see API pp. 15-21 and Complement A_I | ** see API pp. 15-21 and Complement A_I | ||
| − | * [[Van der Waals interaction]] | + | * [[Van der Waals interaction]] ([https://cua-admin.mit.edu:8443/wiki/images/f/f2/2009-03-30-van_der_Waals.pdf 2009 Class notes]) |
| − | |||
| − | |||
| − | |||
| − | |||
* [[Casimir interaction]] | * [[Casimir interaction]] | ||
** [https://cua-admin.mit.edu:8443/wiki/images/c/ce/2009-04-01-Casimir.pdf 2009 Class notes] | ** [https://cua-admin.mit.edu:8443/wiki/images/c/ce/2009-04-01-Casimir.pdf 2009 Class notes] | ||
Revision as of 13:59, 21 April 2009
This chapter explores interactions between photons and atoms, starting from the QED Hamiltonian, using at first a perturbative approach which can be depicted diagramatically. Specifically, we discuss the van der Waals and Casimir interactions as an illustration of this approach. We then present an analysis of a two-level atom excited by light with a frequency nearly equal to that of the atomic transition, a scenario known as resonant scattering. In this scenario, ordinary perturbation theory fails because of the resonant behavior of the system. However, we show that the perturbative, diagramtic approach can be generalized by "factoring" out the physics of resonance. In this manner, we also obtain a description of the physics of an atom interacting with the vacuum, and thus undergoing spontaneous emission. The result shows both the exponential decay and the level shift expected from analysis of the same scenario using the optical Bloch equations.
- Derivation of the QED Hamiltonian (2009 Class notes)
- Feynman diagrams and perturbative expansion of the time evolution operator
- 2009 Class notes
- see API pp. 15-21 and Complement A_I
- Van der Waals interaction (2009 Class notes)
- Casimir interaction
- Resonant scattering
- 2009 Class notes
- see API pp. 93-97 and pp. 167-174, 180-189
