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April 01, 2005
Class Review — 3/31
Hey Class,
Remember: Homework 2, problem 1 is due 4/7 and problem 2 is due 4/11.
And: Class is cancelled on 4/5.
Lecture notes will be up on the website today or tomorrow. There will be no pre-flight for next class.
Yesterday in class we learned about:
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A quick answer to what happens inside of a simple laser (single-mode, gain medium has three levels). The number of photons in the laser mode increases dramatically at a "threshold" pumping rate. Well above that threshold, the number of photons in the mode is described by a Poisson distribution that has a larger variance than a coherent state.
The Jaynes-Cummings Hamiltonian. This Hamiltonian describes the interaction of an atom with a single mode of the quantum EM field. The J-C Hamiltonian has two terms, emission + |e> -> |g> and absorption + |g> -> |e>, which results in a Rabi rate that depends on the number of photons in the mode. We saw how micromaser experiments are a realization of the J-C Hamiltonian, and how one can observe "vacuum Rabi oscillations." Note that the J-C Hamiltonian does not describe atoms in free space.
Spontaneous emission, as described by the Wigner-Weisskopf theory (which is not pertubation theory). The W-W solution is a solution to Schrodinger's equation (quantum EM field + quantum atom), in the limit that our quantization volume gets very large. An atom in the excited state decays exponentially to the ground state with a rate that depends on the dipole matrix element squared.
Cheers,
Brian
Posted by Brian at April 1, 2005 12:23 PM
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