MIT5_74s09_pset6

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.74 Introductory Quantum Mechanics II Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Nonlinear Spectroscopy Problems, Part 1 Spring 2009 1. Nonlinear Response Function In analogy to the derivation of the linear response function, derive the quantum form of the second-order (nonlinear) response function. 2. Second Order Response Functions Draw the Feynman and ladder diagrams for the two correlation functions of the second order nonlinear response, Q 1 and Q 2 , and write expressions for the phenomenological time-domain response functions of these systems and corresponding frequency-domain nonlinear susceptibility. Assume that you have a three level system for which the eigenstates of the system Hamiltonian are a , b , and c , and also assume that E a < E b < E c . We want to describe the behavior of two experiments shown here. Two pulses, both with frequency 10 = 21 = 5.74, NLS Problem Set Page 2 3. Nonlinear Experiments on an Anharmonic Vibration Here we will consider two time-domain third-order nonlinear experiments on an anharmonic vibration. For high vibrational 2 frequencies we will only occupy the ground state at equilibrium ( eq = |0><0| ), and the response can be represented by a three level system...
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MIT5_74s09_pset6 - MIT OpenCourseWare http://ocw.mit.edu...

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