MIT5_74s09_lec15

MIT5_74s09_lec15 - MIT OpenCourseWare http/ocw.mit.edu 5.74...

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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 .
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p. 10-30 10.3. THIRD-ORDER NONLINEAR SPECTROSCOPIES Third-order nonlinear spectroscopies are the most widely used class of nonlinear methods, including the common pump-probe experiment. This section will discuss a number of these methods. The approach here is meant to be practical, with the emphasis on trying to connect the particular signals with their microscopic origin. This approach can be used for describing any experiment in terms of the wave-vector, frequency and time-ordering of the input fields, and the frequency and wavevector of the signal. Selecting signals by wavevector The question that arises is how to select particular contributions to the signal. Generally, it will not be possible to uniquely select particular diagrams. However you can use the properties of the incident and detected fields to help with selectivity. Here is a strategy for describing a particular experiment: 1) Start with the wavevector and frequency of the signal field of interest. 2) (a) Time-domain: Define a time-ordering along the incident wavevectors or (b) Frequency domain: Define the frequencies along the incident wavevectors. 3) Sum up diagrams for correlation functions that will scatter into the wave-vector matched direction, keeping only resonant terms (rotating wave approximation). In the frequency domain, use ladder diagrams to determine which correlation functions yield signals that pass through your filter/monochromator. Let’s start by discussing how one can distinguish a rephasing signal from a non-rephasing signal. Consider two degenerate third-order experiments ( ω 1 = 2 = 3 = sig ) which are distinguished by the signal wave-vector for a particular time-ordering. We choose a box geometry, where the three incident fields ( a , b , c ) are crossed in the sample, incident from three corners of the box, as shown. (Note that the color in these figures is not meant a b c sig a b c k k k k =+ + a k b k c k top-down view sig k a k + b k c k + k to represent the frequency of the incident fields –which are all the
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p. 10-31 same – but rather is just there to distinguish them for the picture). Since the frequencies are the same, the length of the wavevector k = 2 π n λ is equal for each field, only its direction varies. Vector addition of the contributing terms from the incident fields indicates that the signal k sig =+ k a k b + k c will be radiated in the direction of the last corner of the box when observed after the sample. (The colors in the figure do not represent frequency, but just serve to distinguish the beams). Now, comparing the wavevector matching condition for this signal with those predicted by the third-order Feynman diagrams, we see that we can select non-rephasing signals R 1 and R 4 by setting the time ordering of pulses such that a = 1, b = 2, and c = 3. The rephasing signals R 2 and R 3 are selected with the time-ordering a = 2, b = 1, and c = 3.
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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MIT5_74s09_lec15 - MIT OpenCourseWare http/ocw.mit.edu 5.74...

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