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February 24, 2005
Class review — 2/24
Hi Class,
The pre-flights for Tuesday are all ready to go. Lecture notes and the VPython simulations from today will be posted sometime tomorrow. I'm also going to try to grade homework #1 this weekend.
Let me know if you have more trouble with the pdf files that I've posted.
Today we learned about:
Spin echo. This is a useful trick in a Ramsey experiment, which can take out the effect of a spread in Larmor frequencies (or detunings). Note that this trick ruins a Ramsey experiment for use as a clock.
Density matrices. We use density matrices to talk about real-life measurements of quantum systems. The density matric tells us everything we can know about an ensemble of quantum systems (which we always have to use to make measurements).
Time evolution of the density matrix. We can translate the Liouville equation into equations of motion for the matrix elements of the density matrix. Coherences drive changes in the population, and differences in the population drive changes in the coherences.
Alternative Bloch vector picture based on the density matrix. In this formalism, the x and y components of the Bloch vector are determined by the coherences, and the z component by the difference in the populations. A Bloch vector which has a length less than one represents a mixed state. Classical states all have a Bloch vector which lies on the z-axis.
The Liouville equation with decoherence added in. We're going to talk about this more next time, and look at some examples.
Cheers,
Brian
Posted by Brian at February 24, 2005 04:29 PM
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