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Suppose for the moment that the generalized Rabi frequency is a constant. is then, . With this equation, we can find the angle that the Bloch vector will rotate through in a specified amount of time, or vice versa. Let equal where . The time to move through this angle would be

Suppose that the amplitude of the electric field were not a constant but a function of time. Let that function be a square pulse with a width defined by . This pulse would move the Bloch vector exactly through the angle . This pulse is a pulse.

The Field item on the menu has an option to make a pulse. Select this option from the menu when all the atoms are in the lower state. Set n=1.0.

Figure: A Pulse inverts the population.

As observed in Figure gif, the Bloch vector moves from being parallel to the -w axis to being parallel to the w axis. Looking at , one can see that the population has been inverted. A single pulse moves the system from being in the lower state to being in the upper state. There are no off--diagonal terms after the pulse; so, one has moved the entire system from one eigenstate to another eigenstate. Try setting n=2. This pulse will leave the system in its initial configuration. These pulses are used in the laboratory to set atoms in a desired configuration. Try a few more n values; also, set the Amp=0 and try to construct your own pulse with the amplitude parser. (Hint: h(t) is the Heaviside function)

Andy Antonelli
Wed May 17 14:34:24 EDT 1995