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Coherent States

The coherent state evolves in time and space differently than both the thermal and Fock states. The most compact way to visualize a coherent state is using the Wigner function as in Figure gif.

  
Figure: The Wigner function for a Coherent state for

The average momentum and position of the field oscillate sinusoidally, while the variance possesses a constant value of one half which is represented by a small circle of uncertainty moving around a larger circle. This same information can be observed in a plot of the q, and p, plotted versus time, as in Figure gif.

  
Figure: q, vs t and p, vs t for a Coherent state with .

Notice that Figure gif is quite wavelike; indeed, as the of the coherent state is increased the variance remains constant, but the amplitude of the curve increases. Therefore, as increases, a coherent state behaves more and more like a classical electromagnetic wave. A laser is a source of coherent radiation; therefore, BlochApp can be thought of quantum mechanically as a two--state atom interacting with a coherent electromagnetic field. Plot the E and B for a coherent state. What kind of wavelike character does it have? Compare this result with that for a thermal state. Plot coherent states with larger values of as well.



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