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A Squeezed State

The squeezed coherent state, like a coherent state, is a minimum uncertainty state. As we observed in FieldApp, the electric or magnetic field can be squeezed to a variance smaller than a half by selecting the proper value for the squeezing parameter. In the last section we saw that a coherent state exhibited collapses and revivals. Logically, a squeezed coherent state should do something similar. But what? Set the number of field elements to 75 and initialize a squeezed state with and r=1. Run JCapp.

  
Figure: The oscillation of the probability of the lower state of an atom initially in the upper state interacting with a squeezed coherent state, and .

Compare Figure gif with the coherent state with . Notice that the squeezed coherent state takes longer to collapse. The revival also comes at a later time and lasts for a shorter period, but the amplitude of the revival is significantly greater than the coherent state. The decay envelope for a squeezed coherent state is less steep than that for a coherent state.

  
Figure: The probability of being in the lower state is profoundly affected by the field state. The upper plot shows a squeezed coherent state( and r=0) interacting with the atom, while the other shows a coherent state().

The squeezing keeps the field states in phase longer than a purely coherent state, as seen in Figure gif. Notice how the state seems to be fluted as if the coherent state were quickly stretched out of shape. The is a function of r. The larger r is, the longer the . The exact nature of this function was not found in the literature. As r increases, increases and the revivals come later and later. Therefore, it is probably true that does depend in some way on for a squeezed coherent state as for a coherent state. Run JCApp for a few more squeezed coherent states with various squeezing parameters. Try to get a qualitative feeling for how the squeezing parameter relates to .

The squeezed coherent state is not the only squeezed state that JCApp can initialize. Set JCApp in a squeezed vacuum state. If the squeezing parameter has a very low value, then the atom should just oscillate as observed in the first section. However, as r increases one can observe a number of higher frequencies riding on top of the vacuum fluctuations. As the squeezing parameter becomes fairly large the high frequencies begin to interfere with the vacuum fluctuations and the system becomes chaotic. Set up a squeezed vacuum state with and confirm these statements.



next up previous contents index
Next: Epilogue Up: Simulations Previous: A Coherent State



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