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Coherent Squeezed State

The squeezing of a coherent state can be visualized in a number of ways. A coherent state is a squeezed state with r=0. The squeezing is best visualized in terms of the Wigner function in Figure gif. The average momentum and position oscillate sinusoidally just as a coherent state. The difference lies in the oscillation of the variances of the momentum and position. Every one--fourth of a period the variances squeeze and inflate. A q, and p, versus time plot illustrates this squeezing of the variance as well as in Figure gif.

Figure: The Wigner function for a Squeezed Coherent state with and .

Figure: q, vs t and p, vs t for a Squeezed Coherent state with and . The dip is due to the squeezing of the variances.

Try a number of different squeezing parameters. Remember that the larger the squeezing parameter is made, the more field states are required to accurately simulate the system. Plot B and E. How does the squeezing seem to affect these variables? You may want to increase the time step and the number of calculations per step so that the animation of the squeezing will be faster.

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