Time Evolution of Squeezed Quantum States of the Harmonic Oscillator
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This Demonstration shows the behavior of a minimum-uncertainty (Gaussian) squeezed wave packet for the quantum harmonic oscillator. The squeezing is described by a complex number , with
. In polar coordinates,
,
. The variable
determines the magnitude of squeezing and
determines the phase angle. There are also the translation controls
and
. The graphic at the top shows the time evolution of the phase-space Wigner quasi-probability distribution (which is positive definite in this case). The two lower graphics show the time evolution of the
-space and the
-space probability distributions that can be obtained by integrating the Wigner distribution over momentum
or over position
, respectively. They exhibit the so called "breathing" phenomenon—periodic change of the width and the height of the wave packet.
Contributed by: Arkadiusz Jadczyk (April 2015)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Details and further references can be found in [1].
Reference
[1] A. Jadczyk, "Comment on 'The Minimum-Uncertainty Squeezed States for Atoms and Photons in Cavity'". arxiv.org/abs/1502.06444.
Permanent Citation