Wigner function
Wigner function is an alternative description of a quantum state, used primarily in quantum optics. Its domain is the phase space. In many respects it behaves like a probability dostribution, although it can reach negative values (which substitute complex phase in explaining interference phenomena). It is shown here for several important states of a 1D harmonic oscillator. Especially time evolution and position probability density reconstruction are particularly simple, compared to wave function approach, in this formalism.
Initial state:
Plot:
Tips for trying:
- In paused mode, you can control displacement and squeezing. Try resetting the vacuum state and reaching a coherent state, squeezed vacuum, phase- or amplitude-squeezed states.
- Gaussian states behave in terms of quadratures just like ensembles of classical trajectories. Imagine for comparison a group of sinusoids with equal frequency but with randomized amplitudes and phases. Can anything similar be said for the states featuring negativity?
- Note with the single-excitation state, how negative (red) values of the Wigner function can cancel out positive (blue) down to exact zero but never below.
- Watch the birth and decay of interference fringes when two packets meet (with cat states). How does their distance affect your observation?