Quantum Harmonic Oscillator — Coherent & Squeezed States
Wigner quasi-probability distribution W(x,p) in phase space
State Parameters
Coherent amplitude |α|:
2.0
Phase φ (deg):
0
Squeezing r:
0.0
Squeeze angle θ (deg):
0
Dynamics
Animate: phase space rotation
Start Rotation
ω·t speed:
1.0
⟨n⟩ = |α|²
ΔxΔp ≥ ½ℏ
Squeezed: Δx = e^{−r}/√2
Δp = e^{+r}/√2
Theory
Wigner function:
W(x,p) = (1/π)∫ψ*(x+y)ψ(x−y)e^{2ipy}dy
Coherent state |α⟩: Gaussian
displaced from origin
Squeezed: elliptical Gaussian
one quadrature below vacuum
W≥0 always for Gaussian states
Negative W → non-classicality