page_title: Squeezed states of light
section_title: Representation of squeezed states by quasi-probability densities
hierarchical_section_title: Squeezed states of light / Representation of squeezed states by quasi-probability densities
caption_attribution_description: English: Wigner function of a squeezed vacuum state.
context_page_description: In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases has a quantum uncertainty smaller than that of a coherent state. The term squeezing thus refers to a reduced quantum uncertainty. To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state.
context_section_description: Quantum states such as those in Fig. 1 (a) to (e) are often displayed as Wigner functions, which are quasi-probability density distributions. Two orthogonal quadratures, usually and , span a phase space diagram, and the third axes provides the quasi probability of yielding a certain combination of . Since and are not precisely defined simultaneously, we cannot talk about a 'probability' as we do in classical physics but call it a 'quasi probability'. A Wigner function is reconstructed from time series of and . The reconstruction is also called 'quantum tomographic reconstruction'. For squeezed states, the Wigner function has a Gaussian shape, with an elliptical contour line, see Fig.: 1(f).
caption: Fig. 1(f): Left: Wigner function of a squeezed vacuum state. Right: Connection to Fig. 1 (e).
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