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A galery of Wigner functions

Vacuum state

This is the simplest quantum state altogether: no light! But even when we switch off the light, the uncertainty principle holds valid, so both position and momentum exhibit some fluctuations. These are the vacuum fluctuations and they are the same for X and P – so the Wigner function is a round hill centered at the origin of phase space.

Coherent state

This state is emitted by a laser. Its Wigner function is the same as for the vacuum state, but displaced in the phase space so there is a nonzero average for the electric field.

Thermal state

This is the state of radiation a heated black body emits. It has no phase and its photon statistics is that of Bose-Einstein. By room temperature the thermal state is to a good approximation vacuum.

Squeezed vacuum state

The first nonclassical state on this page. The uncertainty in one quadrature is reduced at the other quadrature’s expense. The product of the two is however the same as for the vacuum: this is a minimum uncertainty state.

See our experimental work on generating squeezed light.

Single-photon Fock state

The name says it all – a state containing exactly one photon. We did an experimental project on this one, too!

Four-photon Fock state

Schrödinger cat state

This is a coherent superposition of two coherent states: |a> and |-a>. It is hard to generate experimentally, but the Wigner function is instructive to look at. We see two round hills at the top and at the bottom, associated with each coherent state involved. If our ensemble were an incoherent, statistical mixture of these two states, its Wigner function would just feature these two hills. But because the superposition is coherent, the Wigner function exhibits an additional, highly nonclassical feature in the middle: a fine structured interference pattern with negative regions.

Star state

This state is an analog of the squeezed state, but is generated (in theoreticians’ notebooks) by means of 3-photon, rather than 2-photon, down-conversion.


Squeezed single-photon Fock state

A limiting case of the "odd" Schrödinger cat state |α> - |-α> for small α.


 Gerd Breitenbach’s page featuring another gallery of quantum states.