Editing Squeezed coherent state (section)

==Examples==
Depending on the phase angle at which the state's width is reduced, one can distinguish amplitude-squeezed, phase-squeezed, and general quadrature-squeezed states. If the squeezing operator is applied directly to the vacuum, rather than to a coherent state, the result is called the squeezed vacuum. The figures below{{clarify|reason=Without explaining the experimental setup, this is pretty weak. Is it a laser?|date=September 2016}} give a nice visual demonstration of the close connection between squeezed states and [[Werner Heisenberg|Heisenberg]]'s [[uncertainty relation]]: Diminishing the quantum noise at a specific quadrature (phase) of the wave has as a direct consequence an enhancement of the noise of the [[complementarity (physics)|complementary]] quadrature, that is, the field at the phase shifted by <math>\tau/4</math>{{clarify|reason=The variable tau is not defined.|date=March 2023}}.

{{multiple image
 | align = center
 | width1 = 228
 | width2 = 180
 | width3 = 399
 | image1   = noise squeezed states.jpg
 | caption1 = Measured quantum noise of the electric field (3π-interval shown for the first two states; 4π-interval for the last three states)
 | image2   = wave packet squeezed states.jpg
 | caption2 = Oscillating wave packets of the five states.
 | image3   = Wigner function squeezed states.png
 | caption3 = [[Wigner quasiprobability distribution|Wigner functions]] of the five states. The ripples are due to experimental inaccuracies.
 | footer = Different squeezed states of laser light in a vacuum depend on the phase of the light field.<ref>{{cite journal|last1=Breitenbach|first1=G.|last2=Schiller|first2=S.|last3=Mlynek|first3=J.|s2cid=4259166|title=Measurement of the quantum states of squeezed light|journal=Nature|date=29 May 1997|volume=387|issue=6632|pages=471–475|doi=10.1038/387471a0|url=http://users.unimi.it/aqm/wp-content/uploads/Breitenbach-1997.pdf|bibcode=1997Natur.387..471B}}</ref> Images from the top: (1) Vacuum state, (2) Squeezed vacuum state, (3) Phase-squeezed state (4) Arbitrary squeezed state (5) Amplitude-squeezed state
}}

As can be seen in the illustrations, in contrast to a [[coherent state]], the [[quantum noise]] for a squeezed state is no longer independent of the phase of the [[light wave]]. A characteristic broadening and narrowing of the noise during one oscillation period can be observed. The probability distribution of a squeezed state is defined as the norm squared of the wave function mentioned in the last paragraph. It corresponds to the square of the electric (and magnetic) field strength of a classical light wave. The moving wave packets display an oscillatory motion combined with the widening and narrowing of their distribution: the "breathing" of the wave packet. For an amplitude-squeezed state, the most narrow distribution of the wave packet is reached at the field maximum, resulting in an amplitude that is defined more precisely than the one of a coherent state. For a phase-squeezed state, the most narrow distribution is reached at field zero, resulting in an average phase value that is better defined than the one of a coherent state.

In phase space, quantum mechanical uncertainties can be depicted by the [[Wigner quasi-probability distribution]]. The intensity of the light wave, its coherent excitation, is given by the displacement of the Wigner distribution from the origin. A change in the phase of the squeezed quadrature results in a rotation of the distribution.