# Dictionary Definition

squeezing n : the act of gripping and pressing
firmly; "he gave her cheek a playful squeeze" [syn: squeeze]

# User Contributed Dictionary

## English

### Verb

squeezing- present participle of squeeze

# Extensive Definition

In physics, a squeezed coherent
state is any state of the quantum
mechanical Hilbert
space such that the uncertainty
principle is saturated. That is, the product of the
corresponding two operators takes on its minimum
value:

- \Delta x \Delta p = \frac2

The simplest such state is the ground state
|0\rangle of the
quantum harmonic oscillator. The next simple class of states
that satisfies this identity are the family of coherent
states |\alpha\rangle.

Often, the term squeezed state is used for any
such state with \Delta x \neq \Delta p. The idea behind this is
that the circle denoting a coherent state in a quadrature diagram (see
below) has been "squeezed" to an ellipse of the same area.

## Mathematical definition

The most general wave
function that satisfies the identity above is the squeezed
coherent state (we work in units with \hbar=1)

- \psi(x) = C\,\exp\left(-\frac + i p_0 x\right)

where C,x_0,w_0,p_0 are constants (a
normalization constant, the center of the wavepacket, its width, and
its average momentum).
The new feature relative to a coherent
state is the free value of the width w_0, which is the reason
why the state is called "squeezed".

The squeezed state above is an eigenstate of a linear
operator

- \hat x + i\hat p w_0^2

and the corresponding eigenvalue equals x_0+ip_0
w_0^2. In this sense, it is a generalization of the ground state as
well as the coherent state.

## Examples of squeezed coherent states

Depending on at which phase the state's quantum
noise is reduced, one can distinguish amplitude-squeezed and
phase-squeezed states or general quadrature squeezed states. If no
coherent excitation exists the state is called a squeezed vacuum.
The figures below give a nice visual demonstration of the close
connection between squeezed states and 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 complementary quadrature,
that is, the field at the phase shifted by \pi/2.

From the top:

- Vacuum state
- Squeezed vacuum state
- Phase-squeezed state
- arbitrary squeezed state
- Amplitude-squeezed state

As can be seen at once, in contrast to the
coherent
state the quantum noise is not independent of the phase of the
light
wave anymore. A characteristic broadening and narrowing of the
noise during one oscillation period can be observed. The wave packet
of a squeezed state is defined by the square of the wave function
introduced in the last paragraph. They correspond to the
probability distribution of the electric field strength of the
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 Wigner distribution
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.

## Photon number distributions and phase distributions of squeezed states

The squeezing angle, that is the phase with
minimum quantum noise, has a large influence on the photon number distribution of the
light wave and its phase
distribution as well.

# Synonyms, Antonyms and Related Words

abuse of terms, catachresis, clamping, clamping down,
compression,
concentration,
contorting, crush, decoction, distillation, distortion, eisegesis, error, expression, garbling, gloss, infusion, malentendu, malobservation, misapplication, misapprehension,
miscitation,
misconception,
misconstruction,
misexplanation,
misexplication,
misexposition,
misintelligence,
misinterpretation,
misjudgment,
misquotation,
misreading, misrendering, mistranslation, misunderstanding,
misuse of words, nip,
perversion, pinch, press, pressing, pressure, rendering, rendition, soaking, squeeze, steeping, tightening, torturing, tweak, twisting, wrenching