Squeezed coherent state

The product of the standard deviations of two such operators obeys the uncertainty principle: Trivial examples, which are in fact not squeezed, are the ground state

The idea behind this is that the circle denoting the uncertainty of a coherent state in the quadrature phase space (see right) has been "squeezed" to an ellipse of the same area.

[6][7][8] The most general wave function that satisfies the identity above is the squeezed coherent state (we work in units with

The squeezed state above is an eigenstate of a linear operator and the corresponding eigenvalue equals

The figures below[clarification needed] 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

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.

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.

The opposite is true for the phase-squeezed light, which displays a large intensity (photon number) noise but a narrow phase distribution.

Nevertheless, the statistics of amplitude squeezed light was not observed directly with photon number resolving detector due to experimental difficulty.

Recent studies have looked into multimode squeezed states showing quantum correlations among more than two modes as well.

Single-mode squeezed states, as the name suggests, consists of a single mode of the electromagnetic field whose one quadrature has fluctuations below the shot noise level [clarification needed] and the orthogonal quadrature has excess noise.

this can be expanded as, which explicitly shows that the pure SMSV consists entirely of even-photon Fock state superpositions.

For example, the field produced by a nondegenerate parametric oscillator above threshold shows squeezing in the amplitude difference quadrature.

[17] Two-mode squeezing is often seen as a precursor to continuous-variable entanglement, and hence a demonstration of the Einstein-Podolsky-Rosen paradox in its original formulation in terms of continuous position and momentum observables.

Bright squeezed light can be advantageous for certain quantum information processing applications as it obviates the need of sending local oscillator to provide a phase reference, whereas squeezed vacuum is considered more suitable for quantum enhanced sensing applications.

The AdLIGO and GEO600 gravitational wave detectors use squeezed vacuum to achieve enhanced sensitivity beyond the standard quantum limit.

will correspond to the population difference in the two level system, i.e. for an equal superposition of the up and down state

Here, metrological enhancement is the reduction in averaging time or atom number needed to make a measurement of a specific uncertainty.

The definition of the QPS is based on the introduction of joint momentum-coordinate quantum states denoted

are the basic quantum states which corresponds to wavefunctions that are covariants under the action of the group formed by multidimensional Linear Canonical Transformations.

[24] It follows from this definition that the structure of the quantum phase space depends explicitly on the value of the momentum statistical variance.

It is this explicit dependence that makes this definition naturally compatible with the uncertainty principle.

[26] At the classical limit, when the momentum and coordinate statistical variances are taken to be equal to zero (ignoring the uncertainty principle), the quantum phase space as defined previously is reduced to the classical phase space.

crystal; similarly travelling wave phase-sensitive amplifiers generate spatially multimode quadrature-squeezed states of light when the

Sub-Poissonian current sources driving semiconductor laser diodes have led to amplitude squeezed light.

[28][29] Much progress has been made on the creation and observation of spin squeezed states in ensembles of neutral atoms and ions, which can be used to enhancement measurements of time, accelerations, fields, and the current state of the art for measurement enhancement[clarification needed] is 20 dB.

[39] Various squeezed coherent states, generalized to the case of many degrees of freedom, are used in various calculations in quantum field theory, for example Unruh effect and Hawking radiation, and generally, particle production in curved backgrounds and Bogoliubov transformations.

Recently, the use of squeezed states for quantum information processing in the continuous variables (CV) regime has been increasing rapidly.