squeezed
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position
x
{\displaystyle x}
and momentum
p
{\displaystyle p}
of a particle, and the (dimension-less) electric field in the amplitude
X
{\displaystyle X}
(phase 0) and in the mode
Y
{\displaystyle Y}
(phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle:
Δ
x
Δ
p
≥
ℏ
2
{\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}\;}
and
Δ
X
Δ
Y
≥
1
4
{\displaystyle \;\Delta X\Delta Y\geq {\frac {1}{4}}}
, respectively.
Trivial examples, which are in fact not squeezed, are the ground state
|
0
⟩
{\displaystyle |0\rangle }
of the quantum harmonic oscillator and the family of coherent states
|
α
⟩
{\displaystyle |\alpha \rangle }
. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with
Δ
x
g
=
Δ
p
g
{\displaystyle \Delta x_{g}=\Delta p_{g}}
in "natural oscillator units" and
Δ
X
g
=
Δ
Y
g
=
1
/
2
{\displaystyle \Delta X_{g}=\Delta Y_{g}=1/2}
.
The term squeezed state is actually used for states with a standard deviation below that of the ground state for one of the operators or for a linear combination of the two. 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. Note that a squeezed state does not need to saturate the uncertainty principle.
Squeezed states of light were first produced in the mid 1980s. At that time, quantum noise squeezing by up to a factor of about 2 (3 dB) in variance was achieved, i.e.
Δ
2
X
≈
Δ
2
X
g
/
2
{\displaystyle \Delta ^{2}X\approx \Delta ^{2}X_{g}/2}
. As of 2017, squeeze factors larger than 10 (10 dB) have been directly observed.
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x
{\displaystyle x}
and momentum
p
{\displaystyle p}
of a particle, and the (dimension-less) electric field in the amplitude
X
{\displaystyle X}
(phase 0) and in the mode
Y
{\displaystyle Y}
(phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle:
Δ
x
Δ
p
≥
ℏ
2
{\displaystyle \Delta x\Delta p\geq {\frac {\hbar }{2}}\;}
and
Δ
X
Δ
Y
≥
1
4
{\displaystyle \;\Delta X\Delta Y\geq {\frac {1}{4}}}
, respectively.
Trivial examples, which are in fact not squeezed, are the ground state
|
0
⟩
{\displaystyle |0\rangle }
of the quantum harmonic oscillator and the family of coherent states
|
α
⟩
{\displaystyle |\alpha \rangle }
. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with
Δ
x
g
=
Δ
p
g
{\displaystyle \Delta x_{g}=\Delta p_{g}}
in "natural oscillator units" and
Δ
X
g
=
Δ
Y
g
=
1
/
2
{\displaystyle \Delta X_{g}=\Delta Y_{g}=1/2}
.
The term squeezed state is actually used for states with a standard deviation below that of the ground state for one of the operators or for a linear combination of the two. 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. Note that a squeezed state does not need to saturate the uncertainty principle.
Squeezed states of light were first produced in the mid 1980s. At that time, quantum noise squeezing by up to a factor of about 2 (3 dB) in variance was achieved, i.e.
Δ
2
X
≈
Δ
2
X
g
/
2
{\displaystyle \Delta ^{2}X\approx \Delta ^{2}X_{g}/2}
. As of 2017, squeeze factors larger than 10 (10 dB) have been directly observed.
View More On Wikipedia.org