Talk:Squeezed coherent state

"The most general wave function that satisfies the identity above" WHICH "identity above"? It's not clear — Preceding unsigned comment added by 31.131.246.13 (talk) 07:07, 17 September 2018 (UTC)

Variable r in Operator representation of squeezed coherent states

Where is r defined? Maybe I'm just not seeing it. Sigfpe (talk) 05:12, 26 July 2015 (UTC)

I think this was copied from *Quantum Optics* by Walls & Milburn. They define r to be the modulus of ζ. However, the parts of the article that involve r might only be valid when ζ is real. I've never thought about states with complex squeezing parameters. Thisrod (talk) 05:54, 6 January 2017 (UTC)

Wrong definition?

I believe that a squeezed state refers to any state where the uncertainty in one quadrature of two non-commuting operators is less than the standard quantum limit. I.e., if $[A,B]=C$ then $\Delta A\Delta B\geq C/2$. In that case, the standard quantum limit is $SQL={\sqrt {C/2}}$. If the uncertainty in A is less than the standard quantum limit, then we say that the state is squeezed with respect to A. —Preceding unsigned comment added by 24.7.65.235 (talk) 02:28, 22 April 2008 (UTC)

Agreed, generally squeezed states refer to some state at the minimum bound of the HUP where one observable gets a smaller share of the uncertainty at the expense of the other. There is certainly a problem with the whole premise of the start of this article. The text is actually talking about a minimum uncertainty state (which all coherent and vacuum states of the harmonic oscillator satisfy). Its only `squeezed' when the uncertainties are no longer equal. In responce to the comment above, one has to be careful with the term standard quantum limit as it means different things to different people. Fincle (talk) 00:19, 17 June 2015 (UTC)

Bad Reference 7

Resolved

 – See edit. AgadaUrbanit (talk) 15:15, 12 September 2011 (UTC)

Reference 7 is behind a restricted access server. Please delete reference 7 and provide a reference to a published account of the same or similar work. — Preceding unsigned comment added by 130.68.20.187 (talk) 15:01, 12 September 2011 (UTC)

one i too much?

In: "The squeezed state above is an eigenstate of a linear operator

${\hat {x}}+i{\hat {p}}w_{0}^{2}$"

I think the i should only occur in the eigenvalue and not the operator.

Unclear

The definition section does not define the terms used in the example section that follows immediately afterwards. So,

• What is amplitude-squeezed, phase-squeezed or quadrature-squeezed?
• What is a 'squeezed vacuum'? Calling it an 'absense of excitation' keeps it completely mysterious.
• What does noise have to do with coherent states? Why is it quantum noise and not some other noise? (or rather, how do we know its quantum noise, and not something else?) How does one write down the equations for noise? Normally, noise is some stochastic process, or, from measure theory, related to some measure over some space; what's the process? what's the measure space?
• Noise suggests we are working with a mixed states, not a pure states .. !? right?? Yet the standard definitions of coherenet states give eqns for pure states. So ...?
• The squeezed state is prepared as the eigenstate of some operator, as defined in the definition section. Fine. But the measurements are made using some other observables ... which ones? What basis are the written in?

Inquiring minds want to know. User:Linas (talk) 00:06, 1 December 2013 (UTC) — Preceding unsigned comment added by 72.71.200.4 (talk)

Agreed, the article is not really complete. 178.39.122.125 (talk) 06:14, 1 September 2016 (UTC)

Where does Figure 4 Come from?

The Data which shows the decomposition of the squeezed states on photon number states is not the one measure in Reference [6], but available from http://gerdbreitenbach.de/gallery/...

Negative Energy Link

Why does the Negative Energy article link to this one? It seems that the article mentions uncertainty in one quadrature component (of the Heisenberg uncertainty principle) being traded off with another in some way. Does this ever result in negative energy when dealing with certain waveforms? Would any experimental setup ever allow negative energy to be 'produced' in more appreciable quantities? ASavantDude (talk) 23:56, 19 July 2015 (UTC)

Is a squeezed coherent state coherent?

Is a squeezed coherent state coherent? Sometimes the article says it is, sometimes it says the contradiction. All in all it makes little sense. 178.39.122.125 (talk) 06:13, 1 September 2016 (UTC)

Saturate or not?

In the introduction we read "Note that a squeezed state does not need to saturate the uncertainty principle.", while in the Operator section we read "Therefore, a squeezed coherent state saturates the Heisenberg Uncertainty Principle ... with reduced uncertainty in one of its quadrature components and increased uncertainty in the other. What is correct here? — Preceding unsigned comment added by 193.83.106.80 (talk) 17:19, 22 March 2018 (UTC)

Basic definition of why it's "squeezed" before getting into the math?

I looked at this article, and found it mostly incomprehensible. Then I looked at this IOP science page ( https://iopscience.iop.org/article/10.1088/1464-4266/7/5/B01 ), which starts with

"Quantum squeezed states are a consequence of uncertainty relations; a state is squeezed when the noise in one variable is reduced below the symmetric limit at the expense of the increased noise in the conjugate variable such that the Heisenberg uncertainty relation is not violated."

By only requiring the reader to know the Heisenberg Heisenberg Uncertainty Principle (which is pretty common knowledge, and it doesn't even REALLY require the reader to understand that), this single sentence is able to explain more to a relative layman like me than this entire Wikipedia article as it currently stands. (That might be an exaggeration. The third paragraph of this article explains this pretty well. It's just messy in how it says it and weirdly far down, and it made me feel like that might be tangential to the page's main point and there was something more important I wasn't understanding.) It also gives the background as to what the basic idea this article is even supposed to be talking about is, to help such readers figure out what the specifics are trying to say and what is and isn't important to whyever they looked this up. I hesitated to edit the beginning of this article because I wasn't certain that I actually understood, and didn't want to mess up any important nuance in the beginning of the article, particularly with regards to the "coherent" part, since I'm not sure if there's such a thing as an "squeezed incoherent state", and with regards to the number of dimensions, since I'm not sure if a "coherent state" necessarily considers both of the variables needed to make the "squeezing" necessary, though I would think that it would, since those are variables that are necessarily related by the Heisenberg Uncertainty Principle. I will suggest a change though. Currently, the beginning of the article looks like this:

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 $x$ and momentum $p$ of a particle, and the (dimension-less) electric field in the amplitude $X$ (phase 0) and in the mode $Y$ (phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle:

$\Delta x\Delta p\geq {\frac {\hbar }{2}}\;$ and $\;\Delta X\Delta Y\geq {\frac {1}{4}}$ , respectively.

Wigner phase space distribution of a squeezed state of light with ζ=0.5.

Trivial examples, which are in fact not squeezed, are the ground state $|0\rangle$ of the quantum harmonic oscillator and the family of coherent states $|\alpha \rangle$. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with $\Delta x_{g}=\Delta p_{g}$ in "natural oscillator units" and $\Delta X_{g}=\Delta Y_{g}=1/2$. (In literature different normalizations for the quadrature amplitudes are used. Here we use the normalization for which the sum of the ground state variances of the quadrature amplitudes directly provide the zero point quantum number $\Delta ^{2}X_{g}+\Delta ^{2}Y_{g}=1/2$).

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. $\Delta ^{2}X\approx \Delta ^{2}X_{g}/2$. Today, squeeze factors larger than 10 (10 dB) have been directly observed.

I would suggest SOMETHING like this:

In quantum physics, a coherent state is said to be squeezed when the uncertainty in one observable is sufficiently reduced that, following to the Heisenberg Uncertainty Principle, the uncertainty in the complementary variable is greatly increased.

Such a quantum state is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position $x$ and momentum $p$ of a particle, and the (dimension-less) electric field in the amplitude $X$ (phase 0) and in the mode $Y$ (phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle:

$\Delta x\Delta p\geq {\frac {\hbar }{2}}\;$ and $\;\Delta X\Delta Y\geq {\frac {1}{4}}$ , respectively.

Wigner phase space distribution of a squeezed state of light with ζ=0.5.

Specifically, the term squeezed state is 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.

Trivial examples, which are in fact not squeezed, are the ground state $|0\rangle$ of the quantum harmonic oscillator and the family of coherent states $|\alpha \rangle$. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with $\Delta x_{g}=\Delta p_{g}$ in "natural oscillator units" and $\Delta X_{g}=\Delta Y_{g}=1/2$. (In literature different normalizations for the quadrature amplitudes are used. Here we use the normalization for which the sum of the ground state variances of the quadrature amplitudes directly provide the zero point quantum number $\Delta ^{2}X_{g}+\Delta ^{2}Y_{g}=1/2$).

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. $\Delta ^{2}X\approx \Delta ^{2}X_{g}/2$. Today, squeeze factors larger than 10 (10 dB) have been directly observed.

DubleH (talk) 08:39, 13 August 2022 (UTC)

Looking at the page on squeezed states of light has confirmed my fear of not knowing exactly what I'm talking about and my choice to not edit the article myself. I assumed that a "squeezed coherent state" was a subtype of a "coherent state", but that article says that "light is in a squeezed state if its electric field strength Ԑ for some phases $\vartheta$ has a quantum uncertainty smaller than that of a coherent state" and "must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state." This implies that a squeezed coherent state is actually NOT a coherent state at all, but rather a state that is squeezed relative to a "coherent state". Alternatively, maybe a "squeezed coherent state" IS a coherent state, and the article on squeezed states of light just meant that such a state must be squeezed relative to some OTHER coherent state in order for it to be meaningfully called "squeezed". I honestly couldn't tell you yet. DubleH (talk) 08:58, 13 August 2022 (UTC)