# What is squeezing: Definition and 18 Discussions

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

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}
. (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

Δ

2

X

g

+

Δ

2

Y

g

=
1

/

2

{\displaystyle \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.

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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1. ### I How can I model squeezed states in 3D optical modelling software?

I would like to model squeezed light and its evolution (such as when passing through lenses after being generated) using optics software such as OptiFDTD or ZEMAX. However, I don’t see any way to make such states…my plan was to simulate an Optical Parametric Amplifier to generate these states...
2. ### I Finding ##\partial^\mu\phi## for a squeezed state in QFT

I'm trying to apply an operator to a massless and minimally coupled squeezed state. I have defined my state as $$\phi=\sum_k\left(a_kf_k+a^\dagger_kf^*_k\right)$$, where the ak operators are ladder operators and fk is the mode function $$f_k=\frac{1}{\sqrt{2L^3\omega}}e^{ik_\mu x^\mu}$$...
3. ### I What are the units of the squeezing parameter?

As I understand it, when the squeezing operator acts on an annihilation/creation operator, a function of sinh(r) and cosh(r) is produced, where r is the squeezing parameter. I've been reading some papers that say that up to '15 dB of squeezing' have been produced in a laboratory. Does this mean...
4. ### Simple Harmonic Oscillator Squeezing

I'm working through https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_06.pdf, and I'm stumped how they got from Equation 5.26 (##\vert 0_{\gamma} \rangle \equiv \frac{1}{\sqrt{cosh\gamma}} exp(-\frac{1}{2}tanh\gamma \hat{a^\dagger}\hat{a^\dagger}...
5. ### Expectation value of operators and squeezing in the even cat state

I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25. How do I derive the given equations?
6. ### Back pressure on a pipe by squeezing it shut

Hi all, I'm new to the forum and was after a bit of guidance. At work we are looking into purchasing a new dosing unit, however I'm unsure if the design that has been drawn up is going to work. The units design revolves around the principle that a flexible tube is compressed closed by...
7. ### Fluids - Squeezing flow - How to find force, work, and flux

Homework Statement The initial separation of the pistons is 2cm. They are submerged in water at room temperature. I need to calculate the work required to have two pistons touch, find the volumetric flux of the water as a function of time, and the force at a given time Homework Equations...
8. ### What are the forces acting while squeezing a ball?

Hi, I am new to this forum. I am currently working on a project in the field of tangible user interface. I am developing a game in which a pressure sensor squeezable ball is the input controller. I am done with the game. Now I need to design a squeeze ball. My next aim is to find out the...
9. ### Forces while squeezing toothpase tube

When I squeeze tube of toothpaste, I am working with 2 squeeze forces toward tube. Why it moves vertically from horizontally applied force (when I think of paste as a group of particles inside a tube I cannot imagine that) ?
10. ### Prove Squeezing Theorem with Natural Log: Find Limit as n->∞

Homework Statement Use the natural logarithm function to prove that (nn/en-1)< n! < ((n+1)n+1/en). Then use the squeezing theorem to find the limit as n approches infinity of nth root of (n!) all divided by n. Homework Equations The Attempt at a Solution I'm not sure where to...
11. ### Effect of squeezing a capacitor on energy stored

2 parallel capacitors, 3uF each, connected in series to 10V battery. One capacitor's separation is then reduced to 30% of its initial value. What is the total energy stored of the capacitors? C tot = 1 / ((1/3e-6) + (1/3e-6)) = 1.5e-6F U initial = (0.5)(1.5e-6)(100) = 7.5e-5 J After...
12. ### Squeezing a piston and its effect on temperature

Homework Statement If a piston is compressed, how is the temperature affected? Homework Equations U=Q + W The Attempt at a Solution My soln: I thought that U=k.e. = (3/2)nRT=(3/2) pV ? Since PV is constant (P1V1=P2V2), shouldn't temperature be constant? Answer sheet: My...
13. ### Squeezing f(x) Between g(x) and h(x): Cos, Sin, & Tan

f(x)=x4 cos(2/x6) g(x) <= f(x) <= h(x) how to get g(x) and h(x) by using the squeeze theorem?? I know is something like this -1 <= x <= 1 But how do i implement it here, and especially to the cos, sin, and tan??
14. ### Why does squeezing a hose make the water go further?

Why does squeezing a hose make the water go futher? According to the continuity equation, A1v1 = A2v2, reducing the area of the opening will cause the velocity to increase. However, according to Bernoulli's eqn, increase in velocity will cause a decrease in pressure, so that will mean that...
15. ### Help with Squeezing a Pair of 3101302 Products

can some one help me out wit this it says to squeeze them a little bit but i have no idea what they are saying i have a pair just like em but i can't make em do anything this site says, can anyone offer any help? http://scientificsonline.com/product.asp_Q_pn_E_3101302
16. ### Prove Squeezing Theorem for n Natural Numbers

Any nice proofs for this? 2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1} I hope the tex came out alright. have fun! ps. n is any natural number.
17. ### Squeezing a capacitor, how does it effected the charge?

I can't seem to get this one to work. Two parallel-plate capacitors, 7.0 µF each, are connected in parallel to a 10 V battery. One of the capacitors is then squeezed so that its plate separation is halved. (a) Because of the squeezing, how much additional charge is transferred to the...
18. ### Immune Cells Squeeze Through Cellular Barriers

Our immune cells are able to squeeze themselves through cellular barriers such as the lining of blood vessels and bowel epithelium. I am wondering: how do they do that, exactly which cells do it, and are they also able to go through tight junctions?