Squeezed states of light and their applications in laser interferometers - by Roman Schnabel 2017 - Article review

This document contains article review "Squeezed states of light and their applications in laser interferometers" by Roman Schnabel written in 2017
To order to read the article select:https://arxiv.org/abs/1611.03986



1 Introduction - page 4.

In practice, laser light is often in a mixture of coherent states producing excess noise in the interferometric measurement.
But even if the laser light is in a (pure) coherent state its detection is associated with noise, usually called `shot-noise'.
More experimental (practical) data is required to understand this.
This arises from the quantisation of the electro-magnetic field, which, for a coherent state, results in Poissonian counting statistics of mutually independent photons.
Quantisation can not be the physical reason. More practical data is required.
The most used meaning of quantisation involes the energy levels of the different electrons in an atom.

Figure 1: Poissonian and squeezed photon statistics

The upper boundary of each area represents the probability distribution of detected photon number n, when
More detail is required of what photon number n, n+1, n+2 etc mean.
The broader curve shows the `Poissonian' distribution, which describes the counting statistic of mutually independent particles, i.e. those of the coherent state.

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Figure 2: Squeezed-light enhanced Michelson interferometer

Due to interference with the broadband squeezed vacuum, the interferometer's output light on the photo diode shows reduced variance in the photon number statistic, as shown in Fig. 1.
(b) Simulated data for photo diode measurements.
What is the reason that simulated data is used and not the result of a real performed experiment?
Without squeezing (1), the signal of the laser interferometer is not visible.
With squeezing (11), the shot noise is reduced and, here, a sinusoidal signal visible.
Because simulated data is used, what is the use.

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Let us consider a laser interferometer that uses light in a coherent state.
Firstly, the light beam is split in two halves by a beam splitter.
The two beams travel along different paths and are subsequently overlapped on a beam splitter where they interfere exactly as classical waves would do.
This raises the question: What is the cause that classical waves interfere and what is the difference the beams studied and classical waves.
(The answer maybe lies in the previous text)
The electric fields superimpose, thereby producing the phenomenon of interference.
Why mention electric fields?
The simplest example of interference are water waves.
Up to this point there is no reason to argue light might be composed of particles.
Why this sentence? What is the definition of particles?
Secondly, the new (still coherent) beams that result from the interference are absorbed, for instance by a photo-electric detector.
I expect that many photon detectors are used.
In the case of coherent states the detection process can be perfectly described in the classical particle picture in which the particles appear independently from each other in a truly random fashion, yielding the aforementioned Poisson statistic.
That description is correct insofar as photon detectors are used. The ouput of detectors are photon counts, but that does not mean that photons are particles.
The word random used also raises also a question. The problem is that the photons initially can be considered random, but after interference they are not.
During the detection process, no wave feature of the light is present.
During the detection process the physical interference pattern is quantified, because that is what the photon detectors, do. They count.
Let us have a closer look: A truly random (`spontaneous') event is an event that has not been triggered by anything in the past.
What is meant by event? An event always involves that something changes. The tricky thing is that in reality there are many changes we humans are not aware of.
A collision between two particles (electron and positron) is an event. The cause of the collision was because both particles were on collission course.
The creation of a photon is also an event. A laser produces photons by means of a chemical reaction. For more detail select this link: https://en.wikipedia.org/wiki/Nd:YAG_laser
This allows us to make a clear cut between the first part of the experiment, described by the classical wave picture, and the second part of the experiment, described by the classical particle picture.
Both the interference pattern creation and the measurement of this pattern are part of the same physical process. In some sense both aspects are physical entangled and can not be separated.
Both `worlds' are disconnected.
This sentence is physical not true. . There exist only one physical world.
The subsequent application of two classical pictures is not truly classical, but `semi-classical'.
The concept classical should not be used.
It is indeed the observation that the photons occur individually with truly random statistics that allows this semi-classical description.
A concept like "observation" should be handled with great care. What we observe i.e. measure is not always an accurate picture of what is totally involved. The true reality can be more complex.
What means truly random statistics? See above. The concept of random can only be used in something that is not random. The direction of the magnetic particles (iron filings) used to demonstrate a magnetic field is typical not rondom. The position can be considered random.
Let me point out that in this very reasonable description photons do not exist before they are detected, e.g. absorbed.
This is a wrong interpretation. The photons in each beam interfere which each other. Each beam of light consists of a continuous stream of photons. This can be demonstrated when there is smoke around the beam or when there is dust in the room. Each collision between a photons and a dust particles is an event. At these events the photons are reflected and are detected by the human eye. That is the final moment when the photon seems to exist.
The same happens also when a photon (energy) is detected by a foto electric cell.
Further note, that the famous double-slit experiment with coherent states also allows for the same semi-classical description.
The double-slit experiment with 'individual' photons showing an interference pattern can only be explained by assuming what is counted as one photon, are physical two photons. The one photon counted is divided during the experiment in two. Both parts, each, go to one slit. There after they recombine creating the interference pattern.

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For squeezed states the situation is different.
As before, the interference can be fully described by the classical wave picture. The result of the detection process, however, is different from that of mutually independent random events.
The physical difference between squeezed versus not squeezed should be clearly explained.
Instead, the squeezed probability distribution in Fig. 1 suggests that the probability of detecting a photon decreases with the more photons that are already detected in the same time interval over which a single measurement is integrated.
The squeezed probability function in Fig 1 in some sense does not say anything. What is important are the differences in both process behind the two distribution functions.

2 Observations on light fields in squeezed states - page 9

2.1 Definition of a ‘single mode’ - page 10

2.2 Observations on squeezed states using a single PIN photo-diode - page 11

`PIN' stands for `positive', `intrinsic' and `negative' and is describing the doping of the semiconductor layers.

2.3 Observations on squeezed states using a balanced homodynedetector - page 13

2.4 Observations on two-mode squeezed states using balanced homodyne detectors - page 17

2.5 Observations using photon counters - page 19

3 Theoretical description of squeezed states - page 23

3.1 The quadrature amplitude operators - page 23

3.2 Phase space representations of squeezed states - page 27

3.3 Covariance matrix representation of (single-party) squeezed states - page 32

3.4 Phase space representation of two-mode (bi-partite) squeezed states - page 33

3.5 Covariance matrix representation of bi-partite squeezed states 34

3.6 Photon numbers of squeezed states - page 36

4 Squeezed-light generation - page 39

4.1 Overview - page 39

Squeezed light was first produced in 1985 by Slusher et al. using fourwave-mixing in sodium atoms in an optical cavity

4.2 Degenerate type I optical-parametric amplification (OPA) - page 40

This section provides a graphical description of how degenerate type I OPA/PDC turns a vacuum state into a squeezed vacuum state, and a coherent state into a displaced squeezed state.
The concept of vacuum state should be clearly understood.

4.3 Cavity-enhanced OPA - page 43

4.4 The generation of squeezed light for laser interferometry - page 48

4.4.1 High squeeze factors { minimizing decoherence - page 50

4.4.2 Squeezing in the gravitational-wave (GW) detection band 52

4.4.3 The first squeezed-light source for GW detection - page 54

4.4.4 Generation of two-mode (bi-partite) squeezing - page 55

4.5 Conclusions - page 56

Reflection 1 -

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