# A Squeezed Light & NonLinear Optics

1. Jan 19, 2017

### sanman

We're hearing things in the news these days about Squeezed Light, and how it can be used to improve everything from LIGO detectors, to positional sensors, to Quantum Computing.

What is Squeezed Light, what useful applications is it being investigated for, and how does it provide this extra utility/benefit?

Squeezed Light is apparently created inside Non-Linear Crystals -- but does it have to remain confined within such crystals or within some special environment like a QED cavity?
Can Squeeze Light exist/propagate in regular open space?

Can Squeezed Light be used in Holography in the same way that regular light is?

It's been said that Squeezed Light exhibits noise levels below that of the ambient noise in the natural Vacuum.
Would it be possible in principle to manipulate Squeezed Light through interference, to create a macroscopic zone of space with noise levels that are lower than that of the ambient noise in the natural Vacuum?

2. Jan 21, 2017

### jfizzix

To understand squeezed light, it's important to understand how the uncertainty principle applies to quantum states of the electromagnetic field.

In particular, just as there is the energy-time uncertainty principle, it is possible to create a "number-phase" uncertainty principle for states of the electromagnetic field.
$\Delta n \Delta\phi\geq\frac{1}{2\pi}$
This relation is an approximation, but the alternative entropy-based relation:
$H(n) +h(\phi)\geq\log(2\pi)$
is rigorous.

With these relations, we can understand that when the field is in a true single photon state, it's phase is totally uncertain, and the light from many such single photons will be incoherent (i.e., will not interfere). Alternatively, when the field has a well-defined phase, its photon number uncertainty is large giving rise to "shot noise" uncertainty in coherent states such as lasers.

Ordinary laser light has a more or less fixed relation between its photon number uncertainty and its phase uncertainty. The number uncertainty goes as the square root of the intensity while the phase uncertainty goes as one over the square root of the intensity. Thus, to have ordinary laser light capable of very sensitive phase measurements, it must be very intense. Indeed, the laser at LIGO is approximately 200 watts. This doesn't sound like much compared to an incandescent light bulb, but this hudreds of thousands of times brighter than an ordinary laser pointer (and that many times more dangerous if you catch it in your eye).

Squeezed light involves generating light whose phase (or number) uncertainty is significantly smaller than what comes out of ordinary lasers. This can be used to make even more sensitive measurements of phase (which is what the next improvements to LIGO will entail).

Squeezed light is indeed created inside nonlinear crystals. A laser shining into a properly aligned nonlinear crystal can generate squeezed light (i.e., some of the laser light is converted into squeezed light). Fortunately, once the squeezed light exits the nonlinear crystal, it stays squeezed. It just can't become more squeezed without traveling through more or longer nonlinear crystals.

I expect squeezed light can be used in holography just as effectively as ordinary laser light is. The additional precision in phase may allow for higher resolution holograms, but this is outside my speciality.

The quantum electromagnetic vacuum has some non-zero minimum energy known as zero-point energy. As far as I know, the only way to have a region of space whose zero-point energy is lower than outer space, would be to place that region inside an optical cavity. The vacuum inside macroscopic cavity would indeed have a smaller zero-point energy, but this difference would be too small to measure. As far as I know, squeezing cannot help reduce vacuum noise because the mean photon number is already zero and the phase uncertainty is maximal. Such amplitude squeezing of the vacuum state would also violate other uncertainty relations.

3. Jan 22, 2017

### sanman

Hmm, so any noise contribution from a Squeezed Photon would add itself by constructive superposition to the existing noise of the Vacuum, but there's no way to reduce existing noise without magically being exactly out of phase with it, for destructive interference purposes.

Tell me - has anyone considered doing Bell's Inequality experiment with Squeezed Photons? Is there a chance that using Squeezed Light instead of regular light would affect the results of the experiment? I thought that Squeezed Light is being investigated for Quantum Computing purposes because its modified probability distribution makes it easier to measure. So I was just wondering if that would similarly apply in Bell's Inequality, whereby it might be possible for Alice and Bob to measure entangled photons from each other without them collapsing into random values/states, but instead collapsing into highly probable values/states. Any opinions on that?

4. Jan 23, 2017

### sanman

Sir, what do you make of the experiment described in this article?

https://www.sciencedaily.com/releases/2017/01/170118132244.htm

They seem to have locally depressed the Vacuum fluctuations at some point, and elevated them in some adjacent spot. Thus the Uncertainty Principle was not violated.

Does this sound possible/plausible?

They seem to have (briefly) made a "dent" in the Vacuum. If we push down on something and it bulges up in an adjacent spot, can this behavior be compared with that of a "fluid" in its loosest sense?

It seems to me that these new tools like Squeezed Light and Femtosecond laser measurement are the shiny new tools in the toolbox to investigate the Vacuum and probe its nature.

5. Jan 23, 2017