(Really) Weird Science

Here's a fun challenge for you... next time you're bored and feel like finding an interesting rabbit hole to go down (after you've watched all the episodes of Fredrick Knudsen's fascinating Down the Rabbit Hole YouTube series, of course) try this prompt in ChatGPT:

"What is one thing that’s happening on the forefront of science and technology that I am probably not aware of but should be?"

If you're using the paid version of ChatGPT it should by now have figured out what you're into and will almost certainly find something interesting for you to think about. What did it recommend to me, you ask? It suggested I delve into a topic that sounds so futuristic that I promise you're going to read it in the voice of Geordi LaForge when you see it...

Quantum Topological Photonics

Let's break it down word by word using my own less than perfectly technical style.

Quantum - the fundamental state of existence where very tiny bits of matter kind of smear together in weird ways and don't work like we think they should. Theorized by scientists to try to explain a bunch of stuff that otherwise doesn't make any sense at all.

Topological - the underlying structure of things that doesn't really change when you squash or stretch them. Think of a topoligical map that shows the trends of mountains and valleys, but not necessarily their exact shapes.

Photonics - the study of controlling and manipulating electromagnetic radiation. That means everything from very long radio waves through visible light to x-rays to cosmic gamma radiation. Yeah, it's all the exact same stuff, just vibrating at different frequencies.

Putting It All Together

So how do these three concepts fit together? Well to hear Science Daily talk about it in terms of "hidden 48-dimensional world in quantum light", you'd think it might be some psychedelic setting for the next Marvel's Ant Man movie. But breathless "science communication" making real concepts sound like marketing clickbait aside, it is actually a thing and it's actually quite fascinating. Yeah, I said actually twice. That's how cool this stuff is. Let me tell you about it.

Now you may or may not have been aware that radio waves and x-rays are the same thing as visible light, just either jiggling in waves so long that your eyes can't detect it (but a metal rod can!) or so short that it passes right through your skin and flesh to cast ghostly shadows of your bones. But you probably do know a bit about visible light... maybe you've even seen some of it around here and there. Usually it's chaotic... all the colors mixed together or certain colors reflected and absorbed by materials, wiggling in all different directions. It's pretty cool that we can detect these weird distortions in the fabric of reality with some globs of cells in our faces but the truth is we use it for so much more than just not bumping into things. We entertain ourselves by flashing it in our faces, slosh it around with weird metal sticks to talk about nothing to folks on the other side of the world, and use it to see who's at the door without having to get up off the couch... we even trap it in small metal boxes to heat up our cold coffee... but despite all that, we know almost nothing about it. Or at least I thought so until I discovered we know a LOT more about light's nature than I ever imagined.

So strap in and let's do some discovering!

Dimensions

Before we go any further, let's address this idea of "48 dimensions" from the article I linked. Without getting into a complex discussion of Hilbert space (a complete vector space equipped with an inner product, generalizing Euclidean geometry to infinite dimensions crucial in quantum mechanics for representing physical states as wave functions) I'd just like to de-hype Science Daily's dramatic headline by saying "48 dimensions" doesn't mean 48 spatial dimensions like a bad Marvel movie or some sort of H.P Lovecraft monster lurking in the space between spaces... in this case "dimension" means somethng more like "properties". As a casual example, imagine you have a friend. Your relationship has one dimension. Now imagine you also work together. That's two dimensions. Roommates? Three dimensions. Occasional drunken hookups too? Maybe another dimension or two or three on top of the rest. It's not about height, width and depth, it's about multiple overlapping spectra (pun intended) along which things can happen, some of which interact with each other and some of which may not.

"Common" light has a few dimensions you're well aware of. Color and intensity are the easiest ones. Those map to frequency for color and amplitude for intensity. You can easily tell a bright white light from a dim red one. If you're a photographer or enjoy really expensive sunglasses, you might also be aware of polarization... that's the direction of motion of the light along the EM (electro-magnetic) wave. Normal sunlight wiggles, as I mentioned earlier, in all directions... but certain types of polarizing filters can block and reveal only the light moving, say, up and down... or side to side... or in a circle clockwise or counter clockwise. Yeah, all of that is happening. This is the effect you see when wearing your $400 Ray Bans in a car with tinted windows... those spots or bands of color you see... polarization interference. Or when you rotate your polarizing filter on your camera to remove the glare of light reflecting off of water or glass... you're just stripping out the light which those materials aligned with their reflective surfaces.

Here Comes the Rabbit

Are you still with me? Good. Those "dimensions" of light I just mentioned... frequency and amplitude... are purely "physical" if such a thing can be said. Polarization is kind of physical and also kind of quantum... it's complicated. But the point is that these are things we're all quite comfortable doing with light. Garden-variety photonics, you might say. It starts to get interesting, though, when we become aware of light's quantum properties and start learning how to utilize them. Those are the "48 dimensions"... and let me tell you, they're pretty weird. Here's three for a start:

Berry Curvature

This relates to how the internal structures of light (like phase and polarization) evolve as they move through certain systems. In specially designed materials or structures, this curvature can cause different modes of light to behave differently... or example, bending slightly in different directions or evolving with different phase relationships... even if they share the same frequency and path.

These geometric effects can help keep different modes of light from interfering with each other, even when they overlap in space, as they occupy different geometric “modes.” With the right encoder and decoder, those modes can be separated again at the receiver, not by frequency or amplitude, but by their underlying geometric structure.

Imagine you had a Rubik's Cube in your hands and wanted to rotate it, one turn at a time, through every possible combination... by the time you got back to the starting point, it wouldn't be in exactly the same position... it will have shifted a bit. The degree of shift is the equivalent of Berry Curvature.

And if that's not weird enough for you, it gets weirder.

Orbital Angular Momentum

You can think of this property of light being kind of like spin... except at a distance from the center of spin. Think of a ball running along a corkscrew... there's nothing in the "center" of the corkscrew except for air so as the ball moves down the screw, it orbits that central space. That's the orbit part. Now add angular momentum... how many orbits it makes as it moves... the more "turns" the corkscrew has, the more "windings" of the ball as it spins around the center space as it travels. But here's the trick... this isn't mechanical motion like a ball on a screw... differences in OAM don't mean the wave is moving slower or faster through space, but rather that its internal structure is rotating more rapidly around the axis.

What good is this, you might ask? Well it's another "dimension" you can encode and decode in light... imagine 20 different signals with the exact same frequency and amplitude, but different number of phase rotations... they all travel together in the same wave but can easily be separated at the other end, like 20 different kids in the same school bus.

But it gets weirder still!

Floquet Bands

Now we're going beyond shaping the light itself and instead we're shaping the environment it moves through in order to change the way the light behaves as it moves through the space.

Let's say you took regular light moving through some system, like a gas or a microchip, but then applied some consistent, repeated influence to the medium... like periodically modulating an antenna, pulsing the voltage of a circuit, or flexing the properties of a material. By doing so, you create a system that changes in time in a regular manner. Light moving through that system doesn’t just pass through unchanged, it begins to interact with that rhythm. Each variation of this time based influence creates new, structured states that the same light can occupy... detectable "dimensions" that, once again, can be encoded and recovered.

Floquet bands aren’t unique frequencies in the usual sense, but additional “layers” the signal can occupy, created by the periodic structure of time itself, which becomes part of the geometry, similar to how sand on a vibrating plate can create different standing wave patterns at different rates of vibration (cymatics), but with light.

The Shape of Things to Come

It's all still light that we're talking about here... what makes it interesting, though, the underlying beauty of it is... that it's also geometry. And that's where the "topological" comes in. We're not just dealing with the shape of waves any more, we're dealing with the shape of things that are almost impossible to imagine. The classical properties of light are geometry, to be sure... vibration, amplitude, rotation... which we are all quite adept at manipulating. But now we're learning about light's more fundamental nature... and we're seeing that it's geometry all the way down... down, across, sideways and slantways. More importantly, we're learning how to impart these properties onto light in laboratory environments, how to prevent noise, corruption and interference from affecting that encoded light while we're manipulating it, and also how to separate it all out and use it to transmit information.

The Long and the Short of it (Pun Intended, Again!)

Sure, most of what we can do in Quantum Topological Photonics it is only useful in very small regions of very specific microchips for highly specialized computers... but it's a relatively young field and it won't stay that way for very long, I suspect it won't be too many years before you can buy a quantum multiplexing wireless mic system where instead of using digital encoding to protect your vocalist from getting stomped on by a refrigerator motor or a passing delivery truck, you'll be able to use some form of quantum encoding to blend dozens of channels of audio into a single receiver, dramatically more protected from interference.

In fact, early versions of this kind of technology are already being explored in labs. That inscrutable diagram up there... that's a design for a Quantum Secure Direct Communications network which may soon allow secure, eavesdrop resistant communications without pre-shared encoding keys over traditional networks by directly measuring quantum states of photons.

If these three weren't enough, there are many more geometric “dimensions” to play with that we haven't even touched on. And the cool thing is that they stack. Just like amplitude, frequency and polarity can all coexist and be manipulated independently in the same light, so, they say, can these other 48 dimensions. Just trying to think about it makes my head warm and though I clearly don't understand it as fully as a domain specialist, it's still the most exciting developing technology I've heard about in a long time. We aren't just learning new ways to transmit signals, we're learning about the fundamental structure of the medium itself, as well as new and seemingly magical ways to shape the space in which those signals live.

PS: The reason all of this works is something called orthogonality... the ability for different structures to overlap in the same space and time without interfering with each other, as long as you know how to look and listen for them. That's what we're learning to do with light at a level that is surprisingly advanced for this stage of human development and that, I think, is very cool.