# Quantum optics

As we briefly touched on before, we need special types of light to take advantage of quantum effects. A (not-so-)surprising fact of quantum optics, the study of the quantum mechanical properties of light, is that just weakening the strength of a light source such as a laser or a light bulb does not make quantum effects apparent. This is even the case if it is weakened so much that on average a pulse of light only contains a single particle (photon), or even less than one. Shining a laser through a dark material for instance will never produce an interesting quantum state of light. There is a full mathematical explanation for why this is true and why the non-linear optics which is at the core of our technology is needed, but here we will keep the explanation on more of a conceptual level.

**Non-linear optics**

There are special states of light which do exhibit quantum effects, and the key to making these states is also the core of our technology, non-linear optics. The problem is to produce states where the particle nature of light becomes apparent. Non-linear optics addresses cases where photons are allowed to interact with each other through an underlying material. This allows us to turn more mundane types of light, such as those produced by a laser, into more interesting types of light. One example here is a pulse of light which contains exactly one particle, or photon. Without interactions between them, the particles will act independently, with no influence from the other ones, so without non-linear optics, we can produce pulses where there is one particle **on average**, but not to produce a pulse which we know for sure has exactly one. If we work out how much material it would take to absorb almost all of the light particles, there is a decent chance that we are instead left with zero or two (or more) photons. If light particles are able to interact through a non-linear medium it is clear to see that this limitation can be overcome. Members of our hardware team have done excellent work in this direction.

While a single particle state is probably the conceptually easiest quantum state of light to understand, there are many others, and our non-linear optics technology is the key to unlocking them.

The key concept in our nonlinear crystals is **resonance**. Physical processes have to conserve energy and momentum. This means that we can carefully control what happens to the light when it interacts with these crystals. Since light acts as a wave, controlling resonances amounts to making sure a full number of waves fit into parts of the crystal, this is exactly how a musical instrument creates pure tones, but with vibrations rather than electromagnetic fields. Many of our devices use whispering gallery modes similar to the resonances in sound which let you hear someone whisper on the other side of the dome in St. Paul’s Cathedral in London and many other famous buildings. An example of work involving some of our team with these modes can be found here.

How strongly these crystals make the light interact depends on how strong the local electromagnetic fields can be made, confining light to a smaller space strengthens these fields and therefore the interactions. These interactions need to be made strong, while also being able to faithfully manipulate the light, and this is where our technology shines. One measure of this quality is the Q-factor, which determines how many round trips the light can make in a component before being lost; in this paper our hardware team was able to demonstrate a Q-factor of the order of one hundred thousand, using very similar manufacturing techniques to our core technology. For this reason we are developing a cutting-edge foundry to build the chips we need to do this. We hope to one day make the interactions strong enough that even single particles of light can be made to “bounce” off each other. Some progress in this direction by our team can be found here.

**Quantum effects**

**Superposition**

Having unlocked these quantum states of light, there are many properties of which we can take advantage. Quantum superposition allows a system to effectively explore many possibilities in parallel, although it is only useful if we can also couple it with quantum interference. Quantum interference comes from the fact that unlike probabilities which can only add, quantum amplitudes can add **or subtract**.

**Interference**

Quantum interference can be harnessed as a tool and is at the heart of the famed Grover speedup where a quantum system can search for a solution much faster than any non-quantum method in a way that is rigorously provable. This kind of speedup can have practical implications, for example in solving hard optimization problems faster. Quantum superpositions are fragile since they can be destroyed by interacting with the outside world, but fortunately photons can be relatively easily isolated from their environment, this along with our tools to manipulate photons gives us a path toward harnessing large-scale quantum interference. This fragility is a valuable asset for cybersecurity applications, as it makes it possible to tell if communications are being watched.

## Some Examples

To appreciate how quantum superposition and interference work, imagine a Galton board, with pipes on the bottom where the ball can fall into one of two cups, a winning cup and a losing cup. It is fairly obvious classically that moving a pipe from the winning to the losing cup can only ever decrease your chance of winning. Probabilities can only add. Now let’s imagine a quantum version, quantum mechanically the ball will travel in superposition, and can interfere, in this case, since quantum amplitudes can subtract, moving a pipe from the winning to the losing cup can increase your chances of winning, and could even make it impossible to lose.

Amazingly, this behavior of light has been observed experimentally more than 30 years ago. If identical particles of light hit either side of a special mirror which has a 50% chance of reflecting them and a 50% chance of them going straight through, then the light particles will always be observed to leave in the same direction, meaning one reflects and one transmits. This is because the events where both reflect and both transmit, both lead to one light particle in each direction and therefore cannot be distinguished (go in the same cup in our Galton board analogy). In this case, the amplitudes subtract rather than add due to the physics of reflection, this effect is called the Hong-Ou-Mandel effect, it was first demonstrated in 1987 and now can be routinely observed in quantum optics labs around the world. This effect can only be observed if you can reliably produce single light particles, recall that non-linear optics are the key to creating these states, in fact, a non-linear crystal was at the heart of the setup of this famous experiment even in the 1980s. Building full quantum technology needs capabilities far beyond what was needed for this simple demonstration; in that experiment, pairs could be measured a little more than once per second, and the technology on which we base our devices on can produce millions of high-quality photon pairs per second.

The Hong-Ou-Mandel experiment also highlights a key non-quantum aspect of light, the purpose of the experiment was not actually to show quantum effects, but to use those effects to measure the size of the light particles, and they found that even in the 1980s it was possible to produce waves of light which were only tens of micrometers long, meaning that tens of thousands of them could fit in a single meter of fiber optics. This ties back to a point we were discussing earlier, the mind-boggling amount of information that light can carry. Light is already an ideal platform for processing large amounts of information efficiently, since it is capable of carrying large amounts of information and processing it very quickly. The potential to use quantum effects takes this potential to the next level, making optics and photonics (the manipulation of light where the particle nature is important) key technologies for the processing of information for computing but also for sensing where information is stored in light coming from an object we want to understand.

## Further reading

This page is a high-level overview. If you would like to dig deeper into our research in the area, please see the following links.

Here is an example of our technology being applied to the task of producing single light particles. Some of the tests rely on the Hong-Ou-Mandel effect.

Here is an example of our technology being used to effectively "bounce" single photons off each other.

Here is an example of the extremely high-quality devices we can manufacture to manipulate light.

https://opg.optica.org/optica/fulltext.cfm?uri=optica-6-9-1244&id=420689