by Suzanne van Dam

What if we could make an internet, but quantum? This would allow us to connect distant nodes (e.g. computers) not with classical information, but with quantum information. We can already imagine cool applications, such as secure communication
guaranteed by the laws of quantum physics. But many of the applications may not even have been dreamed up yet,
as happened before with new technology.

A quantum internet made of diamond

In the lab of Professor Ronald Hanson, where I am doing my PhD research, we want to make such a quantum internet, using diamonds as a building block. More specifically, we aim to use a defect in the carbon lattice structure of diamond, where one carbon is substituted by a nitrogen atom (N), and a neighbouring carbon site is left vacant (V): the nitrogen-vacancy (NV) centre. Each NV centre is a node in the quantum network. To entangle two NV centres we use photons to establish the connection between them. Matteo explains nicely in his blogpost why this NV centre works so well as a quantum network node.

Nitrogen-Vacancy centres in diamond can be a node in a quantum network.

In this blogpost I will focus on one of the aspects of these NV centres as a quantum network node: their optical interface. This interface allows us to create a connection between the NV centre, our local quantum bit, and the photons that we use to connect distant NVs. Entanglement can only be established if the photons that two distant NVs emit are at the same frequency. This is because they have to be indistinguishable, such that we can interfere them on a beamsplitter to create a quantum connection between the two NVs. But how do we get those indistinguishable photons at the same frequency from the NV centre?

Photons for a quantum internet

To understand this we need to dive a bit deeper into the inner workings of the NV centre. The Vacancy of the NV contains a pair of electrons, which we can describe quite well as acting like an atom. You may know that electrons in atoms can be in different orbits. When an electron is excited to a higher energy orbit (by applying energy from a laser), it will eventually fall back to the lower-energy orbit, emitting a photon in the process. This photon will have exactly the frequency corresponding to the energy difference between the two orbits (since for photons, energy and frequency have a fixed relationship). So here we have our photon, with a well-defined frequency, that has the same frequency as the photon at a distance, if we do the exact same thing for that distant NV center. You can read more in Norbert’s blog post about how we ensure that we can get exactly the same frequency.

When an atom decays from a higher energy orbital state (excited state) to a lower energy orbital state (ground state), it emits a photon at a frequency f that matches the energy difference E between the orbital states following E=hf (h is Planck’s constant).

This, however, is not the full story. Since the NV centre is not actually a free-floating atom, but embedded in the diamond crystal structure, the change in orbit of the electron changes the positions of the atoms in the crystal, which shakes up the lattice. The vibration that goes into the diamond is called a phonon, and it takes some of the energy away. This means that there is less energy left for the photon, which will therefore have a lower frequency. Because these vibrations can vary in their strength, we cannot rely on these photons to have the same frequency every time; and therefore we cannot make them indistinguishable from the distant ones. We thus cannot use these photons for entanglement generation. And the bad news is: for NV centres, a decay happens together with a phonon 97% of the time!

Looking at the distribution of emitted NV photons, we see that only a few have a frequency of 470.4 THz that exactly matches the energy difference between the orbital states. The rest has a lower frequency (= higher wavelength), because some of the energy is taken away by a phonon – a vibration in the diamond crystal.

Speeding up the quantum internet

This makes a quantum internet slow: entanglement can only be made with the 3% of the photons that are emitted without phonons – we call them the zero-phonon line (ZPL) photons. We thus have to try this many times until by chance a ZPL photon is emitted, which may take a while. Nevertheless, we have been able to do cool things, such as show
spooky action over more than a kilometer, and on-demand entanglement (click on the links to see cool movies!). But, to make a quantum internet with more nodes over larger distances, we have to somehow increase this 3%.

This challenge is what I have spent a large part of my PhD on. It turns out there is a very beautiful way of increasing the number of ZPL photons, called the Purcell effect. Below I will explain how it works; first using physics, and then using a swimming pool-analogy.

How to make an electron jump off a diving board

First, we have to understand how an electron changes orbits. It may seem straightforward that an electron can move from a higher energy orbit to a lower energy orbit. In the end, balls also roll downhill. But, this is a bit more complicated for an electron. Simplifying the situation (read the footnotes for a more accurate description [1]), we can understand it as follows. For the electron to change orbit, it has to be able to dump its leftover energy in an emitted photon. For this photon to be able to exist, there has to be room in the electromagnetic field. If this is not the case, the electron cannot get rid of its energy and will always stay in the higher orbit. But how can the electron know whether there is room for the photon, and thus whether it can decay?

Here is an important role for the electromagnetic field that is permeating space. As a mind-blowingly quantum entity, even in vacuum with no photons, this electromagnetic field has nonzero energy. We call it the vacuum electric field. This vacuum electric field couples to the orbital state, letting the electron know whether it has room to accommodate a photon, if it decays [2]. The amount of room in the electromagnetic field we call the density of states. What is a bit intuitive is that if the vacuum electric field has a high density of states the electron will be more keen to decay [3]!

This is what we call the Purcell effect. If it wasn’t intuitive yet that the electron decay rate will be higher if the vacuum electric field has a larger density of states, imagine you are at the top of a diving board. Would you be more keen to jump off if beneath you there would be a bucket of water or a luxurious swimming paradise?

A swimming-pool analogy of the Purcell effect, that I was told by my colleague Cristian Bonato.

Turn the ZPL into a swimming pool

But, back to the NV centre. Remember that our aim is that the NV centre emits more photons in the ZPL, not combined with a phonon. The Purcell effect gives us a tool to do this. What if we could make the density of states really high for the ZPL, but change nothing for the emission of a photon plus phonon? Following the above analogy, we would like to turn the ZPL into a swimming pool, while the emission together with a phonon remains like a bucket of water. The NV centre would now much more often choose to emit a ZPL photon!

How can we do such a thing? We want to increase the density of states at the very specific frequency that matches the energy difference between the electron orbits. For the NV centre this frequency is 470.4 THz, which corresponds to a wavelength of 637 nm. To make a high electric field density, we can place two mirrors opposite each other, such that the field will bounce back and forth between the mirrors. If the distance between the mirrors is a multitude of the wavelength [4], every time the field bounces back and forth, it has a peak at the same position. With many bounces, this peak becomes higher and higher, and we get a standing wave. Physicists call this constructive interference, and it can make the electric field density of states very high at the point of the peak. If you are into music, you may know the same effect from a tone on e.g. a guitar. The tone corresponds to a standing wave on the string. When you make the string longer or shorter by putting your finger on it, the tone that you hear changes, because the wavelength fitting on the string is different, and thus a different tone forms a standing wave.

If we thus very precisely control the distance between two mirrors, and put the NV centre exactly at the peak of a wave with a wavelength of 637 nm, we get a very high density of states at the ZPL. The NV will then want to emit much faster into the ZPL.

What it looks like in the lab

We now have all the ingredients for what we want to do. In summary, the plan that we have to speed up the quantum internet is as follows. We want to make sure that the electron decays more often into the ZPL than together with phonons. We understand that the NV centre electron can decay because of the vacuum electric field surrounding it. The higher the vacuum electric field density, the faster the decay. So, to make the decay into the ZPL faster, we have to make a high vacuum electric field density at exactly the frequency 470.4 THz (=637 nm). And this we are going to do by putting the NV centre in between two mirrors that are spaced by a multiple of 637 nm.

What all the above means in the lab is that we have to place two tiny mirrors at a distance of less than a hair apart, with a very thin diamond membrane that contains NV centres in between. And since we need the distance between the mirrors to be very precise, there should not be much movement of the mirrors! The movement has to be less than 0.1 nm: about 100,000 times less than the thickness of a human hair.

We expect that if we can make this work, we can make a quantum internet that is 1000 times faster than the current version. That makes it worth spending some time in the lab to make this challenging setup!

This is what the experimental setup looks like. Two mirrors are separated by a few micrometers – less than the thickness of a hair. To keep them at the same distance, we isolate it from the environment with vibration isolation stages. This is altogether put in a cryostat, which is a fridge that can cool down to -269 ◦C. We than shine lasers at the NV centre (and apply electronics) to use it as a quantum network node.

Footnotes

[1] I am glancing over the more accurate description that the orbital states are orthogonal, so no transition between them can spontaneously happen.

[2] The coupling to the vacuum electromagnetic field makes the orbital states no longer good eigenstates (we can use perturbation theory to calculate the new eigenstates!). The new eigenstate is a superposition of orbital excited state plus no photons and the ground orbital state plus a single photon in the electromagnetic field. Time-evolution between the components enables the decay.

[3] The decay rate between excited and ground state is described by Fermi’s golden rule.

[4] To be precise: the round-trip distance should be a multiple of the wavelength (such that the distance between the mirrors has to be a multitude of the half-wavelength).

A fascination for the counterintuitive quantum world brought Suzanne to QuTech. Now she uses diamonds to build a quantum internet. She loves running, when not running experiments.