Manipulating vacuum with mirrors

The Wikipedia definition of vacuum is “a region of space devoid of matter”. In other words, just empty space. Still, within the strange world of quantum mechanics, vacuum is not that “empty”. There are so-called quantum fluctuations (or vacuum fluctuations) which give rise to some interesting physical phenomena and can (to some extent) be controlled!

In a perfect crystal, the atoms are organised in a repeating pattern, called a crystal lattice. If one, or more atoms do not follow this repeating pattern, we have a crystal defect. In everyday life, you might think of something being defect as being broken. However, in solid-state physics, crystal defects prove to be very interesting, and to be of high importance! One example of a crystal defect is the nitrogen-vacancy (NV) centre in diamond. As the name suggests, the NV centre consists of a substitutional nitrogen atom (e.g.  a carbon atom replaced by a nitrogen atom) next to a vacant position (called a vacancy).

Picture1
The nitrogen vacancy (NV) centre is a crystal defect in diamond, consisting of a substitutional nitrogen atom next to a vacancy. The NV centre acts like a trapped ion inside the wide bandgap of the diamond.

The NV centre has a total of 5 valence electrons, two from the nitrogen atom and three from surrounding carbon atoms. The two electrons from the nitrogen atom alongside two from the carbon atoms form pairs, leaving one unpaired electron. The unpaired electron can efficiently trap an electron from a nearby donor [1], leaving the NV centre with a net charge of minus 1. We call these negatively charged NV centres for NV. For the remaining of this article, I will simply refer to NVas NV centres.

Diamond is made out of carbon atoms, where 99% of the carbon atoms are carbon-12 (12C for short).  The nucleus of 12C consists of six protons and six neutrons, meaning that all the nucleons have “paired up” with another nucleon. In addition, all the six electrons also “pair up”. The significance of this pairing, is that the diamond lattice is more or less spin-free. Nitrogen, on the other hand, has one additional proton and neutron, resulting in a net spin of 1. The spin-free lattice of diamond is a good host for the NV centre spin, resulting in a long spin coherence time [2], which is the time for which the spin is pointing along one axes before flipping due to interactions with the environment. When irradiated with green laser light, the NV centre fluoresces bright in red. However, the intensity of this fluorescence depends on the spin state of the NV centre. In other words, it is possible address the NV centre spin optically!

In a previous blog post, Matteo explained how one could use the long spin coherence time of the NV centre to create a quantum network (if you have not read it yet, I encourage you to do so). For the sake of this article, I will quickly summarise the key concepts:

A photon emitted from the NV centre can be entangled with the spin state. Photons from two remote NV centres can interact to form an entangled pair, provided the photons are indistinguishable. Since the photons were already entangled to the spin of the host NV centre, and the photons are entangled with each other, the two remote NV centre spins become entangled to each other [3]! This spin-spin entanglement can then act as a node in a larger quantum network. The entanglement between distant NV centres has been demonstrated in a famous experiment performed by Ronald Hanson’s group at TU Delft, where they used two NV centres separated by 1.3km to demonstrate a loop-hole free Bell inequality violation [4].

One of the biggest challenges for a large scale quantum network based on NV centres, is the low flux of coherent, indistinguishable photons. Firstly, only approximately 3% of the photons emitted from the NV centre are emitted along the so-called zero-phonon line (ZPL), a purely electronic transition resulting in indistinguishable photons with a wavelength of 637 nm. The remaining photon emission is accompanied by the emission of a phonon (a quantised vibration of the crystal lattice). Secondly, with a large refractive index of 2.4, total internal reflection at the diamond-air interface results in the photons primarily being emitted into modes propagating latterly in the diamond. Thirdly, the NV centre possesses a relatively long lifetime of 12 ns, resulting in a low flux of photons. Luckily, all three problems can be solved by engineering of the optical environment, which slowly leads us back to the properties of vacuum. However, before we can start talk about optical engineering, we need to understand the mechanism behind spontaneous emission of photons.

Picture2
The emission spectrum from an NV centre shows a sharp zero-phonon line (ZPL) accompanied by a wide phonon sideband. Only approximately 3% of the emitted photons are emitted along the ZPL.

The rate of spontaneous emission of photons from a NV centre (or any other quantum system), is governed by the coupling between the NV centre and the previously mentioned vacuum fluctuations. Therefore, by controlling the vacuum fluctuations, one can alter the rate of photon emission. One way to control the vacuum fluctuations is by the use of an optical microcavity [5]. An optical microcavity consists of two highly reflective opposite facing mirrors, separated by a small distance. The light inside the microcavity bounces back and forth between the two mirrors, in a similar fashion to the sound wave inside a guitar. Only light, provided the special condition that the cavity length is equal to an integer number of half the wavelength, will be transmitted through the cavity. In addition, provided the separation of the mirrors in the microcavity is comparable to the wavelength of the light, the vacuum fluctuations become confined. In other words, the vacuum fluctuations become stronger inside the cavity, resulting in a stronger coupling between the NV and the aforementioned vacuum fluctuations. Hence, the probability of photon emission into the cavity is enhanced. One can picture this as the photons being funnelled into one direction, and with one specific wavelength. Enhanced emission rates, by confinement of the vacuum fluctuations, is known as the Purcell effect.  We can use mirrors to control the vacuum!

With the use of piezoelectric nano-positioners, the separation between the two mirrors can be controlled with sub nanometre precision. By tuning the cavity length to overlap with the NV zero-phonon line (637 nm), my colleagues at the University of Basel have experimentally demonstrated Purcell effect from single NV centres [6]. The experimental evidence to back of this claim, is the reduction of the lifetime from 12 ns outside the cavity, to 7 ns inside the cavity. This experiment shows that, with the use of two mirrors, one can address and solve the three problems with the NV centres mentioned above; the broad emission spectra, the low extraction efficiency and the long lifetime.

Picture3
Schematic figure of the tuneable microcavity used to demonstrate Purcell effect from individual NV centres at the University of Basel. The set of xyz piezo positioners allows in situ tuning, and study of individual NV centres.

The reduction of the lifetime, and hence increased flux of coherent photons, is an important step in the right direction for a large scale diamond based quantum network.  The next steps will be to make better performing cavities, alongside the implementation of spin control inside the cavity. Then, in principle, two NV centres located in two remote microcavities can be entangled, and act as two nodes in a large scale quantum network!

So to look back on this article, the key takeaway message is that we can use two highly reflective mirrors to control the vacuum fluctuations, and hence alter the emission of photons from individual NV centres.  Please have a look at my video for a visual introduction to this work: https://www.youtube.com/watch?v=xeovlntM66U&t=99s

 

Written by Sigurd Flågan, PhD student in Richard Warburton’s group at the University of Basel, Switzerland.

[1]        L. Novotny, Principles of Nano-optics 2nd ed, Cambridge University Press 2012.

[2]        G. Balasubramanian et al, Ultralong spin coherence time in isotopically engineered diamond, Nature Materials 8 383-287 (2009)

[3]        H. Bernien et al, Heralded entanglement between solid-state qubits separated by three meters, Nature 497, 86 (2013)

[4]        B. Hensen et al, Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature 526, 682–686 (2015)

[5]        R.J Barbour et al, A tunable microcavity, J. Appl. Phys. 110, 053107 (2007)

[6]        D. Riedel et al, Deterministic Enhancement of Coherent Photon Generation from a Nitrogen-Vacancy Center in Ultrapure Diamond, PRX, 7, 031040 (2017)

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