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Research Insights with Bryony Lanigan

Bryony Lanigan is a Research Postgraduate in the Department of Physics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Bryony’s research aims to look for any hint of a dark energy candidate called the chameleon field.

  • What led you to study quantum research?

I don’t come from a family of scientists, but I do come from a family who have always encouraged me to do what I wanted. I’ve always loved learning – I was always that annoying child who couldn’t stop asking ‘but why?’ – and as it turns out, you can make a career out of that in research !

During my undergraduate degree, I took part in several short research projects in a wide range of fields, including acoustics, particle physics, and silicon quantum computing, and I enjoyed them all! When I decided that I wanted to pursue a PhD, I wanted to make sure it was something that had applications to a wide range of areas, and atom interferometry certainly fits the bill. I love experimental physics in particular because it’s so hands-on, and you have to understand concepts not just on a theoretical level but also the real-world effects and how they will impact your measurements.

  • Can you tell us about your research area?

I work with atom interferometers that exploit the quantum properties of matter to probe tiny changes in the environment.

First, clouds of Rubidium-87 atoms are laser-cooled to fractions of a degree above absolute zero. Temperature is related to velocity, so laser cooling atoms use lasers to slow atoms down. In one dimension, we can picture atoms moving along a laser beam, where the frequency of light is chosen such that if the atoms are travelling in the opposite direction to the light, the atoms will absorb photons before re-emitting them in a random direction, getting a tiny momentum kick backwards from each photon in the process. Do this with enough photons and in all three dimensions, and you can slow your atoms down and eventually trap them using magnetic fields in the centre of a vacuum chamber in a magneto-optical trap (MOT). This technique, along with methods to cool atoms even further, won the Nobel Prize in 1997. [1]

To use our atoms to probe their environment, we release them from the MOT and pump them all into one energy state. We then use carefully timed laser pulses to put each atom into a superposition of two states which follow different trajectories but recombine at the end when we read out their final state. An important element of this is that it is not the cloud that’s in a superposition – each individual atom is in its own superposition. Any difference between the two paths will be reflected in the final state of the atoms, and by comparing our measured final state to theoretical expectations, we are able to calculate what forces affected our atoms over the course of the interferometer.

  • What are the main aims of your current research?

The aim of my research is to look for any hint of a dark energy candidate called the chameleon field. Dark energy drives the accelerating expansion of the universe, and while we see evidence for it in large-scale galactic surveys, we find no evidence for any local effects. There are many (many, many) theories that attempt to resolve these discrepancies, but we focus on the chameleon field.

A magneto-optical trap (MOT) forming, disappearing and then reforming.

The chameleon field suggests that there is a field that is suppressed by the presence of mass, meaning that in our matter-dense local environment, it is forced to zero, but in the vacuum of intergalactic space, it is free to take on some high background value, pushing space outwards. Testing this is difficult – we’ve barely sent probes out of our own solar system, let alone into intergalactic space! This is not because we can’t create a good vacuum on Earth (we can), but how are we supposed to measure something that is suppressed by the presence of stuff? What do we use to measure it? This is where cold atoms come in: because atoms are so tiny and so not-dense, they would barely suppress such a field but are still affected by it. [2]

To attempt to measure the chameleon field, we have cold atoms inside a vacuum chamber, along with a ball of aluminium. Away from the ball, in the vacuum chamber, the chameleon field will be high, but on the surface of the ball (and inside it) the chameleon field will be forced to zero, meaning that in the region near the ball, there will be a gradient in the chameleon field, and so the atoms would experience a force.

With our interferometer, we measure the acceleration experienced by our atoms, and so we look for any extra acceleration that could be due to the chameleon field. It’s not quite as simple as this makes it seem – we need to control any potential source of error that could show up as acceleration very carefully, as we are trying to detect anomalous acceleration that’s less than a billionth the size of acceleration due to Earth’s gravity – and it takes years to build an experimental setup and characterise it so we can understand any measurements we take.

  • How could this research potentially benefit society?

At its base, my experiment uses atoms as probes to sense tiny changes in acceleration, and so can be applied to sensing other kinds of accelerations – you just need to find the right way of measuring it. Inertial navigation is something that others in my research group work on, and it uses the same fundamental principles that my research does. Using cold atoms as quantum sensors for navigation could provide an excellent alternative to global navigational satellite systems (GNSS) that could be used in places where GNSS is unavailable, e.g. underground, or under the ocean.

  • What are the next steps in your research? Are there any challenges ahead?

There are always challenges ahead, that’s one of the best things about research! Currently, we are trying to iron out the last few problems before taking measurements to try to find evidence of the chameleon field – or, rather, find no evidence of the chameleon field.

Other experiments that have been done have yet to find any evidence of anomalous acceleration that could be linked to a chameleon field, and we are searching right down at the tiniest edge of accelerations. In this field, we spend a lot of time measuring zero, but that’s still progressing science – and we’re still learning a lot about atomic and laser physics as we go.

[1] https://www.nobelprize.org/prizes/physics/1997/summary/

[2] https://iopscience.iop.org/article/10.1088/1475-7516/2015/03/042

Research Insights with Dr Raj Patel

Dr Raj Patel is a Future Leaders Fellow in the Department of Physics. In this blog post, he shares more about his research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London). Dr Patel’s research group investigates experimental quantum optics and photonic quantum information technologies. 

Can you tell us about your research area?

My group conducts research in experimental quantum optics and photonic quantum information technologies. Our primary focus lies in addressing the formidable challenges within the realm of photonic quantum computing, widely regarded as the most intricate and challenging of the quantum technologies. In doing so, our investigations lead us to explore not only quantum computing but also open up new possibilities in quantum communications and metrology.

In our pursuit, we harness the unique characteristics of light, a natural carrier of information that powers our global telecommunications infrastructure through fibre optic networks. Within the quantum domain, light emerges as an exceptionally versatile carrier of quantum information. It possesses the capacity for transmission over long distances and can be generated and manipulated at room temperature. Unlike their counterparts in matter, Quantum states of light remain resilient to environmental noise.

Moreover, the richness of the quantum information encoded in various properties of light—spanning spatial, temporal, phase, polarization, and frequency degrees of freedom—renders it an ideal candidate for high-dimensional quantum information encoding. Over the last four decades, quantum optics has taken the lead as a platform for experimental tests of quantum foundations and the development of emergent quantum information technologies.

The allure of quantum information lies in its ability to process and transmit information with advantages unattainable through classical means. This opens doors to computation and simulation capabilities beyond the reach of conventional digital computers, while also providing communication with superior security, with far fewer resources, than classical approaches. To fully leverage these advantages, our research requires the development of novel materials for generating quantum states of light, manipulation of these states using free-space or integrated optics, and high-efficiency detection methods, including the use of low-temperature superconducting devices.

While quantum optics forms the bedrock of our research, we recognise the intrinsic synergy between quantum optics, photonics, nanophotonics, and low-temperature measurement techniques. Armed with these experimental tools, our goal is to design and construct optical circuits capable of implementing multi-qubit logic, devise quantum algorithms addressing real-world challenges, create quantum simulators with applications in diverse fields such as chemistry, materials science, finance, and mathematics, and design circuits for error mitigation and correction in both near-term and future universal quantum computers.

What led you to study this area?

From my earliest years, I had the desire to become a physicist. This inclination persisted through the culmination of my MPhys at the University of Warwick, where my trajectory seemed destined for a future in astrophysics, specialising in supermassive black holes and galaxy formation. However, a pivotal moment transpired during a group project that investigated the state-of-the-art in quantum computing. Tasked with reviewing quantum algorithms, I found myself at the intersection of my two passions—physics and computer science.

At that time, my university did not offer courses in quantum optics or quantum information, as the field was still in its nascent stages and gaining attention from mainstream science media outlets. The groundbreaking demonstration of Shor’s algorithm by IBM, utilizing NMR, stood as a prominent showcase of experimental possibilities. Making the decision to shift my focus to quantum computing was indeed a leap of faith, given its relative novelty and the absence of established educational pathways. Yet, the potential for immediate and widespread impact of quantum computing research convinced me that this was the right direction.

Embarking on a Ph.D. journey in III-V semiconductor fabrication and quantum optics, followed by postdoctoral experiences in Australia dedicated to linear optical quantum computing, solidified my comprehension of the field. These experiences not only deepened my knowledge but also allowed me to carve out distinct research directions. Now, as I continue my pursuits at Imperial, I draw upon this diverse background to explore and advance various facets of experimental quantum optics and photonic quantum information technologies.

What are the main aims of your current research?

My current research encompasses two primary thrusts aimed at advancing the field of photonic quantum information technologies. The first stream concentrates on the development of photonic hardware with a specific focus on generating quantum states of high purity and manipulating these states with high fidelity.

In pursuit of this objective, we employ nonlinear processes in materials such as periodically-poled potassium titanyl phosphate to generate quantum light within the telecom C-band. The engineering of quasi phase-matching conditions enables the production of pure states at a wavelength conducive to low-loss transmission through both bulk and integrated optics. Recognising that photon loss poses a significant challenge in photonic quantum information processing, our efforts are directed toward minimising this source of error. Collaborating with industry partners, we are actively developing low-loss nanophotonic interconnects to mode-match these source to waveguides and optical fibres.

In parallel, we are designing programmable circuits on-chip using silicon nitride and thin-film lithium niobate. Additionally, we are utilising machine learning to improve measurements employing superconducting transition edge sensors for photon-number resolving detection.

The second stream of our research leverages the developed hardware to conduct experimental demonstrations. One goal is to employ Gaussian Boson Sampling, where squeezed states of light interfere in a large interferometer followed by photon detection, to simulate real-world molecules and address problems in statistics and graph theory. A distinct aspect of our work involves incorporating error mitigation strategies both at the hardware level and in post-processing of measurement outcomes for Gaussian Boson Sampling—a domain that has traditionally lacked such considerations. We are actively exploring ways to produce non-Gaussian quantum states of light, including Schrödinger Cat states and Gottesman-Kitaev-Preskill states. These states, with their error-correcting codes capable of addressing various errors including loss, hold the potential to serve as valuable resources for future fault-tolerant quantum computers. We aim to produce these states with the required quality and squeezing to make them viable for practical error-corrected quantum computing devices.

How could this research potentially benefit society?

The potential societal benefits of our research are multifaceted, driven by the transformative capabilities of quantum computers and the specific applications within photonic quantum information technologies.

Quantum computers hold the promise of revolutionising scientific discovery. Our recent application of Gaussian Boson Sampling to solve graph problems relevant to drug discovery has demonstrated a polynomial speed-up over classical sampling methods. As these devices scale up, we envision a future where photonic quantum computers, in tandem with high-performance computers, play a crucial role in accelerating research and development processes for new drugs. This could significantly expedite the discovery of novel pharmaceuticals, leading to breakthroughs in healthcare.

Beyond drug discovery, these devices could contribute to simulators for statistical processes relevant to finance and weather prediction. The speed and efficiency gains offered by quantum computing in these domains have the potential to revolutionise decision-making processes and enhance our understanding of complex high-dimensional systems and data.

As quantum computers emerge, posing threats to existing cryptographic protocols such as RSA, secure quantum communication becomes increasingly vital. Our research in this area aims to contribute to the development of robust and secure communication methods, ensuring the confidentiality of sensitive information in the face of evolving threats.

The hardware and techniques we are developing are not limited to quantum computing; they also find applications in quantum sensing and precision measurements beyond the shot-noise limit, with resilience to loss. These technologies could have far-reaching implications in medical imaging, spectroscopy and the precise measurement of the position, navigation, and timing of objects.

What are the next steps in your research? Are there any challenges ahead?

Moving forward, our research will focus on advancing the integration of quantum light sources, circuitry, and detectors onto a single chip. Currently, these critical components exist as separate modules, each optimised independently using materials tailored for specific functions. Connections between these modules are established through free-space or optical fibre links. While ongoing efforts to develop photonic interconnects aim to mitigate losses between components, our goal is to move towards full on-chip integration using waveguides. This not only promises to minimise losses but also ensures phase stability, enabling the exploration of applications requiring numerous quantum light sources generating resource states processed by large-depth circuits.

However, a significant challenge lies in the absence of a single material that can be monolithically processed to fulfil the specific requirements of quantum light sources, circuitry, and detection. This complexity introduces a fabrication challenge, necessitating the heterogeneous integration of materials with mismatched optical properties, leading to potential losses. Despite this obstacle, notable progress has been made in integrating nonlinear sources and single emitters with waveguide circuitry. There have also been initial attempts to incorporate superconducting detectors onto chips.

The current landscape is marked by a dynamic research environment where strides in fabrication tools and materials are continually being made. Optimism prevails that, with ongoing advancements, a fully integrated quantum photonic platform will become a reality in the future. As we address these challenges, the pursuit of seamless on-chip integration remains a pivotal step in unlocking the full potential of our quantum information technologies, paving the way for practical applications and broader adoption in various fields.

 

Research Insights with Elizabeth Pasatembou

Elizabeth Pasatembou is a Research Postgraduate in the Department of Physics. In this blog post, she shares more about her research as part of QuEST (Centre for Quantum Engineering, Science and Technology at Imperial College London).

Can you tell us about your research area?

I am part of the Atom Interferometer Observatory and Network (AION) project [1, 2] which is supported by the UKRI Quantum Technologies for Fundamental Physics (QTFP) programme. The broader aim of the programme is to explore how quantum technologies can be utilised to advance our knowledge about the universe by exploring fundamental physics questions.

AION in particular aims to use quantum technology and atoms cooled down to extremely low temperatures to search for gravitational waves, in the previously unexplored mid-frequency band, and ultra-light dark matter as well as new fundamental interactions. We are developing a detector which uses quantum sensors in the form of atom interferometers. The detector will use strontium atoms cooled to the coldest temperatures possible (near absolute zero). The wave-like nature of the atoms allows us to put them in a superposition of states using lasers in the atom interferometer. This creates two different paths which atoms in two different states take. The two paths are made to come back together at the end of the atom interferometer and they interfere creating a pattern. The interference pattern is very sensitive to everything around it including gravity and therefore gravitational waves. By observing any changes to the interference pattern, we can infer whether a gravitational wave, for example, has passed through our detector. The project consists of various stages starting with a 10 m baseline detector currently being built in Oxford. Subsequent stages include a 100 m detector which will pave the way to a 1 km detector with the final stage being the development of a satellite-based detector.

The signals in the atom interferometers produced by gravitational waves and dark matter are extremely small and therefore every aspect of the technologies used needs to be fine tuned to detect this small changes at the quantum level. Therefore, the project is a collaboration between different universities in the UK each working on a different aspect of the detector. At Imperial [3] we are working towards improving the resolution of the detector by cooling down the atoms to as low temperatures as possible to increase the number of atoms that enter the interferometer. We are also working towards entangling atoms in a cavity allowing us to improve the resolution of the detector and the read the resulting pattern with greater resolution.

What led you to study this area?

Interestingly, my journey into this field of study was somewhat serendipitous. I initially chose physics because I had a strong desire to make sense of the world around me and make a meaningful impact. Early on, I recognised that physics serves as the foundation for many groundbreaking technologies.

During my undergraduate degree at UCL, I had the opportunity to delve into particle physics through a research project in my final year. This experience deepened my fascination with the subject, although I remained open to exploring other areas of physics. Consequently, I decided to take a slightly different path by pursuing a master’s degree in space science and engineering.

It was during this time that I stumbled upon the world of quantum technologies when I took an online course on quantum computing. This emerging field captured my imagination, offering a bridge between fundamental physics and practical applications. As I prepared to apply for PhD programs, I found myself torn between my passion for particle physics and newfound fascination with quantum technology.

Then, I encountered my current research project, which felt like the perfect convergence of my interests. This interdisciplinary endeavor, situated at the intersection of quantum technology, particle physics, and space physics, checked all the boxes for me. I eagerly embarked on this journey, and it quickly became clear that I had made the right choice.

Through this experience, I’ve come to realize the immense potential of quantum technologies and their revolutionary impact on people’s lives. My journey, has led me to a field where I can contribute to both the advancement of scientific knowledge and the development of groundbreaking technologies.

What are the main aims of your current research?

For the past two years, I have been working with the rest of the team at Imperial to build our lab from the ground up. Since this is a new project, a lot of my time was spent building the experiment. In the past few months our focus shifted from building the experiment (ultra-high vacuum system and laser and optics systems required to perform cold atom experiments in the lab) to actually testing the setup and performing experiments as well as analysing our results.

Our main aim at the moment is to develop and refine the technology further and to cool as many atoms as possible to the coldest temperatures possible in preparation for atom interferometry. The aim is to cool the atoms down to micro-Kelvin temperatures by trapping the atoms in what we call magneto-optical trap (MOTs). To achieve this we need very complicated laser and optics systems which can manipulate the motion of the atoms by targeting specific energy levels, reducing their motion and therefore cooling them down. All our findings and the refined techniques we use will be incorporated in the real detector which is currently under development in Oxford.

How could this research potentially benefit society?

Through our work with cold atoms, atom interferometers, and quantum sensors – technologies that we are actively developing in our lab – we are not only advancing our research objectives but also contributing to the ongoing development and improvement of these technologies. This, in turn, enhances their potential for various real-world applications

Cold atoms and atom interferometers have a lot of applications outside tests of fundamental physics. As they are a type of quantum sensor which can be used for gravitational field measurements, they have applications in geophysics and for exploring underground resources. Quantum sensors can also be used in Earth observation and monitor various environmental factors e.g. temperature, aiding climate change research. They can be used for improved navigation systems to provide more accurate positioning and navigation even where GPS signals are unavailable.

Atomic clocks are also based on cold atoms and use a lot of the techniques being developed in my research. These are extremely accurate clocks and are used for timekeeping as well as global communication and they are used in global navigation systems and telecommunications. Cold atoms can also be used as qubits in quantum computers which have the potential to revolutionise a lot of fields e.g. drug discovery and cryptography.

What are the next steps in your research? Are there any challenges ahead?

The next steps for the Imperial AION lab is to optimise the cooling of the atomic cloud. To do this, the cooling in the magneto-optical traps will be refined and the atoms will then be loaded into what we call an optical dipole trap to reduce their temperature even further. In an optical dipole trap, the atoms are trapped and manipulated using laser light. In this trap the atoms’s electric dipole moments interact with the electric field of the laser light and when the laser light is to the frequency of the atomic transition of the atoms, a force is experienced by the atoms which causes them to slow down even further.

After this, a technique called spin squeezing will be applied. This technique will enhance the sensitivity of the atom interferometer in the detector as it allows for a reduction of the quantum noise in the measurements. This is achieved by using an optical cavity (a set of mirrors) for the creation of quantum correlation between atoms.

All these techniques require very stable lasers and well aligned optics systems. Manipulating and entangling atoms with lasers is a complex process. It is already challenging enough in a controlled environment like the lab let alone taking these technologies out of the lab and incorporating them into the real detector.

[1] https://aion-project.web.cern.ch/

[2] L. Badurina, et al., “AION: An atom interferometer observatory and network,” Journal of Cosmology and Astroparticle Physics (2020), 10.1088/1475-7516/2020/05/011.

[3] https://www.hep.ph.ic.ac.uk/AION-Project/

 

Research Insights with Dr Max Attwood

Dr Max Attwood is a UKRI Quantum Technology Career Development Fellow in the Department of Materials. His research focuses on developing organic materials for quantum technologies and a type of quantum sensor called the “maser”.

In our latest blog post, Dr Attwood shares more about his research and the potential masers could have on healthcare.

Can you tell us more about your research area?

My research fellowship centres around developing organic materials for quantum technologies, most pressingly, a type of quantum sensor called the “maser”. These masers are the microwave equivalent of a laser, and the word itself is an acronym for “microwave amplification by stimulated emission of radiation”. Such devices have the potential to amplify extremely weak radio/microwave signals within a narrow bandwidth with extremely high signal-to-noise ratios (SNR).

Initially conceived in the 1950s, masers have historically been used as sensor components inside space-facing radio telescopes. However, due to their thirsty consumption of liquid helium that was required to sustain their low-noise characteristics, these classical masers fell from favour after the 1970s, mainly being replaced by cheaper field-effect transistor devices.

Interest in these devices was reinvigorated in 2012 when a team of researchers led by Professor Mark Oxborrow and Professor Neil Alford of Imperial College London demonstrated the world’s first room-temperature solid-state maser.[1,2] Built using an organic crystal of para-terphenyl doped with the “workhorse” molecule known as pentacene, this work represented a significant shift in terms of the maser gain medium and underlying mechanism governing its operation.

When irradiated with yellow light, one electron in the outermost orbital of pentacene becomes spin-inverted, switching the “state” of the molecule from singlet to triplet. In this triplet state, electrons can exist in one of three distinct energy levels that emerge due to interactions between electrons of the same spin. For some molecules such as pentacene, electrons preferentially occupy the uppermost state due to a process of spin-inversion known as “spin-selective intersystem crossing”, thereby generating a strong population inversion. The difference in energy between the uppermost and lowest energy levels corresponds to a microwave frequency of 1.45 GHz. When a microwave photon of 1.45 GHz interacts with a crystal containing lots of triplet state pentacene molecules, it “stimulates” an avalanche of electrons from the uppermost energy level to the lowest. This simultaneously produces an emission of photons at 1.45 GHz, effectively amplifying the stimulating photon by several orders of magnitude – enough to produce an electrical impulse in a coupled detector.

Thanks to these findings, masers can be used to help detect any phenomenon that might operate or occur at a resonant microwave frequency. This includes sensing extremely small deviations in magnetic field strength or perhaps a single electron spin-flip. I’m interested in the latter example because of its potential to work in tandem with quantum spin-based technologies, including memory devices and communication networks. Before masers can become competitive with contemporary devices, we must find materials that improve their energy efficiency and reduce the impact of non-signal (i.e., noise) photons naturally emitted by ambient objects. This means testing new workhorse molecules instead of pentacene and new host molecules instead of para-terphenyl.

What are the main aims of your current research?

Ultimately, my research aims to build a library of efficient organic maser systems capable of sensing at various frequencies and under significantly dulcified operating conditions compared to the current pentacene-based maser.

As a chemist, my job centres around synthesising and analysing new materials with properties that are open and responsive to maser applications. For new host molecules, we look for systems that are chemically inert while also being able to encapsulate a wider range of “workhorse” molecules at a high concentration. In all cases, the more molecules the better!

We manipulate these properties by changing the chemical structure of both guest and host components and determining the operating conditions, sensitivity, and output power of maser devices. In a perfect world, every photon of absorbed light would produce a triplet state with a population inversion!

How could this research potentially benefit society?

A significant advantage of masers over contemporary high electron mobility transistor (HEMT) or superconducting interference device (SQUID) based microwave sensors is their remarkable signal-to-noise. To achieve low-noise figures, these devices require cryogenic refrigeration however, masers operate at room temperature.

High signal-to-noise means that we require fewer repeat measurements of signals to average out background signals. For example, in electron paramagnetic resonance (EPR) spectroscopy, a technique that uses microwaves to detect electron spins, the signal-to-noise ratios are proportional to where is the number of measurements. If we doubled the signal-to-noise ratios, this would result in 4x fewer scans.

This advantage could be used for equipment like nuclear magnetic resonance (NMR) spectroscopy or magnetic resonance imaging (MRI) scanners used in hospitals. Currently, NHS patients can be expected to wait for more than 3 months for an MRI scan, therefore enabling faster scan times could significantly enhance their availability.

What are the next steps in your research? 

Finding materials that exhibit all the qualities required to build a compelling maser device is complex, and we usually must settle for a compromise.

Often, molecules that exhibit a high triplet yield following irradiation with light have short spin relaxation times. This is because the mechanism that enables the formation of triplets, known as “spin-orbit coupling”, also makes it easier for the spin of an electron to flip. Furthermore, we often find that our workhorse molecules are chemically incompatible with known host molecules. Such issues stem from the fact that polar molecules prefer to interact with other polar molecules (like each other).

Therefore, we often rely on glass-forming materials that provide excellent optically clear media forn, but light excitation can cause triplet-state molecules to occupy a disordered and inhomogeneous molecular environment. The consequence is that the spin-spin relaxation time diminishes significantly, causing the spread of emission frequencies to expand, which reduces the output power for any frequency we might like to study. Known as “inhomogeneous broadening”, this effect is minimised in crystals which form highly ordered 3D structures at the molecular level.

One of my primary research goals is to synthesise a universal host that can encapsulate a wide range of candidate maser molecules and significantly expedite the discovery and screening process while also ensuring an ordered crystalline environment. I would also like to build on the available computational tools that can calculate and predict the properties of future maser candidates.

References:

[1]      M. Oxborrow, J. D. Breeze, N. M. Alford, Nature 2012488, 353–356.

[2]      J. Breeze, K.-J. Tan, B. Richards, J. Sathian, M. Oxborrow, N. M. Alford, Nat. Commun. 20156, 6215.