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Entangled in quantum mechanics

Greg Blackman finds out that advances in nonlinear optics are adding to our understanding of quantum mechanics

The physicist Niels Bohr once famously said ‘those who are not shocked when they first come across quantum theory cannot possibly have understood it’. Quantum mechanics today remains a bit of a mystery even among those who study it. The theory had its opponents from its conception, most notably Albert Einstein – Bohr and Einstein held a series of discussions debating quantum physics.

Physically designing an experimental protocol to test the foundations of quantum mechanics proved difficult, and up until the 1960s the debate was mostly philosophical. Today, however, there are methods to generate some of the exotic effects hypothesised in quantum mechanics in order to study it. One of these effects is quantum entanglement, and researchers have been generating entangled photon pairs since the 1980s – the source of which is now mainly nonlinear optics.

Entangled photons are a state of light differing from that exhibited by standard coherent laser light. The concept actually arose from Einstein’s opposition to quantum mechanics in a paper he co-authored in 1935 with Podolsky and Rosen. The state of light exhibited by entangled photons is such that two separated photons will affect each other instantaneously without any form of signalling. This conflicted with Einstein’s notion of locality, in that separate entities should not be affected by each other unless there’s a signal that runs between them, the maximum speed of which is the speed of light. Einstein called this ‘spooky action at a distance’, which is now referred to as quantum entanglement.

Being able to generate entangled photons is integral to studies of the foundations of quantum mechanics, as well as research into quantum cryptography, a method of producing unbreakable codes that are protected by the laws of physics rather than by mathematical complexity, and other forms of exotic communication allowed by quantum mechanics such as quantum teleportation.

The process of forming entangled photons from nonlinear crystals is the exact opposite of second harmonic generation (SHG), explains Dr Ayman Abouraddy, assistant professor at CREOL, college of optics and photonics, University of Florida. ‘These are exactly the same nonlinear crystals as are found in laser devices. The only difference is that they’re performing the operation in the opposite direction.’

Dr Abouraddy and Professor Bahaa Saleh run the quantum optics group at CREOL, which uses nonlinear crystals to generate entangled photons for a variety of experiments, including testing the foundations of quantum mechanics and imaging experiments. The imaging work looks at encoding spatial information in the light beams generated by nonlinear crystals to transmit quantum information, as opposed to transferring it in the temporal domain.

‘When we buy nonlinear crystals, we simply specify the second harmonic generation, because optics suppliers aren’t familiar with the process of forming entangled photons. We then use the crystal in reverse,’ comments Dr Abouraddy. ‘In this sense, it’s a very accessible source of entangled photons. There is work ongoing looking at alternative sources based on quantum dots or on nitrogen vacancies in diamond, but still nobody has managed to completely replace this source and compete with the convenience of using a set of harmonic crystals.’

Tuning light

Nonlinear optics are an integral part of many laser devices, simply because of their ability to tune the coherent laser light emitted from the gain medium to other wavelengths as required by the application. Second harmonic generation (SHG) crystals are a classic example, which halve the 1,064nm wavelength emitted by Nd:YAG lasers to 532nm (green light). This process can be taken further in third (355nm) or even fourth harmonic generations (266nm).

Tuning Nd:YAG laser light to longer wavelengths is also possible through optical parametric oscillation. OPOs containing periodically poled lithium niobate (PPLN) are able to tune a pump wavelength of 1,064nm to any wavelength in a wide range in the infrared, from around 1.5-4.5µm. ‘The reason for the use of nonlinear optical crystals is they offer a means of providing light at wavelengths not easily, economically, or directly obtainable from lasers or other light sources,’ explains Philip Marlowe, product manager, nonlinear optics at optics provider Gooch and Housego.

Dominic Loiacono, general manager at Coherent Advanced Crystal Group, feels there is always a need to improve nonlinear materials, largely because of a desire to go to higher powers and higher throughput. This is not just from a standpoint of the bulk materials and their surface properties, but also optical coatings, he says. One of the aspects Coherent has been focusing on is very high laser-damage coatings for SHG crystals.

‘It’s a horsepower race in the marketplace to increase throughput,’ Loiacono states. ‘To deal with higher laser fluencies we’ve developed a high laser-damage threshold coating for our SHGs, which offer approximately 80J/cm2 at 1,064nm and 25J/cm2 at 532nm.’

Along with performance, price is another important factor. Coherent can now grow crystalline lithium borate (LBO) boules greater than 2kg each. This allows the production of very low-cost components. Recently, Coherent launched a beta-barium borate (BBO) Q-switch using only one BBO crystal. Typically, BBO Q-switches use two 25mm crystals, because the length of material required is too long for most boules. With the ability to grow large crystalline boules, Coherent can produce BBO crystals up to 50mm in length. This improves the overall performance of the Q-switch, explains Loiacono, enabling higher power, higher repetition rates, and much lower loss in the laser cavity, because there aren’t as many surfaces.

One of the advances in nonlinear crystal development is the advent of periodic poling during the 1990s, which improves the nonlinear properties of a crystal through quasi-phase matching. Marlowe at Gooch and Housego says it is important to minimise any imperfections resulting from fabrication techniques so that transmission is limited only by the material’s intrinsic properties. This is especially critical at short wavelengths, where any features or impurities become more significant and have a greater effect on the light passing through. However, Marlowe adds that certain functions of the material can be enhanced: ‘Nonlinear crystals that have a very short coherence length, like lithium niobate, can be quasi-phase-matched through periodic poling. Periodic poling is used in order to gain higher conversion efficiencies for a lower intensity input in a particular wavelength range.’

SHG in reverse

The advances made in nonlinear optics fabrication have aided work into quantum mechanics using entangled photons. ‘We’re benefitting from the developments in optical components over the last few years,’ notes Dr Abouraddy.

In the mid-1980s, physicists started to recognise that parametric fluorescence, which is the noise in parametric interactions in nonlinear crystals like BBO and lithium niobate, is due to quantum interactions and is nothing more than entangled photon pairs, says Dr Abouraddy. ‘If one could use that noise, then this work becomes accessible on any optical table,’ he says. Leonard Mandel at the University of Rochester, for instance, carried out experiments using this source of entangled photons that are landmarks in quantum optics. ‘Any time a new idea comes up in second harmonic generation it benefits this field when operated in reverse,’ Dr Abouraddy comments. ‘Periodically poled crystals made a big impact; then chirped periodically poled crystals, which have been shown to create the widest bandwidth of entangled photons to date; and now periodically poled nonlinear waveguides are becoming a new topic of research.’

Second harmonic generation operates by combining two photons to generate a single photon at a shorter wavelength, with the energies of the two input photons adding up to the energy of the generated one. This is called phase matching, whereby the energy and momentum of the incoming photons match those of the generated photons. Spontaneous parametric down-conversion, the process used to generate entangled photons, is the opposite process – i.e. a single UV photon breaks into two longer wavelength photons under the same phase-matching conditions.

‘Using these photon pairs we can do some extremely dramatic experiments,’ states Dr Abouraddy. The area that has been commercialised to some extent is that of quantum cryptography for secure information transmission. There are a couple of companies commercialising this in the US and Europe, according to Dr Abouraddy, and some banks are already using it.

Quantum cryptography was developed to counter the threat of quantum computation, which potentially has the power to break all existing codes used for secure communication. These codes are based on factoring large numbers, and currently there isn’t an efficient way of doing this. A quantum computer, on the other hand, would be able to do it very efficiently. ‘That created a big scare and led to the development of a better way of transmitting data securely,’ explains Dr Abouraddy.

Quantum cryptography is the only scheme that is absolutely secure. ‘It’s not based on mathematical complexity; it’s based on the properties of single photons, which are very sensitive to tampering,’ says Dr Abouraddy. ‘It’s not that it codes it in a complicated way, because any mathematical code, eventually, can be broken. Instead, quantum cryptography is a way of transmitting information physically with a guarantee that nobody has tampered with it. The very foundations of quantum mechanics guarantee it!’

The work into quantum cryptography and quantum mechanics in general relies, in part, on the developments being made in nonlinear crystals. While physicists may not be able to fathom all the implications thrown up by quantum physics, the research using entangled photons generated by nonlinear optics is yielding interesting results.

Silicon photonics

Advances in electronics, in being able to shrink circuitry down to nanometre scales, have revolutionised the speed of today’s computing and communications. The next revolution, according to Professor Larry Dalton, director of the National Science Foundation’s Center on Materials and Devices for Information Technology Research, will come in the form of integrating photonics and electronics on the same chip.

Chip-scale electronic-photonic integration promises much in terms of increased speed of optical communications. This is, in part, down to developments in organic nonlinear optical materials, of which new polymers provide extremely fast response times and are well suited as high-speed electro-optic modulators and switches.

‘Organic materials are very light and have superfast response times, because of the nature of their electrons,’ explains Dalton. ‘If you apply an electric field to an organic material the electrons respond in about 10fs. That means you have an inherent device-operational bandwidth of hundreds of terahertz – that’s roughly a million times faster than we currently operate. You can convert electrical signals to optical signals very quickly at hundreds of terabits of information per second.’

Professor Dalton’s research group in the Department of Chemistry at the University of Washington has been developing novel organic electro-optic materials, as well as nanoscale structuring methods. An electro-optic modulator is used to convert electrical information into optical signals in an optical fibre. Current modulators are based on inorganic materials like lithium niobate, which modulate their refractive index in response to an electric field.

Lithium niobate’s electro-optic effect comes from moving ions, which are heavy and therefore slower to move around. The crystal also doesn’t bond well with silicon. Polymers, on the other hand, are very compatible with a diverse range of materials and bond well.

‘In the past we’ve been working at slow speeds – megahertz or even kilohertz. There hasn’t been much of a driving force to have gigahertz or terahertz range bandwidth,’ notes Dalton. However, he adds that now there is a growing demand for gigahertz and terahertz bandwidths with the proliferation of the internet and increased communication.

The need for higher bandwidth in turn drives electronic-photonic integration onboard silicon chips. ‘Electrons can’t carry information for long distances without loss, and as we go to higher speeds and more information the problem becomes worse for shorter distances. This is why we really want to carry information by photons, even over only a few inches,’ explains Dalton.

One of the reasons why organic electro-optic materials are particularly well suited to integration on silicon chips is their low power dissipation. ‘With photonics there is the same type of problem that you have with electronics, namely you can’t have any type of heat generation,’ says Dalton. ‘Therefore, we have to have devices that use very little power and the big breakthrough for organic electro-optics is that the electro-optic coefficients are so high that the drive voltage requirements are low and we’re not generating any power. In fact, we can operate these at liquid helium temperatures.’

Organic materials are also light and can be processed easily. ‘They flow, and they can be prepared by vapour phase deposition, by solution deposition, circuits can be fabricated by nanoimprinting and soft lithography,’ Dalton says.

In addition, compared to inorganic materials like gallium arsenide and indium phosphide, organic materials are non-toxic and much cheaper.

‘The biggest aspect that has held back silicon photonics in the commercial sector up until now is market demand,’ states Dalton. At the moment, the main market for organic electro optics is in the defence sector. Companies like Intel, Boeing, and IBM are also now starting to develop projects in this area. ‘The event will occur when a portable computer is released with an integrated photonic-electronic chip that gives you millions of times more capability than you have right now,’ he says. ‘But generating that chip is not trivial.’

US company Lumera, now part of Gigoptix, is one of the few companies commercially producing modulators using organic electro-optic materials. Silicon photonics and organic optoelectronics are relatively young technologies, Dalton says. ‘It’s probably going to be another 10 years or so before the point where these technologies drive out other established devices. Silicon photonics and organic electro-optics are probably the dominant technologies of the future, just because of all the advantages they have, but it’s going to be a slow integration process.’