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POTENTIAL FOR QUANTUM COMMUNICATIONS. Shortly afterwards it was proposed by Gabriel Molina-Terriza and co-workers at the University of Barcelona that OAM could be used to encode information in much the same way in which spin angular momentum can be used in quantum cryptography to encode information in the form of polarisation (left- and right-hand circular polarisation are the quantum-mechanical spin eigenstates with respective spins of -hbar and +hbar per photon) (Gabriel Molina-Terriza, Juan P. Torres, and Lluis Torner, Management of the Angular Momentum of Light: Preparation of Photons in Multidimensional Vector State of Angular Momentum, Phys. Rev. Lett. 88, 013601 (2002)). But OAM has a big advantage: whereas a single photon has only 2 distinct spin states, it has in principle infinitely many distinct OAM states. Information can be encoded either way (or as different colours), or in both ways simultaneously, thereby multiplying the number of distinguishable states. In principle, a single photon can in this way carry an arbitrarily large amount of information. The only trouble was that no method had been found that could distinguish all these OAM states with good efficiency.
This is where our work comes in.
ORBITAL ANGULAR MOMENTUM SORTER
HISTORY. Together with theoreticians Steve Barnett and Sonja Franke-Arnold from the University of Strathclyde, Jonathan Leach, Johannes Courtial, and Miles Padgett, were investigating quantum-mechanical entanglement of the OAM of down-converted photons (independently from Zeilinger's group). The project was lead by Miles. It became apparent that an efficient way to measure the orbital angular momentum of individual photons with good efficiency would be immensely useful for this work. Amongst other things it would also be of potentially great importance for communications (see above). Miles convinced Johannes that this is an interesting and important problem, who - a few days later - came up with the design of the OAM sorter.
EXPERIMENT. An experimental demonstration was set up which could sort 4 different OAM states (to distinguish more states, the setup would have had to be extended by more interferometers, making the experiment much more difficult - see below). A possible way was identified to demonstrate that our setup can indeed sort single photons: the intensity of light passing through the mode sorter can be lowered to levels corresponding to less than one photon being in each interferometer at any one time (on average). This is sufficient to demonstrate sorting of individual photons - a well-rehearsed argument.
WEI AND XUE'S IMPROVEMENTS Haiqing Wei and Xin Xue (from Gazillion Bits Incorporated, CA, and McGill University, Canada) proposed a simplification of our original OAM sorter. The original OAM sorter treats states with odd values of l just like those with even values, after making their l values even (i.e. make them an integer multiple of 2; similarly, l values are turned into integer multiples of 4, 8, 16, etc. later in the sorting process). Making the odd l values even can be done simply by adding +1 to the l value with a 'spiral phase plate' or equivalent component (like, for example, a hologram of a spiral phase plate). However, this is problematic because in practice such components work with only limited efficiency. Wei and Xue realised that the phase shift due to a rotation of the beam for odd l values differs from that for even l values only by a constant phase. This constant phase can be subtracted simply by introducing an additional phase shift in the other arm of the interferometer, so that an interferometer that sorts even l values can, just by changing the path length in the other arm, be used to sort odd l values.
Wei and Xue also brought to our attention that together with Andrew Kirk from McGill University, Canada, they have also described a method for sorting Hermite-Gaussian (HG) modes which predates our OAM sorter (X. Xue, H. Wei, and A. G. Kirk, Beam analysis by fractional Fourier transform, Opt. Lett. 26, 1746-1748 (2001)). This HG mode sorter and our OAM sorter, although developed independently, are strikingly similar: both setups use a 'tree' of Mach-Zehnder interferometers to sort the incoming light in successive stages, but in one arm of each Mach-Zehnder interferometer the HG mode sorter performs a fractional Fourier transform operation whereas our OAM sorter rotates the beam. In conjunction with a cylindrical-lens mode converter, the HG mode sorter could be used as a Laguerre-Gaussian (LG) mode sorter; as LG modes are in OAM eigenstates, such a device could therefore be used as a single-photon OAM sorter.
There are a number of problems associated with this technology that need to be overcomebefore it becomes practical. One obvious problem is the interferometric stability required in each of the numerous interferometers - in order to distinguish 2N states with our mode sorter, 2N-1 interferometers are required. (Just keeping the 3 interferometers required for distinction of 4 states aligned keeps Jonathan quite busy.) It might be possible to modify the scheme so that 2N states can be distinguished with only N interferometers (all the interferometers in any one of the N stages are identical). A reduction in the size of the setup - which at the moment takes up about 1 square meter of optical table - might help make individual interferometers more stable.
Even if these problems can be solved, orbital angular momentum encoding is unfortunately not compatible with today's optical fibres. The trouble is that optical fibres - at least most fibres in use today and to the best of our knowledge - alter the light's OAM state. For example, it was shown in our group a couple of years ago that a multi-mode fibre, which was 'stressed' in the middle (a piece of weight was resting on it), converted light with no OAM into light with an OAM of 1hbar per photon (D. McGloin, N. B. Simpson, and M. J. Padgett, The transfer of orbital angular momentum from a stressed fibre-optic waveguide to a light beam, Appl. Opt. 37, 469-472 (1998)). Bending of fibres also tends to cause difficulties. All this would suggest that, at the very least, one would have to be very careful when sending OAM-encoded photons over optical fibres. Future work might change this, of course.
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