Photons can have half-integer values of angular momentum when they are confined to fewer than three dimensions. That is the conclusion of physicists in Ireland, who have revived an experiment first done in the 1830s to show that photons are not limited to having just integer values of angular momentum. The discovery could have applications in quantum computing and could also boost the capacity of optical-fibre data transmission.

The angular momentum of light comes in two varieties: spin and orbital. Spin is associated with optical polarization, which is the orientation of light’s electric-field oscillations. Orbital angular momentum rotates a light beam’s wavefront around its propagation axis, giving it a corkscrew shape.

Individually, the two types of angular momentum come in multiples of the reduced Planck’s constant, ħ. For spin, those multiples are either +1 or –1, while the orbital variety can take any integer value. To date, physicists have assumed that a photon’s total angular momentum is simply the sum of these two parts and that it therefore comes in integer multiples of ħ. But in the latest research, Paul Eastham of Trinity College Dublin and colleagues have shown that the total angular momentum can in fact take on half-integer values.

Hollow cylinders

Inspiration for the work, says Eastham, came from celebrations of the 200th anniversary of the birth of Irish mathematician William Hamilton in 2005. Hamilton and physicist Humphrey Lloyd showed, in the 1830s, that a beam of light passing through a “biaxial” crystal takes on the shape of a hollow cylinder. The void at its centre is now known to be caused by the light acquiring orbital angular momentum. The bicentennial prompted renewed interest in this effect among physicists in Ireland, says Eastham, who joined Trinity College in 2009 and then started to think about exactly how such beams behave quantum-mechanically.

Eastham drew on work from the early 1980s regarding matter particles confined to two dimensions, in particular Frank Wilczek’s prediction that electrons travelling on a plane around a magnetic flux could have non-integer angular momentum. Eastham and colleagues Kyle Ballantine and John Donegan realized that a similar effect could occur within a beam of light having spin and orbital momentum. Given that Maxwell’s equations require rotational symmetry in three dimensions for the normal summing of a photon’s angular momentum, and noting that the symmetry of a beam in a biaxial crystal is limited to rotation about its axis of propagation, they worked out that the beam’s photons should have half-integer angular momentum.

Topological defects

“The vortex of a beam with orbital angular momentum is a topological defect; it is a knot that you can’t untie,” he says. “We realized it is possible to make beams with a more complicated topological defect, where both phase and polarization vary across the beam.”

To demonstrate light’s fractional angular momentum experimentally, the team shone a laser beam through a biaxial crystal preceded by a polarizer and then split the beam inside an interferometer. Employing a technique devised by Miles Padgett at the University of Glasgow in the UK, they rotated the beam in one arm of the interferometer before recombining it with the (un-rotated) beam travelling through the other arm, and then measured the output.

To analyse the beam’s total angular momentum, the researchers rotated the orbital and spin components by different amounts: 180° and 90°, respectively. This enabled them to sort photons into two groups with half-integer values: those having +ħ/2 and others having –ħ/2. To make sure individual photons had angular momentum of ħ/2 – rather than half of them carrying ħ and the other half zero – they measured the beam’s “shot noise”. This noise will be lower if the quantum of angular momentum flow is smaller, which is what they observed.

Quantum computing

“In my undergraduate physics lectures I learnt that light has integer angular momentum, but we have now shown that it doesn’t have to,” says Eastham, who adds that he hopes the research will encourage others to “look more at the implications of low dimensions in optics”. He also points, somewhat tentatively, to possible applications of the work, including an optical analogue of “topological” quantum computing and a new way of exploiting angular momentum to increase bandwidth in optical-fibre communications.

Michael Berry of the University of Bristol describes the demonstration as “a new wrinkle on the old subject of the angular momentum of light, supported by a clever experiment”. Padgett says that the Trinity group has provided a “lovely treatment of light transmission through biaxial crystals, particularly as regards the angular momentum content of the light”. However, he adds that it is not clear whether the new findings could be applied to fibre-based communications.

The research is published in Science Advances.