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ScienceWise - Jul/Aug 2007

First Observation of 2D Bloch Oscillations

Article Illustration
Left: Optically induced two-dimensional lattice in a biased photorefractive crystal with optically imposed index gradient.
Right: Real and Fourier space of the output beam monitoring different stages of a Bloch oscillations. The white square depicts the first Brillouin zone. The light inside the square is the oscillating part, while the three parts outside are tunnelled radiation. The arrows indicate the direction of the index gradient.

Using wave particle duality to make the first direct observation of a phenomena that underpins all electronic technologies

Some important scientific theories have become established and accepted by indirect observation of phenomena they create, because the underlying fundamental process can’t itself be directly observed. For example planets orbiting distant stars are detected by the star’s wobble not by direct observation of the planet. Whilst undoubtedly of great value to science, such indirect observations are often not just quite as exciting as the first actual photograph of such a planet promises to be. In a similar way the phenomena of Bloch oscillations and Zener tunnelling, theoretically predicted in the 1920s, are now a firmly established part of our understanding of solid state physics despite the fact that until now, no one has been able to directly observe them.

Bloch oscillations are phenomena experienced by electrons moving through a periodic lattice under the action of an external force. A perfect example of this is the flow of an electric current through silicon when a voltage is applied. If the same electrons were flowing through space under the influence of the same voltage they would simply accelerate and gain energy in a uniform manner. However the presence of a regular pattern of potential dips and humps created by atoms of the crystal lattice leads to some interesting phenomena.

There are some energy values the electron can’t have because of resonance with the lattice. These forbidden energies lie within what physicists call band gaps. As the energy of accelerating electrons approaches the gap edge, they are strongly back scattered by the lattice. Such acceleration and back scattering causes electrons to wobble back and forth in space, an effect called Bloch oscillations. Of course if moving electrons are backscattered in this way and just wobble back and forth one might ask how conduction is possible at all? The answer lies in Zener tunnelling. Some electrons are able to quantum tunnel across band gaps, thus enabling overall movement.

Understanding the basic building blocks of solid state physics, including Bloch oscillations and Zener tunnelling, enables us to build computers, mobile phones and every other modern device. Despite this, until now there has been no direct observation of either phenomena because it is impossible to directly observe the motion of individual electrons in a lattice. However, in a collaborative effort between ANU and the University of Jena, a group of researchers have recently become the first scientists in the world to directly observe Bloch oscillations and Zener tunnelling in two dimensional structures by employing nonlinear optics and a bit of lateral thinking.

Essentially their idea was that since you can’t observe electrons in an atomic lattice why not look at photons in an optical lattice? Wave particle duality is one of the basic postulates of quantum mechanics and it tells us that any particle can behave like a wave and visa versa. So the physics and mathematics that describe electrons in a periodic potential are similar to those describing light in an optical potential. However, unlike electrons, it is possible to make direct measurements of both the spatial distribution and momentum of light emerging from a lattice. The latter measurement is vitally important, because the momentum of propagating waves/particles is what governs how they interact with the lattice they are moving through. One of the nice features of optics is that a simple spherical lens produces a Fourier transform of a wave profile forming an image of the momentum distribution of that wave.

The researchers created a two dimensional optical lattice by generating a stationary laser interference pattern in a nonlinear material. The pattern of bright and dark spots modifies the local optical properties of the material inducing a regular series of regions with high and low refractive index. This means that a light beam passing through the material can experience a periodic lattice of a very similar type to that experienced by electrons passing through the regular rows of atoms in a crystal such as silicon. The nonlinear nature of the optical material also enabled the scientists to generate the equivalent of the voltage difference across a crystal needed to generate Bloch oscillations. By superimposing a smooth intensity gradient on the interference pattern used to generate the lattice, they were able to create a refractive index gradient which in effect, accelerates light in a similar way to electrons in a potential difference.

As expected, the results confirm the long established theories of Bloch and Zener. However, they also reveal many interesting and surprising complexities that arise from the lattices of higher dimensions.

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