Doughnuts and pretzels are, in many respects, at two opposite sides of the pastry world: a doughnut is soft and sweet while a pretzel is crunchy and savoury.
However, the most noteworthy difference between a doughnut and a pretzel (at least from the point of view of a mathematician) has nothing to do with the taste: a doughnut is pierced by just one hole while a pretzel by three holes.
The number of holes is a simple example of a so-called topological invariant, a property that changes in discrete steps. (Obviously, we can drill or fill in a whole hole, not half a hole.) So what has all of this to do with this year’s physics Nobel prize?
David J. Thouless from Washington University, Seattle, F. Duncan M. Haldane from Princeton University, and J. Michael Kosterlitz from Brown University, Providence, this year’s Nobel laureates in physics, have shed light on the role of topology in the framework of so-called phase transitions.
A phase transition is a qualitative change of the properties of matter that occurs as a result of the change of some external condition. An example from our everyday life is the transformation of water into ice or, more generally, the transition from the liquid to the solid phase.
Often phase transitions are accompanied by the breaking of a symmetry. For example, the translational symmetry is present when all points in space are on equal footing in the liquid phase, while it is broken in a solid where the atoms sit only in particular, equally spaced, positions.
In the phase transitions investigated by Thouless, Haldane, and Kosterlitz, no symmetry breaking occurs but rather a topological invariant changes step-wise.
A phase transition of this type occurs when electrons are confined at a flat interface between two materials and are exposed to particularly low temperatures and strong magnetic fields. An electric current injected in a bar-shaped device induces a voltage across the bar (a phenomenon known as the Hall effect). When the Hall resistance (the voltage across the bar divided by the current) is plotted as a function of the magnetic field, a series of plateaus appear. Each plateau corresponds to a different topological phase. The inverse height of the plateaus (expressed in units of the appropriate combination of fundamental constants) is, with a great precision, a whole number... just like the holes of a pastry.
Main 1: (a) A gas of electrons is confined at the interface of two materials. (b) The black arrow indicates the direction of the magnetic field, the right arrow the direction of the injected current. As it is customary for electric diagrams, the voltmeter, used to measure the voltage across the bar, is represented by the letter V in a circle. (c) Hall resistance (the voltage across the bar divided by the current) as a function of a magnetic field measured in units of h/e^2, where h is the Planck constant and e the charge of the electron.
Did you know?
• All the matter that makes up the human race could fit in a sugar cube – atoms are 99.9999999999999 per cent empty space.
• Almost all the universe is missing – current physics predicts that dark matter and dark energy have a 95 per cent effect on the universe’s energy budget.
• The speed of light decreases significantly when it enters a medium; for instance, in glass, light travels at three-quarters its speed in vacuum or empty space.
• In quantum physics, some particles can become entangled, which means that even if they are extremely far away from each other they can affect one another.
For more trivia see: www.um.edu.mt/think
Sound bites
• Quantum internet – We need to be able to detect single photon states efficiently: The internet works by sending information along communication lines between large supercomputer hubs where our searches and clicks are redirected to their final destination. In quantum communications these signals are sent by means of photons. These are elementary massless particles that carry electromagnetic energy from one place to another. Another way of looking at them is that they are the quantum equivalent of light. These particles carry an extremely small amount of energy each. For instance, a regular household light bulb produces roughly one hundred billion billion photons per second.
Now in quantum communication the goal would be to have detectors and emitters on either end that can detect single photons so that each photon would carry part of the information being sent, very much like the internet today, where each segment of a message is sent separately. These detectors have existed for some time now but not in any usable form, that is, they were not efficient or durable enough to be used in real networks. Recently a Polish-British team of physicists changed all this and actually built a small and efficient device that can measure these small signals reliably. This work opens the door to the possibility of actually building quantum networks and quantum computers that utilise the communication potential of single photon systems. www.sciencedaily.com/releases/2016/11/161122122715.htm
• Quantum memory – How long can quantum memory hold onto information? The other side of the problem with quantum computing is quantum memory. Currently data is stored in computers using hard disks where memory is kept using magnetic fields in different areas of the disk. The other way that memory is stored is by means of very small transistors which store data by one of two electrical settings. Quantum computers, however, would not be able to use this kind of memory storage and would need a quantum memory of some kind.
For a quantum computer to store data it would have to use the weird world of quantum mechanics where a particle can be in a superposition of two states, such as a coin being both heads and tails, but this superposition only lasts for a very short period of time. After this, the data is irrevocably lost. A team at the Technical University (TU) of Vienna has made an important step forward in preserving this data for up to 10 times the previous current time. In collaboration with a team of Japanese researchers they are using microwaves to set the state of only a few specific atoms in a memory unit. In their case they are interested in nitrogen crystals, where they set the state of some nitrogen atoms. This change then propagate to the remainder of the atoms, thus preserving the data for a much longer time. www.sciencedaily.com/releases/2016/11/161123090708.htm