###### 8 January 2010

# Physicists discover golden ratio in the quantum realm

##### by Kate Melville

An international team of researchers have for the first time observed a nanoscale symmetry hidden in solid state matter that shows the same attributes as the well known golden ratio from art and architecture. The new discovery appears in the current issue of *Science*.

To reveal the hidden quantum symmetry, the researchers worked with the magnetic material cobalt niobate in "chains" only one atom wide. When applying a magnetic field at right angles to an aligned spin the magnetic chain transforms into a quantum critical state. "The system reaches a quantum uncertain - or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical," explained researcher Prof. Alan Tennant, from the Helmholtz-Zentrum Berlin f�r Materialien und Energie in Germany.

By tuning the system and artificially introducing more quantum uncertainty, the researchers observed that the chain of atoms acts like a nanoscale guitar string. "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618..., which is the golden ratio famous from art and architecture," explained principal author of the paper, Dr. Radu Coldea, from Oxford University.

Dr. Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material," he adds.

The observed resonant states provide a dramatic illustration of the way in which mathematical theories developed for classical physics may find application in nanoscale science. "Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state," noted Prof. Tennant.

Related:

Breakthrough in controlling superposition quantum states

Tantalizing glimpse of macroscopic quantum effects

Quantum "Uncollapse" Muddies Definition Of Reality

Atoms Coaxed Into Quantum "Cat" State

###### Source: Helmholtz Association of German Research Centres