A surprising similarity between ultracold gases of "Rydberg atoms" and wireless telecommunications networks has been spotted by mathematicians and physicists at the Eindhoven University of Technology in the Netherlands. Using algorithms designed to boost the performance of certain wireless networks, Jaron Sanders and colleagues have gained insights into why these atoms sometimes form crystalline structures. As the algorithms can also be used to control such structures, ensembles of Rydberg atoms could therefore be created in specific quantum states and used in quantum-information applications. The technique could even one day be used to create quantum-logic gates using Rydberg atoms.

At the centre of the new work is a protocol called "carrier sense multiple access" (CSMA), which involves a collection of nodes – say Wi-Fi base stations – each of which can receive and transmit wireless data. Before a node sends a signal, it uses its receiver to sense whether nearby nodes are also transmitting. If another signal is sensed, the node holds off transmitting until the airwaves are clear – the goal being for the network of nodes to maximize its use of available bandwidth by minimizing interference between nodes.

Blocking the neighbours

Sanders, who is a mathematician, realized that this tendency for a wireless node to switch off when its neighbours are switched on is shared by Rydberg atoms in an ultracold gas. Such atoms are unusual in that they have an electron that has been promoted to a very high-energy state – usually by firing laser light at the gas. This means that the atom can be very easily polarized because its electron is so far from the nucleus. This property changes the energy levels of neighbouring atoms, preventing them from absorbing light and becoming Rydberg atoms themselves. In fact, this "dipole blockade" effect has already been used to create "slow light", while the dipole interactions between Rydberg atoms have been used to create quantum logic gates.

Sanders and colleagues modelled their Rydberg gas as a collection of atoms that are located at fixed positions, which is a reasonable assumption for a gas at microkelvin temperatures. An atom is then placed in a Rydberg state by being made to absorb laser light at two frequencies. The rate at which atoms make the transition is analogous to the rate at which a wireless node turns on. The rate at which Rydberg atoms decay, meanwhile, is analogous to the rate at which a wireless node turns off.

The dipole blockade can be modelled by assuming that all atoms within a certain radius of a Rydberg atom cannot be excited until that Rydberg atom decays. Meanwhile, to simulate the fact that each node in a real wireless network switches on and off at a rate that depends on the precise traffic in that part of the network, the team's model allows the laser intensities to vary within the gas, which affects both the excitation and decay rates.

Crystalline lattices emerge

In their work, the researchers were then able to investigate the behaviour of the Rydberg gas based on their understanding of CSMA networks. They could then calculate the probabilities that specific configurations of Rydberg and non-Rydberg atoms would occur. These calculations revealed that the most probable configurations resemble regular crystalline lattices of Rydberg atoms. Given that experiments have shown that some Rydberg gases do form crystalline structures, the team says that its analysis provides a model for understanding why this occurs in analogy to wireless networks.

Using an algorithm originally designed for maximizing the throughput of a wireless network, Sanders and colleagues also examined how the laser intensities for individual atoms should be configured for a desired structure to emerge. This work is important because it could therefore be used for creating specific structures of Rydberg atoms that could be used as specially prepared quantum states or as quantum logic gates.

Better wireless neworks

Sanders told physicsworld.com that the team is now thinking about how its control algorithm could be implemented in the lab. As well as opening the door to quantum logic gates made from ultracold Rydberg gases, creating these systems in the lab could actually lead to better wireless networks. The reason is that maximizing the performance of CSMA networks is a mathematically difficult problem and Rydberg gases could provide a way of simulating network performance.

The research is described in Physical Review Letters and a preprint is available on arXiv.