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Collective Dipole-Dipole Theory

What is collective behaviour?

When light is shone on an atom, if the frequency of the light closely matches the energy difference between two energy levels in the atom, the light can create an electric dipole moment in the atom. This electric dipole radiates more light, which can interfere with the original light to produce a variety of scattering effects, such as reflection and modified refractive index. 

 

 

If there are more atoms nearby, then the light scattered from the first dipole can create more dipoles in the neighbouring atoms, which also radiate light, resulting in a collection of dipoles all scattering light back and forth between themselves. The overall behaviour of the collection can be very different to the behaviour of just a single atom, and so the atoms are said to be behaving collectively.

 

 

The dipole--dipole interaction between two dipoles, due to the scattering of light between them, has some very interesting characteristics. The means the behaviour of these collective ensembles can be incredibly varied:

 

 

The aim of this project is to investigate how arranging atoms in different ways affects this collective behaviour, as well as whether it is possible to tailor this behaviour to realise specific useful phenomena.

 

1D chains

 

The simplest system to consider first is where the atoms are arranged neatly in a one-dimensional (1D) array. The regular spacing between the atoms means the eigenmodes (like the normal modes) of the system are neat and seem to display some obvious patterns.

 

 

We observed that an infinite chain of dipoles can behave in just the same way as a single dipole between two mirrors. This is because a dipole next to a mirror essentially sees a reflection of itself in the mirror and interacts with this effective image dipole just as if it were interacting with a real dipole placed behind the mirror. A dipole between two mirrors sees an infinite chain of image dipoles (similar to the effect of standing between two mirrors and seeing your reflection repeating endless times off into the distance). We are simply replacing the image dipoles with real dipoles, and seeing the same effects.

 

Read more at Phys. Rev. A (2016)

 

Collective EIT

 

The interference between the collective eigenmodes of the atomic ensemble can interfere with each other. This is because, unlike normal modes in a conventional oscillating system, the modes are not orthogonal and so they can overlap with each other. When they overlap, they can produce distinctive asymmetric Fano resonances.

 

This effect can be so strong however that you can create a transparency window in the atomic resonance, which is similar in appearance to conventional Electromagnetically-Induce Transparency (EIT). EIT is due to the quantum interference between the excitation pathways between different energy levels in a single atom. In Collective EIT, the energy levels are now collective energy levels of the atomic ensemble, rather than different energy levels in a single atom. 

 

 

We found particularly good examples of collective EIT can occur in exotic lattices known as kagome lattices

 

Read more at Phys. Rev. A (2015)

 

Atomic mirrors

 

If we put a single atom in the focus of a very tightly focused laser beam, the light scattered by the dipole interferes destructively with the laser light downstream of the atom, meaning the atom is essentially blocking the light from passing it. However, for a single atom this is very difficult because the light must be incredibly tightly focused (to less than a wavelength) or placed in some carefully constructed reflective system such as a giant mirror that bends all the way around it. 

 

 

We can get round this limitation by replacing the single atom with a two-dimensional (2D) lattice of atoms, separated by a little less than a wavelength. Here, the collective behaviour of the dipoles combined with the Bragg diffraction of the lattice means that close to 100% of the light can be blocked, even for a relatively small number of atoms (around 50 can already produce around 98% extinction). 

 

Read more at Phys. Rev. Lett. (2016)

 

Topology

 

By modifying the internal energy levels of the atoms, we can realise non-trivial behaviour known as topological insulators. Recognised by the 2016 Nobel Prize, topological insulators are systems which exhibit insulating behaviour in their bulk (in the centre of the material), whilst allowing conduction around the edge (the amount of conduction is typically quantised). We found that we could recreate this same behaviour in 2D honeycomb lattices simply by adding a B-field to the atoms. An advantage of topological insulators is that the conduction around the edges is relatively robust to defects in the lattice, i.e. if some of the lattice sites are missing an atom, or the atoms are slightly off centre from where they should be, the conduction is still confined to the edges of the lattice. 

 

 

Read more at Phys. Rev. A (2017)

 

Future

 

There are a number of different avenues we are interested in exploring related to collective dipolar behaviour. These include:
 

  • experimental modeling - in the last few years experiments have begun to probe regimes where we would expect to see the kind of collective effects mentioned earlier. A lot of simulations we have done have been motivated by what would be interested to observe in an experiment, and so now the goal is to use the theories we have constructed to produce qualitative and quantitative modeling of experiments. 
     

  • dipoles in other systems - the dipolar behaviour mentioned above is not limited just to atoms but can be realised in many different systems, including quantum dots, polar molecules, ions, metamaterials, plasmonic nanostructures, radio antennae... It will be interesting to see whether the effects we have seen in atoms could be realised also in these other systems.
     

  • combination with quantum technologies - many of these collective effects could be combined with quantum systems to significantly improve their behaviour. For example, the mirror behaviour of the 2D lattices provides a way of very effectively coupling light with an atomic ensemble. The long lifetimes (subradiance) of some of these collective ensembles could be used to realise very long quantum state storage. Understanding and controlling the energy shifts is also important for frequency measurements in optical lattice clocks. 
     

  • more exotic ensembles - the variety of effects already observed in different atomic systems suggests there is still a wealth of different behaviour to be discovered!
     

 

Find out more

Please feel free to contact Rob Bettles if you are interested in discussing or finding out more about any of these (or other) topics.