One of the fundamental rules of quantum mechanics dictates that all particles in nature are either “fermionic”, or “bosonic”. The difference between the two is very important: any two fermionic particles are not allowed to occupy the same quantum state, in contrast to bosonic particles, which may occupy the same state, irrespective of their number. As a result, matter is usually associated with fermionic particles, while radiation and the carriers of forces are associated with bosonic particles.

Clearly this classification is in the heart of quantum mechanics. While the behaviour of fermionic particles is easy to confirm, the behaviour of bosonic particles has proven more difficult to probe. Einstein predicted already in the 1920s that an ideal gas of bosonic particles may undergo a phase transition to a phase in which a macroscopic number of such particles occupy a single, coherent quantum state, the so-called Bose-Einstein condensed state. Apart from strongly-interacting systems, like e.g., liquid Helium, the experimental discovery of this phenomenon in more dilute systems had to wait many decades.

In recent years, there has been tremendous progress in achieving this phase transition in two different systems, namely in dilute vapours of atoms and in polaritons in semiconductors. In the field of cold atoms this phase transition to a Bose-Einstein condensed phase was realized in vapours of (bosonic) alkali-metal atoms in 1995. These celebrated experiments clearly marked the beginning of a new era in quantum physics.

Part of the vitality of the field of cold atoms is due to the fact that the systems investigated are very clean, very dilute and very cold. The ability that we have to probe them optically has made possible measurements with a precision difficult to match in other systems. In addition, most of the properties of these gases are tunable externally. For example, one may control the density, the temperature, the external potential – and thus the effective dimensionality – and even the coupling strength between the atoms. Finally, many different species of atoms, each with a variety of internal states, may be used experimentally – a fact that has contributed to the richness of the field.

With regards to semiconductors, new prospects for monolithic semiconductor structures, comprising a “microcavity” with embedded semiconductor material, were put on a firm footing by technological progress in semiconductor growth during the 1980s. The interaction of cavity modes in such a structure with the two-dimensional excitons – the elementary optical excitations in a direct-gap semiconductor quantum well – was shown in 1992 to enter the “strong coupling” regime. Such a system shows a new spectrum of states, the coupled exciton-photon modes, known as “exciton polaritons”. Because the polaritons are bosons, there is an enhanced scattering probability into the lowest-energy state if it is already occupied; very large populations have been shown to develop under appropriate circumstances. The research community is now convinced that these cavity polaritons show true Bose-Einstein condensation, and the condensate has become the subject of research rather than an elusive goal.

Remarkably, the two fields of cold atoms and of exciton polaritons have much in common. The most important link between the two fields is the phenomenon of Bose-Einstein condensation. The macroscopic occupancy of a single quantum state of the system gives rise to fascinating and often counterintuitive effects, which show up in both fields. These include the collection of effects associated with “superfluidity” (quantized vortex states, persistent currents, nonclassical moment of inertia, etc.), collective effects, coherence effects, lasing, nonlinear effects, etc. Interestingly, there are some differences between the two systems, too. Probably the most important is the fact that exciton-polaritons decay, emitting light, and as a result they have to be pumped continuously. Also, the atomic systems require much smaller temperatures than polaritons, as they are many orders of magnitude heavier than polaritons, and thus more “classical”.

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