Polariton condensates

A feature rather than a bug

Recent work on Bose–Einstein condensation of short-lived 'quasiparticles' in solid-state systems opens up the new field of non-equilibrium condensates.

When an ensemble of bosons is cooled to low-enough temperatures, a substantial fraction of the particles spontaneously enter a single quantum state. This phenomenon is known as Bose–Einstein condensation (BEC), and the most famous experiments are those involving atomic gases. But the past couple of years has seen a flurry of work on BEC in systems where the condensates consist not of free atoms in a gas, but of so-called quasiparticles in solid-state systems. One class of such quasiparticles is polaritons, which are formed from electronic excitations coupled to photons in a microcavity. A number of BEC-like effects have been observed in this type of system, including a bimodal momentum-space distribution with a narrow peak at zero momentum1,2,3, long-range off-diagonal order2,3, spatial condensation in a macroscopic trap3, spontaneous symmetry breaking4, flow without dispersion5, and a dramatic increase of coherence as measured in first-order and second-order correlation measurements6.

Two papers in this issue now report canonical features of polariton BEC that further strengthen the connections between the BEC of free atoms and the BEC of electronic quasiparticles in solids (Table 1). On page 706, Konstantinos Lagoudakis and colleagues7 present evidence for the existence of quantized vortices in a polariton BEC, whereas Shoko Utsunomiya and co-workers8, writing on page 700, observed a linear Bogoliubov excitation spectrum. Both phenomena are associated with (but not direct tests of) superfluidity in these systems. More importantly, however, they add to a consistent body of work that can build the basis for studying BEC away from thermal equilibrium.

Table 1 Types of condensates. Both trapped atoms and excitonic condensates can also be made strongly interacting by changing various experimental parameters.

A microcavity polariton is a charge-neutral bosonic quasiparticle in a solid. Don't be hung up on the term 'quasiparticle' — to all intents and purposes they are 'real' particles that move freely as a gas. Polaritons have very light mass, about ten thousand times less than a free electron, they interact weakly with each other, like atoms, and they have a finite lifetime (but their total number is approximately conserved during their lifetime). Polaritons live in a two-dimensional plane, where they can move freely for macroscopic distances, and they can be held in a macroscopic harmonic-potential trap in that plane3. Experimental techniques exist that can be used to determine the momentum-space and real-space distribution of the polaritons simultaneously, and there are also methods for looking at long-range coherence and various statisticalproperties.

At one point, there was debate about whether the polaritons maintain their bosonic character (known as 'strong coupling' between the photon part and the electronic part) at densities high enough to condense, but it is now standard to show that the polaritons remain good bosons in the strong-coupling regime when the above-mentioned effects occur, including the spatial condensation. When the strong coupling breaks down, the system becomes a standard laser. Recent experiments9,10 demonstrate that polariton BEC and standard lasing can occur as two quite separate transitions at the same place in the same sample, at different densities.

The lifetime of the polaritons in these experiments may seem dauntingly short: a few picoseconds. But the absolute time, of course, is irrelevant; what matters is the ratio of the lifetime to the equilibration time, which is of the order of the particle scattering time. If the lifetime is long compared with the equilibration time, it is proper to treat the system as being in equilibrium11. In the case of polaritons, at low density the picosecond lifetime is short compared with the time of equilibration via phonon emission and absorption. As the polariton density is increased, however, polariton–polariton scattering becomes more important, and can become short compared with the lifetime. It never seems to become less than a factor of five or so below the lifetime, however. When the polaritons condense, a new radiative channel of coherent, laser-like photon emission is opened up. Raising the polariton density just increases this coherent emission, and eventually destroys the condensate by an effect known as phase-space filling.

As a result, the momentum distribution measured in the experiments never fits an equilibrium Bose–Einstein distribution. Instead there are three regions of momentum space: a higher-energy 'reservoir' of excitons (which are similar to polaritons, but with much longer lifetime and much heavier mass, on the order of the electron mass); the low-energy polariton states; and a 'bottleneck' region in between. Each of the three regions has a different characteristic temperature. Numerical models12,13,14 show that Bose statistics of the particles have an important role in the build-up of the condensate, but the constant inflow of hot polaritons prevents equilibration of the low-energy polaritons with particles in higher energy states.

Is the polariton system therefore uninteresting, because it has incomplete equilibrium? As the classic sales phrase has it, “it's not a bug, it's a feature”. Weakly interacting condensates in equilibrium are now thoroughly understood. Much atom-trapping work has turned to non-condensates and fermionic systems. In excitonic and polaritonic condensates, a new knob can be turned, which is the lifetime of the particles. The surprising thing is that despite the incomplete equilibrium, so many of the canonical telltales of condensation can still be observed in polaritonic condensates. But what, exactly, determines the point of breakdown, when we can no longer speak of a condensate because the lifetime is too short? Which properties of a condensate are robust against non-equilibrium perturbations? These questions can be asked very generally in regard to any system of bosons, but polaritons provide a test bed for experimental investigations.

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Snoke, D. A feature rather than a bug. Nature Phys 4, 673 (2008). https://doi.org/10.1038/nphys1064

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