Bottleneck effects in the relaxation and photoluminescence of microcavity polaritons. F. Tassone, C. Piermarocchi, V. Savona, A. Quattropani and P. Schwendimann in Phys. Rev. B 56:7554 (1997).  What the paper says!?

This text studies theoretically the dynamics of polariton relaxation in a microcavity (they often refer to the bulk which was then still considered an important case).

In the present work, we study the dynamics of microcavity polaritons. Our aim is to understand the fundamental processes underlying the PL, both in station- ary and time-resolved regimes, and to understand the simi-

larities and differences with the bulk system.

They correctly anticipate the highly-dynamical nature of the relaxation due to the exciton-photon composition of the particles:

One of the major issues in the study of optical properties of bulk polaritons has been the description of the photolumi- nescence (PL) process, which is the result of the interplay between radiative recombination and energy relaxation

through the interaction of excitons with phonons.

While they recognize the strongly out-of-equilibrium character—

the simple pic- ture of PL from a thermalized polariton distribution is fun-

damentally incorrect.

—they arrive at conclusions that are in retrospect contrary to the main results of the field as it would later emerge, in particular, they predict stronger emission from the upper branch—

we find that polariton emission mainly originates from the upper branch at low

lattice temperatures.

—and they also consider that the strong-coupling zone is difficult of access, especially the lower branch that is depleted due to a bottleneck effect:

it is quite difficult to populate the polaritons in the strong-

coupling region. This is a bottleneck effect

The bottleneck is a sort of anti-BEC, it prevents polaritons to gather in the ground state but have them pile up instead at finite k. It is «caused by a combination of the slowdown of relaxation [...] and increased radiative recombination rates.» The field would explode precisely due to the effective building up of a condensate there, which is never mentioned despite prior literature on this possibility. They mainly consider low densities, which is the reason for such limitations. In fact, in their Boltzmann equations, they indeed cancel stimulated emission for that reason:

The terms containing (n+1) correspond to stimulated polar- iton emission, and are hereon approximated by unity because

of the low density considered.

This prevents the possibility of condensation. There is otherwise a good coverage of the microscopic details of the relaxation.

The description of the bottleneck effect can be regarded as one of the main results of this text:

We first notice that in a first step of the relaxation, the excitons cool down to the bottom of the excitonlike branch by phonon emission. At this point a bottleneck in further relaxation into

the strong-coupling region is produced

The effective re- combination times in these systems vary by orders of mag- nitude, being very short for photonlike polaritons, and much longer for excitonlike polaritons. When the interaction with phonons is taken into account, the relaxation times due to phonon scattering become much longer for the photonlike polariton than for the excitonlike polariton. This effect is due to the reduced exciton content in the photonlike polariton and to the increased slope of its dispersion. The combination of the increase of radiative rate and decrease of the relaxation rate in passing from the excitonlike to photonlike modes re- sults in a depletion of polaritons in the photonlike region, and in the absence of any further energy relaxation in this region. This overall dynamics of the 3D polariton has thus

2been called a bottleneck dynamics.

The relaxation into the final state is considered to be a single step from the exciton reservoir:

Luminescence from both the upper- and lower-branch results from one-phonon scattering events from

the excitonlike thermally populated reservoir.