Dispersion relation of an exciton-polariton quasi-particle BEC using a polymer film.
Dispersion relation of an exciton-polariton quasi-particle BEC using a polymer film.

Phase transitions between solid, liquid, gas and plasma are common to most matter and have been extremely well studied. The existence of another, the so-called fifth state of matter is much less known, although it was predicted in the 1920s by Satyendranath Bose and Albert Einstein. It requires identical particles that follow the Bose-Einstein statistics, i.e. having integer spin. In the phase transition from a dilute gas to such a Bose-Einstein condensate (BEC) atoms and molecules lose their individual character and collectively join the lowest quantum state. The long-range coherence between the particles establishes a macroscopic blob of quantum fluid which can exhibit unique properties like superfluidity, much different to the other states of matter.

As this phase transition stems from the increase in the particles’ deBroglie wavelength with decreasing temperature, it takes place at temperatures on the order of micro-Kelvin where the wavepackets of the particles become large enough to overlap. It required 70 years and the development of novel cooling techniques such as laser cooling and evaporative cooling to reach this regime. In 2001, the Nobel prize was awarded to researchers from JILA in Boulder, CO (USA) and from MIT in Boston, MA (USA) for the creation of BECs using dilute gases of alkali atoms levitated in ultrahigh vacuum chambers by magnetic and optical fields. Subsequently, the field of ultracold atomic gases flourished, bearing out many fascinating ground-breaking experiments that harnessed the unprecedented control and manipulation possibilities of this quantum matter on the macroscopic scale.

Because the critical temperature of a BEC phase is inversely proportional to the particles’ mass, the push for higher transition temperatures and therefore potential applications concentrated on quasi-particles such as excitons (electron-hole pairs), magnons (quantized spin waves) and exciton-polaritons (excitons dressed with a photon inside an optical microcavity). They can have many orders of magnitude lower effective mass than atoms. An important prerequisite is that (at least partial) thermalization of the quasi-particles occurs, i.e. that they can scatter off each other thereby exchange energy and momentum. The trade-off is that these quasi-particles decay after a very short time, for example, picoseconds in the case of exciton-polaritons, which makes such a BEC a quasi-equilibrium phenomenon that requires continuous pumping and strongly limits the coherence time. Nevertheless, especially exciton-polariton BECs are very promising for optical device applications because photons that leak out from the microcavity carry the properties from the BEC to the outside. Hence, the coherence of an exciton-polariton BEC leads to laser-like coherent photon output – the so-called polariton lasing – that can have orders of magnitude lower threshold than conventional lasers which require population inversion.

In 2006, the first exciton-polariton BEC was created at a temperature of 5 K in a CdTe microcavity grown by molecular beam epitaxy [1]. Shortly after, other semiconductor microcavities from GaAs, GaN and ZnO followed, some of them operating even at room temperature. Additionally, polariton lasing has been demonstrated using organic single-crystals in a microcavity [2]. However, only a handful of laboratories world-wide are able to fabricate structures with the required quality of the crystalline thin films. It was only very recently when an exciton-polariton BEC in a non-crystalline system, using a spin-coated conjugated polymer as active layer has been demonstrated [3].

Key signatures of these BECs are the energy and momentum distributions of the exciton-polariton quasi-particles that are described by the Bose-Einstein distributions rather than the classical Maxwell–Boltzmann law. As a result of the stimulated scattering into the condensate state, nonlinear light output versus excitation power is observed. The emission is slightly blue-shifted due to the repulsive polariton–polariton and polariton–exciton interaction. The long-range phase coherence is readily measured as interference fringes when passing the emitted light through a Michelson interferometer. Furthermore, signatures of superfluidity like quantized vortices and solitons can be observed, which show up as distinct phase defects in the interferograms. The polarization of the photons adds another degree of freedom that enables the creation of spinor condensates which support half-quantum vortices.

Since the first exciton-polariton BECs, many fundamental studies of this peculiar solid state quantum fluid have been carried out [4]. The non-equilibrium nature makes it often challenging to exactly match the observations to thermal equilibrium BEC theory but also adds new opportunities to explicitly study this transient regime, which is hardly accessible otherwise. For ultra-fast opto-electronic devices, the short picosecond lifetime might even be an advantage. Yet, in terms of applications the BECs are still in their infancy. With the shift to soft materials that operate at ambient conditions [3] and the first demonstration of an electrically pumped polariton laser [5], things might change. Still, there is a long way to go until we might see very power-efficient polariton lasers or polariton-based optical switches. Nevertheless, these macroscopic quantum fluids already allow us to literally look at quantum mechanics “at work” and are giving us exciting possibilities to peek and poke into a whole world of quantum phenomena.

Further reading

1. J. Kasprzak, et al., Nature, 443 (2006), pp. 409–414

2. S. Kéna-Cohen, S.R. Forrest, Nat. Photonics, 4 (2010), pp. 371–375

3. J.D. Plumhof, et al., Nat. Mater., 13 (2014), pp. 247–252

4. I. Carusotto, C. Ciuti, Rev. Mod. Phys., 85 (2013), pp. 299–366

5. C. Schneider, et al., Nature, 497 (2013), pp. 348–352

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DOI: 10.1016/j.mattod.2014.05.013