# Condensation of Excitons and Polaritons

## Excitons and Polaritons

Excitons are excitations in semiconductors, consisting of a bound electron and hole (missing electron); they may be created by shining light on a semiconductor, exciting an electron to a new excited state; both the electron and the hole corresponding to the old state of the electron can move about independently, but because of electric interactions, the electron is attracted to the hole, and they may form a bound state. In appropriately engineered systems, such as coupled quantum wells — thin layers of differing semiconductor, choosen to trap electrons or holes — excitons can be made relatively stable and have a significant lifetime.

Microcavity polaritons are mixtures of photons (quantised particles of light) and excitons ; this mixing is achieved using mirrors to build a cavity that confines light, and placing a quantum well that confines excitons between these mirrors.

## Condensation

Condensation in this context refers to a phase transition, generally at low temperatures, below which the quantum system behaves coherently; roughly one may think of this as all particles behaving identically; i.e. many particles occupying the same quantum mechanical wavefunction. It is this coherence, resulting from sharing the same wavefunction, that means quantum mechanical effects may become visible on large scales

Examples of such condensates include superconductivity (where there is flow of current without electrical resistance) and superfluidity of liquid Helium (where there is fluid flow without mechanical resistance). Superconductivity and superfluid Helium are however somewhat exceptional as quantum condensates: they are the true equilibrium states of the given material. The last decade has seen an increasing range of other quantum condensates in systems which are not in perfect equilibrium. These include cold dilute gases of alkali atoms and very recently condensates of quasi-particle excitations in semiconductors, microcavity polaritons

Microcavity polaritons can form quantum condensates at much higher temperatures than the cold atomic gases, but are further from equilibrium due to the finite lifetime of the polaritons. While the equilibrium condensate, and the highly non-equilibrium laser have been extensively studied, exploration of systems between these two limits have has only begun recently.

## Non-equilibrium

One particular area of interest is in understanding how the properties of condensates consisting of particles with finite lifetimes differ from these two extreme limits of the Laser and the equilibrium condensate. My work to date has addressed questions about: how correlation functions, studying the coherence between polaritons in different places, are modified; how spatial structure, such as seen in the adjacent figure, becomes modified; and how the conditions required for condensation change.

# Recent articles on polaritons

- Coherently driven microcavity-polaritons and the question of superfluidity Nat. Commun. 9 4062 (2018) (DOI: 10.1038/s41467-018-06436-2)
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators Nat. Commun. 9 3322 (2018) (DOI: 10.1038/s41467-018-05617-3)
- Orientational alignment in cavity quantum electrodynamics Phys. Rev. A 97 053836 (2018) (DOI: 10.1103/PhysRevA.97.053836)
- Exact States and Spectra of Vibrationally Dressed Polaritons ACS Photonics 5 249 (2017) (DOI: 10.1021/acsphotonics.7b00916)
- Raman scattering with strongly coupled vibron-polaritons Phys. Rev. A 94 23843 (2016) (DOI: 10.1103/PhysRevA.94.023843)
- Excitonic spectral features in strongly coupled organic polaritons Phys. Rev. A 93 033840 (2016) (DOI: 10.1103/PhysRevA.93.033840)
- Polariton condensation with saturable molecules dressed by vibrational modes Eur. Lett. 105 47009 (2014) (DOI: 10.1209/0295-5075/105/47009)
- Non-Equilibrium Bose-Einstein Condensation in a Dissipative Environment p. 447 of Quantum Gases Finite Temp. Non-equilibrium Dyn. (2013) Eds. N. P. Proukakis, S. Gardiner, M. J. Davis, and M. H. Szymanska (DOI: 10.1142/9781848168121_0030)
- Universality in Modelling Non-equilibrium Pattern Formation in Polariton Condensates p. 19 of Phys. Quantum Fluids (2013) Eds. A. Bramati and M. Modugno (DOI: 10.1007/978-3-642-37569-9)
- Power-law decay of the spatial correlation function in exciton-polariton condensates Proc. Natl. Acad. Sci. 109 6467 (2012) (DOI: 10.1073/pnas.1107970109)
- Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate Phys. Rev. B 81 235302 (2010) (DOI: 10.1103/PhysRevB.81.235302)
- Polarized polariton condensates and coupled XY models Phys. Rev. B 78 205316 (2008) (DOI: 10.1103/PhysRevB.78.205316)
- Spontaneous Rotating Vortex Lattices in a Pumped Decaying Condensate Phys. Rev. Lett. 100 250401 (2008) (DOI: 10.1103/PhysRevLett.100.250401)