# Polariton BEC

Semiconductor microcavities provide an excellent playground for studying condensation in a dissipative environment. Strong interactions between conﬁned photons and quantum-well excitons lead to new quasi particles called microcavity polaritons which can be studied via far- and near-ﬁeld techniques, and their interaction properties manipulated externally by changing both the pump power and the energy detuning between photons and excitons.

Microcavity polaritons, being made from fermionic particles and photons, have several special features. Due to the large wavelength of their photonic component and non-linearities associated with their under-lying fermionic structure the physics exits the regime of weakly interacting bosons at even modest density. Polaritons in planar microcavities are two-dimensional (2D) particles which can be trapped either in stress-induced harmonic potentials or in natural traps provided by microcavity disorder.

### Coherence in a 2D polariton condensate

Below the superfluid transition in a 2D condensate we have bound vortex-antivortex pairs and power-law decay of first order spatial coherence g1

Above the transition vortex-antivortex pairs unbind and g1 decays exponentially

How g1 decays in a polariton condensate which is also 2D can be found here:

*Power-law decay of the spatial correlation function in exciton-polariton condensates*

Georgios Roumpos, Michael Lohse, Wolfgang H. Nitsche, Jonathan Keeling, Marzena Hanna Szymańska, Peter B. Littlewood, Andreas Löffler, Sven Höfling, Lukas Worschech, Alfred Forchel, and Yoshihisa Yamamoto

PNAS (2012)

### BEC of Polaritons in CdTe microcavities

First unambiguous demonstration of polariton BEC:

Occupation of different momentum (nearer image) and energy/momentum (further image) states across the condensation transition from left (uncondensed) to right (condensed).

*Phase diagram for condensation of microcavity polaritons: From theory to practice*

F. M. Marchetti, M. H. Szymańska, J. Keeling, J. Kasprzak, R. André, Le Si Dang, P. B. Littlewood

Phys. Rev. B**77**, 235313 (2008)*Coherence properties and luminescence spectra of condensed polaritons in CdTe microcavities*

M. H. Szymańska, F. M. Marchetti, J. Keeling, P. B. Littlewood

Solid State Commun.**144**, 364 (2007)*Bose-Einstein condensation of exciton polaritons*

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, Le Si Dang

Nature**443**, 409 (2006)

### Condensation in nonequilibrium driven-dissipative system: laser-BCS-BEC crossover

*Keldysh Green’s function approach to coherence in a non-equilibrium steady state: connecting Bose-Einstein condensation and lasing*

J. Keeling, M. H. Szymańska, P. B. Littlewood

chapter in*Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures*

Springer-Verlag, ISBN: 978-3-642-12490-7, arXiv:1001.3338 (2010)*Mean field theory and fluctuation spectrum of a pumped, decaying Bose-Fermi system across the quantum condensation transition*

M. H. Szymańska, J. Keeling, P. B. Littlewood

Phys. Rev. B**75**, 195331 (2007)*Non-equilibrium quantum condensation in an incoherently pumped dissipative system*

M. H. Szymańska, J. Keeling, P. B. Littlewood

Phys. Rev. Lett.**96**, 230602 (2006)*Polariton condensation and lasing in optical microcavities: The decoherence-driven crossover*

M. H. Szymańska, P. B. Littlewood, B. D. Simons

Phys. Rev. A 68, 013818 (2003)*The crossover between lasing and polariton condensation in optical microcavities*

M. H. Szymańska, P. B. Littlewood

Solid State Commun. 124, 103 (2002)

### Disorder and Polariton BEC

*Absorption, Photoluminescence and Resonant Rayleigh Scattering Probes of Condensed Microcavity Polaritons*

F. M. Marchetti, J. Keeling, M. H. Szymańska, P. B. Littlewood

Phys. Rev. B**76**, 115326 (2007)*Thermodynamics and excitations of condensed polaritons in disordered microcavities*

F. M. Marchetti, J. Keeling, M. H. Szymańska, P. B. Littlewood

Phys. Rev. Lett. 96, 066405 (2006)

### BCS-BEC crossover in microcavities

*BCS-BEC crossover in a system of microcavity polaritons*

J. Keeling, P. R. Eastham, M. H. Szymańska, P. B. Littlewood

Phys. Rev. B 72, 115320 (2005)*Polariton condensation with localized excitons and propagating photons*

J. Keeling, P. R. Eastham, M. H. Szymańska, P. B. Littlewood

Phys. Rev. Lett. 93, 226403 (2004)

### General

*Collective coherence in planar semiconductor microcavities*

J. Keeling, F. M. Marchetti, M. H. Szymańska, P. B. Littlewood

Semicond. Sci. Technol.**22**, R1-R26 (2007)*Condensation and lasing of microcavity polaritons: comparison between two models*

F. M. Marchetti, M. H. Szymańska, P. R. Eastham, B. D. Simons, P. B. Littlewood

Solid State Commun. 134, 111 (2005)*Models of coherent exciton condensation*

P. B. Littlewood, P. R. Eastham, J. Keeling, F. M. Marchetti, B. D. Simons, M. H. Szymańska

J. Phys.: Condens. Matter 16, S3597 (2004)*Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions*

P. R. Eastham, M. H. Szymańska, P. B. Littlewood

Solid State Commun. 127, 117 (2003)**Some remarks on the ground state of the exciton and exciton-polariton system**

P. B. Littlewood, G. J. Brown, P. R. Eastham, M. H. Szymańska

Physica Status Solidi (b) 234, 36 (2002)