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Quantum Optoelectronics


Semiconductor microcavities are nanostructures that consist of a planar Fabry-Perot cavity with one or more embedded quantum structures (wells, wires, dots etc), sandwiched between two Bragg mirrors. Coupling between the exciton resonance and the cavity mode may lead to either crossing or anticrossing of the real parts of the eigenfrequencies of the structure modes (called exciton – polariton modes). Excitons-polaritons are half light, half matter quasi particles, combining the properties of excitons and photons, they can be interpreted as virtual exciton-photon pairs, whose propagation in the crystal is just a result of multiple virtual absorption and emission processes of photons by the excitons. 

The cavity and the exciton modes in the momentum space anticross in the strong-coupling regime and new eigenstates are formed, which we call them polaritons. Polaritons are mixed cavity photon and exciton bosonic quasiparticles. Due to their photonic component they have 8 orders of magnitude lighter mass than atomic gases and can condense at temperatures as high as the room temperature. Polaritons have two main modes, which are called the upper polarton and the lower polariton mode. The lower polariton mode acts like a trap. However, note that these modes are only in the momentum space (k) and not in the real space!

When weakly interacting Bosonic particles trapped in an external potential are below the temperature of quantum degeneracy they go through a thermodynamic phase transition during which phase correlations spontaneously build up and the system enters a macroscopic coherent state.  The critical density is the density at which the interparticle distances are comparable to their de Broglie wavelength. Under such condition, a large fraction of the particles condense in the lowest quantum state of the external potential and quantum effects become apparent on macroscopic scales. This state of matter is called a Bose-Einstein condensate. For atoms and molecules the cooling is initially done by laser cooling and the particles are then further cooled by evaporative cooling techniques.

We optically pump the cavity using (a usually off-resonant laser) and create an electron-hole plasma in the quantum wells. The electron holes immediately form bound excitons. The excitons cool by exciton-exciton and exciton-phonon relaxations (right panel). Further cooling to the ground state occurs by parametric scatterings (such as in optical parametric oscillators (OPOs)). In the OPO scattering two polaritons collide, with one going to higher energies and the other one falling into the bottom of the trap. Since the polaritons are half photons, they have a very short lifetime (10s of picosecond). But if the cooling process occurs faster than their decay rate, polaritons at the ground state could reach critical densities and a condensate could form at the bottom of the dispersion.

Microcavities are fascinating tools for studying condensed matter physics ranging from fundamental physics such as superfluidity to future possible applications like spinoptronic devices.


"Crossover from photon to exciton-polariton lasing"

We study on a real-time observation of the crossover between photon and exciton-polariton lasing in a semiconductor microcavity. Both lasing phases are observed at di.erent times after a high power excitation pulse. Energy, time and angle resolved measurements allow for the transient characterization of carrier distribution and e.ective temperature. Both in photon and polariton lasing regimes close to equilibrium distributions of the respective quasiparticles are recorded.

Transient dispersion images in false logarithmic color plot

"Spontaneous coherence and symmetry breaking in a polariton and photon laser"

Exciton-polaritons are composite bosons formed due to strong exciton-light coupling in microcavities. Condensates of exciton-polaritons are characterised by a spinor (two-component) order parameter describing their phase and polarisation. The build up of the order parameter leads to the build-up of a vector polarisation of light emitted by the condensate. Here we report on the spontaneous formation of polarisation and coherence in an exciton-polariton condensate in a planar GaAs quantum-well microcavity under pulsed excitation. We have measured the Stokes vector of light emitted by the polariton condensate after each excitation pulse. These single-shot measurements evidenced the build-up of stochastic polarisation with the Stokes vector changing randomly from pulse to pulse. Below threshold the polarisation noise does not exceed 10%, while above threshold we observe a total polarisation of about 50% after each excitation pulse, while the  polarisation averaged over the ensemble of pulses remains nearly zero. The stochastic polarisation build-up is accompanied by the build-up of spatial coherence of the condensate, documented by Michelson interferometry measurements. The formation of a stochastic spinor order parameter of the condensate is observed both in strong and weak-coupling regimes, which indicates a striking similarity between polariton and photon lasers.


2D histogram of linear and diagonal components of the pseudo-spin vector for P < Pth (a) and P = 2.4Pth (b) on the x-y plane of the Stokes sphere. The mean (c,f ), the standard deviation (d,g) and the total degree of polarisation (e,h) for linearly (left panel) and circularly (right panel) polarised pump. Above threshold (marked by a red line) we observe the build-up of total degree of polarisation while the average polarisation remains close to zero for linearly polarised pump. The theoretical simulation is shown in solid blue.

"The Non-linear Optical Spin Hall Effect and Long-Range Spin Transport in Polariton Lasers"

We study the experimental observation of the non-linear analogue of the optical spin Hall e.ffect under highly non-resonant circularly polarized excitation of an exciton polariton condensate in a GaAs/AlGaAs microcavity. The circularly polarized polariton condensates propagate over macroscopic distances while the collective condensate spins coherently precess around an effective magnetic .field in the sample plane performing up to four complete revolutions.


(a) Experimental data (a-c) and numerical simulations (e-g) of the Stokes parameters of the emission of a polariton
condensate non-resonantly excited with circularly polarized laser at 2 . Pthr, sx (a,e) sy (b,f) sz (c,g). (d) Emission intensity on a logarithmic color scale. Below the Pthr the e.ect cannot be observed, due to the broad k-space distribution (h-k).

Relevant recent publications:

Author(s):   E. Kammann, T.C.H. Liew, H. Ohadi, P. Cilibrizzi, P. Tsotsis, Z. Hatzopoulos, P.G. Savvidis, A.V. Kavokin, P.G. Lagoudakis.
Source: Phys. Rev. Lett. 109, 036404 (2012)


Author(s): H. Ohadi, E. Kammann, T.C.H. Liew, K.G. Lagoudakis, A.V. Kavokin, P.G. Lagoudakis
Source: Phys. Rev. Lett. 109, 016404 (2012)


Author(s): H. Ohadi, E. Kammann, T.C.H. Liew, K.G. Lagoudakis, A.V. Kavokin, P.G. Lagoudakis

Source: arXiv (2012)


Author(s): N. Somaschi, L. Mouchliadis, D. Coles, I.E. Perakis, D. G. Lidzey, P.G. Lagoudakis, and P.G. Savvidis
Source: Appl. Phys. Lett. 99, 143303 (2011)

Title: "Optical analogue of the spin Hall effect in a photonic cavity"

Author(s): M. Maragkou, C.E. Richards, T. Ostatnický, A.D. Grundy, J. ajac, M.Hugues, W.Langbein, and P.G.Lagoudakis

Source: Optics Letters, Vol. 36, Issue 7, pp. 1095-1097 (2011)


Title: "Longitudinal optical phonon assisted polariton laser

Author(s): M. Maragkou, A.J.D. Grundy, T. Ostatnický and P.G. Lagoudakis

Source: Appl. Phys. Lett. 97, 111110 (2010)

Title: "Spontaneous non-ground state polariton condensation in pillar microcavities"
Authors: M. Maragkou, A.J.D. Grundy, E. Wertz, A. Lemaitre, I. Sagnes, P. Senellart, J. Bloch and P.G. Lagoudakis
Source: Physical Review B 81, 081307 (R)
 (2010) Rapid Comm.