Presentation on theme: "POLARITON CONDENSATION IN TRAP MICROCAVITIES: AN ANALYTICAL APPROACH C. Trallero-Giner, A. V. Kavokin and T. C. H. Liew Havana University and CINVESTAV-DF."— Presentation transcript:
POLARITON CONDENSATION IN TRAP MICROCAVITIES: AN ANALYTICAL APPROACH C. Trallero-Giner, A. V. Kavokin and T. C. H. Liew Havana University and CINVESTAV-DF University of Southampton Ecole Polytechnique Fédérale de Lausanne
two dimensional Gross-Pitaievskii equation The description of the linearly polarized exciton polariton condensate formed in a lateral trap semiconductor microcavity : α 1 and α 2 – self-interaction parameter ω – trap frequency m – exciton-polariton mass
- Explicit analytical representations for the whole range of the self-interaction parameter α 1 +α 2. The main goal -To show the range of validity.
Thomas-Fermi approach Experimentally it is not always the case Analytical approaches
Variational method For non-linear differential equation the variational method is not well establish.
Gross-Pitaievskii integral equation - Green function Green function formalism
The polaritons have two allowed spin projections If the absence of external magnetic field the ‘‘parallel spins’’ and ‘‘anti-parallel spin’’ states of noninteracting polaritons are degenerate. The effect of a magnetic field To find the order parameter in a magnetic field we start with the spinor GPE: We are in presence of two independent circular polarized states Φ±
-Ω is the magnetic field splitting -two coupled spinor GPEs for the two circularly polarized components Φ ± -α 1 the interaction of excitons with parallel spin -α 2 the interaction of excitons with anti-parallel spin The normalization ∫ |Φ ± |dr = N ± Ψ ± (r)= Φ ± (r)/√N ±
Conclusions -We have provided analytical solution for the exciton-polariton condensate formed in a lateral trap semiconductor microcavity. -An absolute estimation of the accuracy of the method −3 < Λ < 3
Λ versus the detuning parameter δ Typical Values GaAs N~10 5 -10 6
-We extended the method to find the ground state of the condensate in a magnetic field