Download presentation

Presentation is loading. Please wait.

Published byAnn Roderick Modified over 4 years ago

1
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

2
OUTLINE Introduction Analytical approaches Results Conclusions

3
Introduction

5
-Photons from a laser create electron-hole pairs or excitons. polariton -The excitons and photons interaction form a new quantum state= polariton. Peter Littlewood SCIENCE VOL 316

6
2 dimensional GaAs-based microcavity structure. Spatial strep trap ( R. Balili, et al. Science 316, 1007 (2007))

8
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

9
- 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.

10
Thomas-Fermi approach Experimentally it is not always the case Analytical approaches

11
Variational method For non-linear differential equation the variational method is not well establish.

12
Gross-Pitaievskii integral equation - Green function Green function formalism

13
-spectral representation -Integral representation -harmonic oscillator wavefunctions

14
Perturbative method It is useful to get simple expressions for μ 0 and Φ 0 through a perturbation approach. ∫|Φ 0 (r)| 2 dr=N

15
Ψ 0 =Φ 0 / √N -small term ∫| Ψ 0 | 2 dr=1

16
-must fulfill the non-linear equation system T is a fourth-range tensor

17
Energy Λ/2

19
The normalized order parameter Ψ 0 H n (z) the Hermite polynomial Ei(z)-the exponential integral; γ-the Euler constant

20
Ψ(r)= Φ(r)/√N r→r/l

21
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±

22
-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 ±

23
Λ 1 =α 1 N + /(2l 2 ћω) Λ 12 =α 2 N - /(2l 2 ћω) η=N + /N - Energies

24
μ + =(E + -Ω))/ ћω =1+0.159*(Λ 1 +Λ 12 )+ 0.0036*F + (Λ 1,Λ 12 ) μ - =(E - +Ω))/ ћω =1+0.159*(Λ 1 / η +Λ 12 η)+ 0.0036*F - (Λ 1 / η, Λ 12 η) F + =(3Λ 1 +2Λ 12 )(Λ 1 /η+ηΛ 12 )+Λ 12 (Λ 1 +Λ 12 ) F - =(3Λ 1 /η+2Λ 12 η)(Λ 1 +Λ 12 )+(Λ 1 /η+ηΛ 12 )Λ 12 η

25
μ + =(E + -Ω))/ ћω μ - =(E - +Ω))/ ћω Λ 1 =α 1 N + /(2l 2 ћω) Λ 12 =α 2 N - /(2l 2 ћω)

26
μ + =1+0.159*(Λ 1 +Λ 12 ) +0.0036*F + (Λ 1,Λ 12 ) μ - =1+0.159* (Λ 1 / η +Λ 12 η)+0.0036* F - (Λ 1, Λ 12 )

27
Order parameter for the two circularly polarized Ψ ± components.

28
Λ 1 =1 Λ 12 =0.4 Ψ ± = Φ ± /√N ± η=N + /N - =1 =0.6 =0.4

29
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

30
Λ versus the detuning parameter δ Typical Values GaAs N~10 5 -10 6

31
-We extended the method to find the ground state of the condensate in a magnetic field

32
-Validity of the method

33
THANKS

Similar presentations

OK

Numerical Method for Computing Ground States of Spin-1 Bose-Einstein Condensates Fong Yin Lim Department of Mathematics and Center for Computational Science.

Numerical Method for Computing Ground States of Spin-1 Bose-Einstein Condensates Fong Yin Lim Department of Mathematics and Center for Computational Science.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google