Localized states in one-dimensional exciton-polariton condensates - - PowerPoint PPT Presentation

Localized states in

• ne-dimensional exciton-polariton condensates

Yan Xue1,2, Michał Kulczykowski1, Nataliya Bobrovska1, Michał Matuszewski1

1Institute of Physics, Polish Academy of Sciences, Warsaw 2College of Physics, Jilin University, Changchun, China

Exciton-Polaritons hole electron photon polariton exciton

• Strong quantum coupling between excitons and photons
• Dressed states of exciton and photons are quasiparticles called polaritons

Exciton-Polaritons

upper polariton lower polariton Semiconductor microcavity

Exciton-Polariton condensation (polariton lasing)

Polaritons are bosons – BEC phase transition can be expected at standard cryogenic temperatures

• r even at room temperature due to a

low effective mass (10-5 electron mass)

T c∼n

2/3

m

Exciton-Polariton condensation

Above threshold pumping power, the ground state becomes massively occupied. The thermal cloud is found to be at 19K. (J. Kasprzak et al., Nature 2006)

Exciton-Polariton condensation in a 1D nanowire

We consider a single isolated nanowire

• J. Bloch et al., Nat. Phys. (2010)

Exciton-Polariton condensation in a 1D nanowire

Mean field approximation + description of the reservoir with a density field Pumping ⇓ Exciton reservoir ⇓ Polariton condensate P(x,t) nR(x,t) ψ(x,t)

Exciton-Polariton condensation in a 1D nanowire

• M. Wouters and I. Carusotto (2007)

Polariton condensate Exciton reservoir

Mean field approximation + description of the reservoir with a density field

i  ψ t =(a+ib) 

2 ψ

 x

2 +(c−id)|ψ| 2 ψ+ie ψ

Sources

What is the difference between a dark soliton and a heteroclinic hole?

Conservative Nonlinear Schrodinger Equation Dissipative Complex Ginzburg-Ladau Equation A dark soliton A heteroclinic hole (source) Tanh-shaped dark soliton solution

• Localized density dip
• Phase “jump” in the middle of the soliton

Bekki-Nozaki hole solution (N. Bekki and K. Nozaki, 1985)

• Localized density dip
• Phase “jump” in the middle of the soliton
• Source of outgoing plane waves

iAt+ Axx−∣A∣

2 A=0

In the limit of vanishing dissipative terms the Bekki-Nozaki solution transforms into the dark soliton.

i  ψ  t =(a+ib) 

2ψ

 x

2 +(c−id)|ψ| 2ψ+ie ψ

• Lifetime of solutions is extremely long compared to all natural timescales
• Eventually, holes decay due to the acceleration instability
• The acceleration is related to the structural instability of CGLE against higher-order

perturbations

• Y. Xue and M. Matuszewski, Phys. Rev. Lett. (2014)

Holes in polariton condensates

Oscillations and explosions Close to the low power stability threshold, the solutions exhibit nontrivial dynamics. Such behaviour is absent in the case of standard complex Ginzburg-Landau equation.

Bright exploding solitons: J. M. Soto-Crespo, N. Akhmediev and A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000)

• Both modes have small growth rates of the order of (1000 ps)-1, which well explains the long period of time

necessary to destabilize the solution

• When the perturbation grows sufficiently large to make the Bogoliubov linearization invalid, the instability

speeds up, leading to abrupt decay of the hole

• The decay is related to the structural instability of CGLE against higher-order perturbations (O. Stiller, S. Popp,
• L. Kramer, Physica D 84, 424, 1995)

Bogoliubov-de Gennes analysis

Spatially modulated pumping A flux of polaritons from areas of stronger pumping to areas of weaker pumping is naturally induced. The solitons are created spontaneously when the flux velocity becomes comparable to the sound velocity. Thus, here the mechanism of hole creation is through the breakdown of superfluidity.

Vortices in the two-dimensional case A vortex can be created from a small seed possessing a quantum of angular momentum. The solution remains stable for a very long evolution time.

• Y. Xue and M. Matuszewski, Phys. Rev. Lett. (2014)

Sinks

Interference vs. sink

Kulczykowski, Bobrovska, Matuszewski, arXiv:1501.07791, to appear in PRB Linear Interference Nonlinear Sink

Sink movement

Kulczykowski, Bobrovska, Matuszewski, arXiv:1501.07791 Equal sources Unequal sources

Spontaneous holes in a nonequilibrium steady state

Result within the truncated Wigner approximation: holes appear spontaneously in the nonequilibrium steady state see also: dark solitons in atomic BECs in thermal equilibrium, T. Karpiuk et al.,

• Phys. Rev. Lett. 109 205302 (2012)

Conclusions

• Mean-field equations of exciton-polariton condensates admit source (hole) and

sink (shock) solutions that have corresponding solutions in the CGLE

• Polariton holes exhibit interesting dynamical properties that are more rich than

those of the CGLE

• Holes (dark solitons) can appear spontaneously in a dynamical steady state

Thank you for your attention!