Light-Matter Correlations in Polariton Condensates 1) Alexey - - PowerPoint PPT Presentation

Light-Matter Correlations in Polariton Condensates

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1) Alexey Kavokin University of Southampton, UK SPIN, CNR, Rome, Italy Alexandra Sheremet Russian Quantum Center, Moscow, Russia Yuriy Rubo Universidad Nacional Autonoma de Mexico, Cuernavaca, Mexico Ivan Shelykh University of Iceland, Reykjavik, Iceland Nanyang University of Singapore, Singapore

• Motivation: experimental work on polariton lasing and BEC of polaritons
• Exciton-polaritons as superposition quantum states of light and matter
• Exciton-Photon (XC) correlators
• Time evolution of the correlators
• Stochastic exciton-photon conversion: interpretation
• Proposed experiments

ICTP, Trieste, August 26th, 2015

Exciton-polariton laser: the concept

A condensate of exciton-polaritons emits light spontaneously No need of the inversion of population! E k

Polariton lasing in CdTe cavities

• M. Richard, …, AK, Experimental evidence

for nonequilibrium Bose condensation of exciton polaritons, Phys. Rev. B 72, 201301 (2005).

• J. Kasprzak et al., Bose-Einstein

condensation of exciton polaritons, Nature, 443, 409 (2006).

Lasers based on bosonic condensates of exciton-polaritons

GaAs, T=40K CdTe, T=50K GaN, T=300K ZnO, T=300K

• E. Wertz et al.,

APL 95, 051108 (2009)

• J. Kasprzak et al.

Nature ,443, 409 (2006)

• J. Kasprzak et al.

PRL ,101, 146404 (2008)

• G. Christmann et al.,

APL 93, 051102 (2008)

• T. Guillet et al, APL 2012

What is an exciton-polariton?

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1)

It is a superposition of a matter quasiparticle (exciton) and a quantum of light (photon)

Exciton-Polaritons: superposition light-matter quasiparticles

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1) What is exciton-polariton? 1) Bohr-Heisenberg: a superposition quantum state. It is neither exciton nor photon until you do the measurement. 2) Einstein-Schroedinger: a chain of emission-absorption acts, it leaves part time as exciton, part time as photon

Do exciton-photon conversions really take place? Difference between weak and strong coupling?

Two Interpretations of Quantum Mechanics

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1) Copenhagen School

Werner Heisenberg Niels Bohr Erwin Schroedinger

Statistical Interpretation

Albert Einstein

• Uncertainty principle
• Collapse of the wave-function
• Matter is real, local and casual
• Wave-function describes real trajectories

Tracing Schroedinger Cats with Exciton-Polaritons

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Bosonic condensates of Exciton-Polaritons: a) Statistical interpretation: b) Copenhagen-school view: Can one experimentally distinguish between these two models?? convert to each other A polariton condensate is a superposition. Its fractions are:

Gedankenexperiment 1

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1) Correlations between photocurrent and photoluminescence noise Statistical: Yes! Copenhagen: No!

Correlators of Interest:

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“Small” exciton-photon correlator “Big” exciton-photon correlator Exciton-exciton coherence: Photon-photon coherence:

Exciton-photon correlators in different models

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1) Copenhagen interpretation: we have polaritons (no excitons, no photons) is formally equivalent to

Text book answers: Coherent state: Number state:

for any polariton statistics!

Thermal state:

The “big” correlator:

(empty upper brunch)

Exciton-photon correlations: XC correlator in the statistical model

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2) Statistical interpretation: no polaritons, excitons convert to photons and backward

Stochastic conversions of excitons to photons and backward are characterised by a time

The probability to find na photons and nb excitons is described by the Boltzmann-master equation: This can be solved assuming some initial condition E.g. a coherent distribution

• r the number state of

N polaritons:

Finite life-time effect:

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The initial condition: a coherent state with 10 polaritons in average In the presence of stochastic exciton-photon conversions In the absence of stochastic exciton-photon conversions

Results of the statistical model:

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Solid lines: coherent initial state Dashed lines: number initial state (10 polaritons) For the “big” correlator dashed and solid coincide: it is independent on the statistics!

Interpretation: the classical limit

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Consider two coupled oscillators with amplitudes A and B

We impose the energy conservation condition If the initial phases of oscillators are random, they are distributed with a function: With this distribution Consequently

= 2/3

Interpretation: the mixing of lower and upper polariton branches

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At t=0 we have all particles at the lower polariton branch The evolution of the energy of the system is given by: At The energy variance per particle is:

Stochastic exciton-photon conversion mixes two polariton branches with a characteristic time Eventually, we achieve the weak coupling regime!

Gedankenexperiment 2 (easier to realise)

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Correlations between upper and lower polariton branches in the Rabi oscillation regime

• J. Berger et al, PRB 54, 1975 (1996)
• N. Kopteva, unpublished, 2015

Polariton Rabi Oscillations

Upper-lower branch correlations: theory

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Results for upper-upper, lower-lower and upper-lower correlators

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Upper-lower correlators strongly go below 1 due to exciton-photon conversions!

Exciton photon correlations: Conclusions

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• Stochastic exciton-photon correlation processes are described

by a “hidden variable”

• If the “Copenhagen” solutions are matched
• If the most interesting regime is hold,

strong deviations of the correlators from the “Copenhagen” prediction are expected

• If the weak coupling regime takes place
• Exciton-photon conversion mixes two polariton branches and

changes the energy of the condensate.

• In the regime of Rabi oscillations, the Upper-Lower correlator is

expected to go below 1 due to stochastic processes

AVK, A.S. Sheremet, I.A. Shelykh, P.G. Lagoudakis and Y.G. Rubo, Exciton-photon correlations in bosonic condensates of exciton-polaritons, Scientific Reports, 5:12020 (2015).