ExcitonExciton--polaritons in semiconductors polaritons in semiconductors and nanostructuresand nanostructures

Lucio Claudio Andreani

Pavia University

Phys. Dept. “A. Volta”

Lucio Claudio Andreani

Dipartimento di Fisica “Alessandro Volta,” Università degli Studi di Pavia, via Bassi 6, 27100 Pavia, Italy

andreani@fisicavolta.unipv.it

in honour of Giuseppe Franco Bassani, Varenna, 27 June 2009

OUTLINE

1. Exciton-polaritons in bulk semiconductors

2. Radiative recombination in bulk and quantum wells

3. Polaritons in planar microcavities

4. Polaritons in photonic crystals

Exciton-photon interaction beyond perturbation theory: exciton-polaritons

Incident photon

Transmitted polariton

Transmitted photon

CdS

stationary exciton-polariton states ⇒ no optical absorption(unless dissipative processes like exciton-phonon interaction are introduced)

Reflected photon

Reflected polariton

Semiclassical theory of polaritons

Transverse waves:

Instantaneous limit: ε(ωT)=∞ ⇒ ωT=ω0

20

22

22

/1

4)(

ωωπβεωε

ω −+== ∞

kc

Longitudinal (unretarded) waves:

Maxwell equations + resonant dielectric polarization

,0)( =Lωε2/1

00

41

+=επβωωL

Longitudinal (unretarded) waves:

UP, LP= upper, lower polariton

LE=longitudinal exciton

ωLT=longitudinal-transverse splitting

ωc=polariton coupling2

LT0ωωω =c

Quantum theory of polaritons:two basic papers, 1958-1960

Polariton propagation and k-vector conservation

Fourier-space picture

q=Kex

Real-space picture

exciton

photon excitonphoton

Wavevector conservation ⇒ interaction between one photon and one exciton

⇒ propagation by exchange of energy between exciton and photon states

The polariton vacuuma reservoir of (virtual) exciton/photon states

0)(21

exp'0 ,

ΣΣ= +−

+kmkllmmlk AAkG =++

21, kk AA photon, exciton creation operators

A. Quattropani, LCA and F. Bassani, Nuovo Cimento D7, 55 (1986)F. Bassani and LCA, in Excited State Spectroscopy in Solids (SIF, 1987, course XCVI)

Dynamically tuning the polariton vacuum: generation of correlated photon pairs via QED phenomena (dynamical Casimir effect)

C. Ciuti, G. Bastard and I. Carusotto, Phys. Rev. B 72, 115303 (2005)

pairs via QED phenomena (dynamical Casimir effect)

Exciton-polariton dispersion in CuCl by nonlinear optical experiments

D. Fröhlich et al., PRL 26, 554 (1971): two-photon absorptionB. Hönerlage et al., PRL 41, 49 (1978): Hyper-Raman scattering

Polariton interference

Reflectance spectrum of a MBE-grown GaAs thin layer in the spectral region of the exciton resonance (left) leads to polariton dispersion (right).

Above the longitudinal frequency: period narrowing ↔ spatial dispersion

Y. Chen, F. Bassani et al., Europhys. Lett. 14, 483 (1991)

1. Exciton-polaritons in bulk semiconductors

2. Radiative recombination in bulk and quantum wells

3. Polaritons in planar microcavities

4. Polaritons in photonic crystals

Bound- and free-exciton (X) luminescence

Low-T photoluminescence spectra are dominated by bound exciton: recombination of free exciton is very weak

GaAs

T=2 K

(D0, X)

Sell et al, PRB 7, 4568 (1973)

free X

Polariton distribution is non-thermal:bottlenecking. Exciton luminescenceis actually polariton escape fromsample � inefficient mechanism

Free-exciton luminescence in QWs

(a) Photoluminescence, (b) transmissionand (c) PL excitation spectra of a GaAsMQW sample at T=1.8 K.

The absence of a Stokes shift betweenemission and absorption indicates thatthe photoluminescence is due to freethe photoluminescence is due to freeexcitons in the MQW sample, unlike inthe bulk.

C. Weisbuch et al., Solid State Commun. 37, 219 (1981)

Intrinsic radiative decay of free QW excitons

Bulk exciton:

q=Kex

photon exciton

QW exciton:

photon exciton

q ||=K ||ex

photon exciton

no absorption or decay:polaritons

photon exciton

⇒ perturbation theory, intrinsic radiative decay

A QW exciton with given in-plane wavevector K ||ex interacts with a continuumof photons with wavevectors q=(q ||=K ||ex, qz) � perturbative regime withirreversible decay � intrinsic radiative recombination mechanism.

LCA, F. Tassone, and F. Bassani, Solid State Commun. 77, 641 (1991)

Fast recombination of QW excitons

B. Deveaud et al., PRL 67, 2355 (1991)

Fit to measured data � radiative decay time = 10 ± 4 ps

Much shorter than typical bulk decay time ~ 1 ns!

QW excitons have an intrinsic radiative decay mecha nism

Stationary polaritons in QWs are nonradiative (evanescent):see LCA and F. Bassani, PRB 41, 7536 (1990)

decay time ~ 1 ns!

1. Exciton-polaritons in bulk semiconductors

2. Radiative recombination in bulk and quantum wells

3. Polaritons in planar microcavities

4. Polaritons in photonic crystals

Planar dielectric microcavity: Fabry-Pérot and leaky modes

0.6

0.8

1.0

Ref

lect

ance

15 pairs GaAs/AlAs Distributed Bragg Reflector (n1=3, n2=3.6), normal incidence

0.7 0.8 0.9 1.0 1.1 1.2 1.30.0

0.2

0.4

Ref

lect

ance

Normalized Frequency

The Fabry-Pérot mode is localized within (or close to) the cavity region � quasi-2D photon states

Strong-coupling regime in semiconductor microcavities

Cavity with 7 quantum wells: splitting at resonance

QW

C. Weisbuch et al, PRL 69, 3314 (1992)

The coupling between cavity modeand exciton gives rise to a vacuum-field Rabi splitting (∼5 meV) atresonance and to mixed modes:

cavity polaritons

QW

Cavity-polariton dispersion curvesAngle-resolved PL (resonance at θ=0)

R. Houdré et al., PRL 73, 2043 (1994)

Polaritons in bulk microcavities

A. Tredicucci, F. Bassani et al., PRL 75, 3906 (1995)

Parametric amplification by stimulated scattering of cavity polaritons

P.G. Savvidis, J. Baumberg, M.S. Skolnick et al., PRL 84, 1547 (2000)

Excitation at “magic angle”θ=16.5° results in stimulated(bosonic) scattering into the lower-branch polariton state at k=0 �

strong amplification ofluminescence (� polariton lasing)

Bose-Einstein condensation of exciton-polaritons

in a CdTe/CdMgTe microcavity with 16 quantum wells at 5 K / 19 K

J. Kasprzak et al., Nature 443, 409 (2006)

1. Exciton-polaritons in bulk semiconductors

2. Radiative recombination in bulk and quantum wells

3. Polaritons in planar microcavities

4. Polaritons in photonic crystals

2D PhC slab with embedded QWs

ω

leaky guided

exciton

photon

Quantum-well exciton interacting with photonic modes � possibility of strong-coupling regime or photonic crystal polaritonsPhC polaritons above the light line are leaky (coupled to ext. e.m. wave)

ka

π

Experimental configuration and parametric processes: towards polariton stimulation?

1

2

3

4

(m

eV)

UPPhotonic mode

-20 -10 0 10 20-3

-2

-1

0

1

E-E

ex (

meV

) Angle, θ (deg)

LP

QW exciton

D. Gerace and LCA, Phys. Rev B 75, 235325 (2007)

Photonic crystal polaritons: structure

Sample from LPN-CNRS Marcoussis (J. Bloch and coworkers)

PhC polaritons: experiment (resonant light scattering and PL)

D. Bajoni, M. Galli, J. Bloch et al. (2009)

Exciton and photon dimensionality

Bulk Quantum Well

Microcavity with QW

Photonic crystal slab with QW

Stationary polariton states are formed when the dim ensionality of photon states is equal to (or, possibly, smaller th an) that of excitons

See proc. Int. School of Physics “E. Fermi”, Course CL (2003), p. 105.

exciton=3D photon=3Dstationary

exciton=2D photon=3D

radiative

exciton=2D photon=2Dstationaryexciton=2D

photon=2Dstationary

CONCLUSIONS

• Polariton effects (i.e., strong radiation-matterinteraction) manifest themselves in many differentsituations

• Polaritons are the crossing point of different areas:semiconductor optics, photonics & nonlinear optics,semiconductor optics, photonics & nonlinear optics,Bose-Einstein condensation, correlations…

• Research on exciton-polaritons is more alive than ever