Bose-Einstein Condensation of Exciton-Polaritons

7/28/2019 Bose-Einstein Condensation of Exciton-Polaritons

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Bose-Einstein Condensation of Exciton-Polaritons

D.W. SnokeR. Balili

B. NelsonV. HartwellUniversity of Pittsburgh

L. Pfeiffer

K. WestBell Labs, Lucent Technologies

Supported by the U.S. National Science Foundationunder Grant DMR-0706331.


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Outline

I. Introduction. What is a polariton?Trapping polaritons

Are they really a gas?

II. Review of BEC behavior in traps

III. Polariton BEC vs. Lasing


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Coulomb attraction between electron and hole givesbound state

net lower energy for pair than for free electron and hole states below single-particle gap

Wannier limit: electron and hole form atom like positroniumExcitonic Rydberg: Excitonic radius:

What is an exciton-polariton?

What is an exciton?

=

Ps

2

a = aPs


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valence states

conduction states

General concepts of excitons

quasi number conservation (Cf. proton decay and H atom BEC)

photon emission: weak probe of instantaneous energy and momentum

distribution

incoherentphononemission

crossover: quasiequilibrium BEC nonequilibrium BEC immediate decay


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Cavity Polaritons

cavity photon:E= c kz

2+

k||2=

c (

/ L)

2+

k||2

quantum well exciton:E= Egap bind +

h2N

2

2mr (2L)2+

2k||

2

2mconst. near k||=0

DWS and Littlewood, Physics Today, August 2010.


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Tune Eex(0) to equal Ephot(0):

cavity photon

exciton

Mixing leads to upper polariton (UP) and lower polariton (LP)

upper polariton

lower polariton

LP effective mass ~ 10-4me Lifetime ~ 10-40 ps


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Why do this?

Effective mass of excitons ~ 2me

Effective mass of cavity polaritons ~ 10-4 me

Tc > 100 K for typical polariton densities

= h / 2mkBT comparable to rs ~ n

-1/2 (in 2D)General condition for quantum effects to be important:

Tc ~ 1 K for typical exciton densities

kBTc~

2n2m

Cavity photons alone have this effective mass, but theyare non-interacting.

polariton = photon dressed with mass and hard core repulsion


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How to put a force on polaritons?hydrostatic deformation:

shear deformation:

E=h2

2m2

hydrostatic compression = higher energy

E symmetry changestate splitting


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x (mm)hydrostatic strainshear strain

finite-element analysis of stress

Bending free-standing sample gives hydrostatic expansion:Trapping Polaritons

fit to experimental exciton line positionusing known deformation potentials:


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position

Energy

Excitons moving inside a semiconductor structure

GaAs coupled quantum wellsLifetime ~ 10 s


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Bending free-standing sample gives hydrostatic expansion:Trapping Polaritons

strain

(arb.u

nits)


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Typical waferproperties

Wedge in the layerthickness

Cavity photonshifts in energydue layerthickness

Reflectivity spectrumaround point of strongcoupling

GaAs MBE 70- QWs


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Trapping as stress is increased

false color:luminescencegrayscale:reflectivity

trapincreasing stress

Balili et al., Appl. Phys. Lett. 88, 031110 (2006).


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40 m

Do the polaritons really move?Drift and trapping of polaritons in trap

Images of polariton luminescence

as laser spot is moved

1.608

1.606

1.604

1.602

1.600

Energ

y[meV]


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superfluid at low Tor high density = h / 2mk

BT, rs ~ n

-1/2 (in 2D)

log n

log T

superfluid

normalE

x

trap implies spatialcondensation

General condition for exchange to be important:

II. Review of Bose Condensation Effects

excited thermal particles


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k

Luminescence intensityat k|| =0 vs. pump powerPump: 115 meV excess energycircular polarized

Threshold behavior with incoherent pump:

electron-hole continuum

exciton states

E

k


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Spatial profiles of polariton luminescence


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Unstressed-- weakly coupled

Weakly stressed Resonant-- strongly coupled

Angle-resolved data


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Angle-resolved luminescence spectra

50 W 400 W

600 W 800 W

x p

R. Balili et al., Science 316, 1007 (2007)


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Momentum distribution of polaritons

0.4 mW0.6 mW

0.8 mW

Maxwell-

Boltzmann fitAe-E/kBT

Energy distribution of polaritonsR. Balili et al., Science 316, 1007 (2007)


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+++=

'12

)()](1)][(1)[()(|)(|2)(

'2'121'2'121'11

21

kk

EEEEknknknknkkMt

kn

Tassone,etal,PhysRevB56,7554(1997).

TassoneandYamamoto,PhysRevB59,10830(1999).

Porrasetal.,Phys.Rev.B66,085304(2002).

Haugetal.,PhysRevB72,085301(2005).

SarchiandSavona,SolidStateComm144,371(2007).

Kinetic simulations of polariton equilibration

Include polariton-phonon, polariton-electron, and polariton-

polariton scattering.Our approach: Treat entire lower band (polariton exciton) as

continuum. Iterate time-resolved equations until equilibrium.


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0.001

0.01

0.1

1

10

100

0 2 4 6 8 10 12

Cavity lifetime = 5 psLattice Temperature = 20 K

Polariton-phonon scattering onlyPolariton-polariton scattering without Bose terms and full polariton-phonon scatteringFull polariton-polariton scattering and full polariton-phonon scattering

SimulatedOc

cupation

E-Emin

(meV)

V. Hartwell, Ph.D. thesis (2008)

phonon scatteringtotally inadequate

to populatepolariton states.


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Fits to data for different densities, same scattering cross section

V. Hartwell and DWS, PRB 82, 075307 (2010).


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Other recent experiments: vortices superfluid soliton motion, suppression of scattering spontaneous symmetry breaking (polarization) first- and second-order coherence spatial phase locking onset time of coherence

BEC in microtraps with discrete states Bogoliubov linear branches Polariton superfluidity in wires (recent)

...applications in optical communications (nonlinear modulation,

low-threshold lasing, cw OPO, optical spin-Hall effect, etc.)

...room temperature polaritons possible with organics, GaN


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Spin vortices:

Lagoudakis et al., Science 326, 974 (2009)

Y.G. Rubo, PRL 99, 106401 (2007)

microcavity polaritons are a spin-1, two-state system


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different linear polarizationdue to anisotropic exchangesplitting of exciton states

theory with Pikus-Bir,anisotropic exchange

Splitting of bright exciton states seenin microcavity

2D bosons with two states


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III. Is there a difference between polariton BEC and lasing?

phase space filling weak coupling

coherent light emitted spectral narrowing linear polarization beamlike emission

(Is current emitted from a superconductor different?output = probe of state of matter)

A

valence band

conduction bandlasing


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lasing without inversionnormal laser

stimulated emission

stimulated scattering

radiative coupling

(oscillators can be isolated)

exciton-exciton interactioncoupling

(inversion can be negligible)


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Spatially-resolved spectra

laser spot center

Stress trap, resonant


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Stress trap, resonant

Angle-resolved spectra


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Unstressed, resonant

Angle-resolved spectrum


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Coherent emission shifted by stress

line position vs. stress

purple diamonds: 2.5xthreshold

coherent emissionfollows exciton shift,not cavity photon:exciton states still

coupled to photons

DWS and Littlewood, Physics Today, August 2010.


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Recent: Josephson Junctions of Polariton Condensates

Lagoudakis et al, PRL 105, 120403 (2010)

CdTe: adjacent traps in disordered potential

spatial resolution:no optical interference


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Lagoudakis et al, PRL 105, 120403 (2010)

phase winding


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GaAs: traps in micropillars

Lydie Ferrier, Alberto Amo, Jacqueline Bloch (CNRS), in preparation.


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Conclusions

1. Cavity polaritons really do move from place to place and act as a gas, and can be trapped2. Multiple evidences of Bose-Einstein condensation of exciton-polaritons in a trap in two dimensions3. Two transitions occur in same sample: BEC in strong coupling regime, and lasing in weak coupling4. Many new experiments including Josephson junctionswhich show unique BEC effects


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Vince Hartwell

David Snoke

Zoltan Vrs

Nick Sinclair

Botao Zhang

Bridget Bertoni Ryan Balili

Chuan YangBryan Nelson Jeff Wuenschell

Annie Wang


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Now on sale...

1. Electron bandsmolecular bonding, disorder, k.p theory

2. Semiconductorsband bending, interfaces, excitons, 2DEG

3. Classical waves in anisotropic materials4. Phonons and photons in solids

second quantization

5. Particle interactions in solidselectron-phonon, electron-photon, etc.

6. Introduction to group theoryselection rules, splitting on change of symmetry

7. Opticscomplex dielectric function, polaritons, nonlinear optics

8. Introduction to many-body theoryband-gap renormalization, plasmons, density functional theory9. Coherence and Correlation

T1 and T2 times, dephasing, Berrys phase10. Spin and magnetic systems

Ising model, spin flip processes11. Condensates, Superconductors, and Lasers

Bose-Einstein Condensation of Exciton-Polaritons

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