Dynamical Condensation of Dynamical Condensation of ExExcciton-Polaritonsiton-Polaritons

H. Deng, G. Weihs, R. Huang, C.W. Lai, S. Utsunomiya, G. Roumpos and Y. YamamotoStanford University and National Institute of Informatics

A. Loeffler, S. Hoefling, and A. ForchelTechnische Physik, Universität Wurzburg

International School of Physics “Enrico Fermi”:Quantum Coherence in Solid State Systems

Varenna (Italy) (July 1 - 11, 2008)

Lecture 1Lecture 1：：CoherenceCoherence properties properties

Dynamical Condensation of Dynamical Condensation of ExcitonExciton PolaritonsPolaritons

G. Roumpos, H. Deng, C. W. Lai, S. Utsunomiya, and Y. YamamotoStanford University, National Institute of Informatics

International School of Physics “Enrico Fermi”:Quantum Coherence in Solid State Systems

Varenna (Italy) (July 1 - 11, 2008)

Lecture 2 Lecture 2 ThermodynamicalThermodynamical Properties Properties

Dynamical Condensation of Exciton-Polaritons

kξ=1

-15o 15o

1.613 eV

8 m

eV

kξ=1-15o 15o

1.613 eV

S. Utsunomiya, C.W. Lai, G. Roumpos and Y.YamamotoStanford University, National Institute of Informatics

A. Loeffler, S. Hoefling, and A. ForchelTechnische Physik, Universität Wurzburg

International School of Physics “Enrico Fermi”:Quantum Coherence in Solid State PhysicsVarenna (Italy) July 1 – 11, 2008

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Lecture 3 Lecture 3 BogoliubovBogoliubov excitation and excitation and superfluiditysuperfluidity

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OutlineOutline

Semiconductor Cavity QED in weak and strong coupling regimes Photon laser vs. exciton-polariton condensation Bosonic final state stimulation, matter-wave amplification and laser without inversion

Experimental tricks toward equilibrium BEC: MQW, blue detuning and lateral confinement

Coherence properties of the condensate: Measurement of first order and and second order coherence functions

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DBR

DBR

SQW in λ/2 cavity

Enhanced (conical)spontaneous emission

Enhanced (single lobe)spontaneous emission

Inhibited (single lobe)spontaneous emission

Red detuning (ωc < ωe) Blue detuning (ωc > ωe)On-resonance (ωc = ωe)

Semiconductor Cavity QED Semiconductor Cavity QED −− Controlled Spontaneous Emission Controlled Spontaneous Emission −− Coherence and Quantum Optics VI (Plenum, New York, 1989) p.1249 Coherence and Quantum Optics VI (Plenum, New York, 1989) p.1249

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Exciton-polariton dispersion relation

Rabi splitting (4meV)

ωexc0 = ωph0

E

k //

QW exciton

Lower polariton

Upper polariton

Microcavity photon (mph ~ 10-5 me)

(mexc ~ 10-1 me)

(meff ~ 2 mph)

Ωosc~ 1 THz

Appl. Phys. Lett. 73, 3031 (1998): Temporal oscillation

UP LP

cavity photon → QW exciton → cavity photon

Nine oscillations

C. Weisbuch et al., Phys. Rev. Lett. 69, 3314(1992): Reflection spectrum

Semiconductor Cavity QEDSemiconductor Cavity QED in Strong Coupling Regimein Strong Coupling Regime−− Dressing Dressing ExcitonsExcitons with Cavity Vacuum Field with Cavity Vacuum Field −−

cavity photon QW exciton collective coupling

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Extended phase coherence reinforced by a cavity fieldsuppressed localization, disorder and inhomogeneous broadeningwhich are notorious enemies to exciton BEC.

Light effective mass by dressing with a cavity fieldmpolariton ~ 10-4 mexciton ~ 10-8 matom

Main decay channel = Photon leakage from the cavity with k and E conservation

direct experimental access to polariton energy-momentum dispersion and populationdistribution

higher critical temperaturelower particle density

suppressed Auger recombination and dissociation of excitons

Dynamical Condensation of Dynamical Condensation of Exciton-PolaritonsExciton-Polaritons: Proposal: ProposalPhys. Rev. A 53, 4250 (1996)Phys. Rev. A 53, 4250 (1996)

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Exciton-PolaritonExciton-Polariton Condensation vs. Photon Laser Condensation vs. Photon Laser

phonon emissionpolariton-polariton scattering

external pumping

Eexciton-polariton

dispersion

leakage of cavity photonsvia mirror

crystal ground state k

stimulated emissionof photons

external pumping

E

crystal ground state k

electron-hole pair(Populationinversion)

spontaneouscooling

stimulatedcooling

k = 0 LP

final bosonic mode cavity photon

final bosonic mode

Exciton-Polariton Condensation Photon Laser

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OutlineOutline

Semiconductor Cavity QED in weak and strong coupling regimes Photon laser vs. exciton-polariton condensation Bosonic final state stimulation, matter-wave amplification and laser without inversion

Experimental tricks toward equilibrium BEC: MQW, blue detuning and lateral confinement

Coherence properties of the condensate: Measurement of first order and and second order coherence functions

Bosonic Final State Stimulation in Polariton-Polariton Scattering

6’

leakage from cavity phonon scattering Polariton-polariton scattering

Spontaneousscattering

StimulatedScattering

Observation of Final State Stimulationin Polariton-Polariton Scattering in a GaAs SQW-Microcavity

nexc = 1.5×109 cm-2

1.2

0.54

theory

Theory: Phys. Rev. B59, 10830 (1999) Experiment: Phys. Rev. B 61, R7854 (2000)

Quantitative agreement between experiment and theory.

• Upper-polariton emission decay time ~ 95 ps• bottle-neck polariton decay time ~ 190 ps

Gain=15

BareExcitonk// = 0:LP

Bottleneckeffect

Bottleneck polariton decay rate = 120 ps

Gain decay rate = 60 ps

Phys. Rev. B 65, 165314 (2002)

Observation of Stimulated Scattering Gainin a CdTe DQW-Microcavity

Nexc=3.4x106Gain =23

Nexc=1.6x106Gain =5.4

Nexc = 0.41x106Gain = 0.34

)exp( 2excNconstg !"

Probe (mW/cm2)Circles: 2×104Squares: 900

Rate equationsolutions

2

1exc

Nconstg !"#

Low Gain Regime High Gain Regime

Phys. Rev. B 65, 165314 (2002)Quantitative agreement between theory and experiment.

)1()1(2

lpexlplpexlpnnbnna ++++

exciton-phononscattering

exciton-excitonscattering

lp

lp

lplp ô

nPn

dt

d!=

Phys. Rev. A 53, 4250 (1996) Phys. Rev. B 59, 10830 (1999)

Matter-Wave Amplification of Polaritons in a CdTe DQW-Microcavity

Polariton condensation threshold observed without electronic population inversion Onset of stimulated cooling

Proc. Natl. Acad. Sci., 100, 15318 (2003)

injected exciton density (cm-2)

Quantum degeneracy threshold

polariton condensation

photonlaser

109 1010 1011 1012

10-1

100

101

102

103

polariton laserELP=1.6166 eVphoton laserECAV=1.6477 eV

no inversion inversion

Pola

riton

s pe

r Mod

e at

k||∼

0

Phot

ons

per C

avity

Mod

e at

k||∼

0

PolaritonPolariton Condensation: Laser without Inversion Condensation: Laser without Inversion

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Real Space Distribution (Proc. Natl. Acad. Sci. 100, 15318 (2003)

photon laserfitted spot size: 26 µm

polariton lasersuppressed ‘expansion’

P/Pth = 1.5polariton photon

below thresholdbroad Gaussian

above thresholdsteep central peak

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OutlineOutline

Semiconductor Cavity QED in weak and strong coupling regimes Photon laser vs. exciton-polariton laser Bosonic final state stimulation, matter-wave amplification and laser without inversion

Experimental tricks from non-equilibrium polariton laser to equilibrium polariton BEC: MQW, blue detuning and lateral confinement

Coherence properties of the condensate: Measurement of first order and and second order coherence functions

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Non-Equilibrium Non-Equilibrium PolaritonPolariton Laser vs. Laser vs.Thermal Equilibrium Thermal Equilibrium PolaritonPolariton BEC BEC

Decisive parameter: Polariton decay rate vs. cooling rate

Non-equilibrium Quasi-equilibrium Thermal equilibrium

t0< tpolariton Tlattice

tpolariton< tlattice < t0Tpolariton = Tlattice

( BEC)

polariton-phonon scatteringlifetime τlattice

phonon phonon

k//

equilibrium is establishedwith a lattice

polariton-polariton scatteringlifetime τpolariton

k//

equilibrium is establishedwithin polaritons

polariton lifetime τ0

k//

polariton decay by leakageof photonic component

leakageof photon

Quantum Degeneracy (n0>1) under Three Conditions

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Experimental Tricks toward Thermal Equilibrium BECExperimental Tricks toward Thermal Equilibrium BEC

Problem1. k=0 polariton lifetime < cooling time

Cavity resonant energy > QW exciton energy(blue detuning

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Signatures of Bose-Einstein CondensationSignatures of Bose-Einstein Condensation- Experimentalist- Experimentalist’’s Wish List -s Wish List -

　Sudden decrease in momentum distribution and E-k dispersion　Sudden decrease in position distribution　Minimum uncertainty wave packet　Spatial coherence (Off-diagonal long range order) and HBT correlation (bosonic final state stimulation and excess noise)

Condensate: Lecture 1

　Bose-Einstein distribution → quantum degeneracy condition equilibrium temperature with lattice

Bogoliubov excitation spectrum

Excitations: Lecture 2 and 3

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OutlineOutline

Semiconductor Cavity QED in weak and strong coupling regimes Photon laser vs. exciton-polariton laser Bosonic final state stimulation, matter-wave amplification and laser without inversion

Experimental tricks from non-equilibrium polariton laser to equilibrium polariton BEC: MQW, blue detuning and lateral confinement

Coherence properties of the condensate: Measurement of the first order and and second order coherence functions

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CryostatCryostat(4K)(4K)

Ti:SiOTi:SiO22 laser laser(pulse)(pulse)

CCD /CCD /Spectrometer (77K)Spectrometer (77K)

red : Near Field imaging / blue : Far Field imagingfocal length

Experimental SetupExperimental Setup

Momentum Distribution (Momentum Distribution (ΔΔkx,kx,ΔΔkyky) of a) of aPolaritonPolariton Condensate in a Free Space Condensate in a Free Space

50 ×50 degrees(Δk=7.5 ×104 cm-1)

~ThresholdBelow Threshold

Condensate aspect ratio~1:2 (anisotropic) Heisenberg limit

Thermal Polaritons aspect ratio~1:1 (isotropic)

+25º

-25º

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Spatial Distribution (Spatial Distribution (ΔΔx, x, ΔΔy) of a y) of a polaritonpolaritonCondensate in a Free SpaceCondensate in a Free Space

(120 µm×60 µm)Pump laser incident angle 60º aspect ratio=2:1

~ThresholdBelow Threshold

Δx: 120 µm 23

Dispersion Characteristics (E vs. k) of a Dispersion Characteristics (E vs. k) of a PolaritonPolariton Condensate Condensatein a Free Spacein a Free Space

Vertical: 6.1 meVHorizontal: 50 degrees

Below Threshold780nm

777nm

~Threshold

ΔθY: 50 degrees (ΔkY≈7.5×104 cm-4)

condensation blue shift due to repulsive interaction (propotional to the number of LP)

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Photon field amplitudeλ/

2 A

lAs

cavi

ty0 1 1.50.5 0 1 2

AlGaAsTi / Au

3 st

acks

of 4

GaA

s Q

Ws

DBR

DBRGaAs Substrate　　

AlAs

SEM image of microcavity

Device configuration Photon field in the cavitySurface image

detuning

(+- 2.5meV)

size of traps

(4-100µm)

• Normal mode splitting 2g~14meV (g=g0 x (NQW)1/2=7meV) with 12 (3stacks x 4QWs) QWs

• Potential modulation ~200µeV

Distribution of polaritons in z-direction toavoid the melting of excitons and allow highpolariton density in area.

Depositing thin metal film modulates the photonfield in the cavity.

30nm

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Further Trick: Lateral Confinement of Further Trick: Lateral Confinement of Exciton-PolaritonsExciton-Polaritons

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27

Minimum Uncertainty Wave Packet- Position Uncertainty Δx, Momentum Uncertainty Δk and Δx Δk Product -

Δk

(104

cm

-1)

0.6

0.4

0.2

86420

5.0

4.0

3.0

2.0

P/Pth

Δx

(µm

)

20µm

0.3Pth Pth 2.5Pth

numerical results based onGross-Pitaevskii equation

Nature Physics (in press, 2008)

ΔkΔx

ΔxΔk=0.98(comparable to theHeisenberg limit of 0.5)

Δx, Δk and ΔxΔkincrease with P/Pth dueto polariton-polaritonrepulsive interaction

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Off Diagonal Long Range Order (Spatial Coherence)Off Diagonal Long Range Order (Spatial Coherence)Phys. Rev. Phys. Rev. LettLett. 99, 126403 (2007). 99, 126403 (2007)

Interference Pattern through Young’s Double Slit Interferometer

Above the threshold Below the threshold

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Macroscopic Spatial Coherence over Whole CondensateMacroscopic Spatial Coherence over Whole Condensate Nature 450, 529 (2007)Nature 450, 529 (2007)

screendouble slit

polaritonwavefunction

x

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HanburyHanbury - Brown and - Brown and TwissTwiss Correlation Correlation –– Bunching Effect - Bunching Effect - Science 298, 199 (2002)Science 298, 199 (2002)

single-mode coherentstate

single-mode thermal state

21

21

2)()(

)()()()(

)2()()(

)(ˆ)(ˆ

)(ˆ)(ˆ)(ˆ)(ˆ

)(nn

jinin

tEtE

tEtEtEtEg i

+=

++=

+!

++!! """

delay τmeasurementwindow

intensity correlation

P/Pth 1 above threshold suggests the excess intensity noise in the condensate.

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-0.3 -0.2 -0.1 0.0 0.1 0.2 0.31.0

1.2

1.4

1.6

1.8

g2(!

=0, k1=

0, k2="k)

"k (µm-1)

pinhole diameter

1 10 1001.0

1.2

1.4

1.6

1.8

2.0

g2(!

=0,

k1=

0,

k2=

0)

Pump Power (mW)

Pth=3mW

(a) (c)

object aperture

pinholes

k1

k2

BS

(b)

(d)

kX

kY

k1 or k2 plane

pinhole

r-space k-space

-1.0 -0.5 0.0 0.5 1.01.0

1.2

1.4

1.6

pinhole diameter

g2(!

=0, k1=

0, k2="k)

"k (µm-1)

HHBT Correlation:BT Correlation:Position and Momentum DependencePosition and Momentum Dependence

ConclusionConclusion

Bosonic final state stimulation, matter-wave amplification and laserwithout inversion observed in exciton-polariton systems.

Blue detuning and lateral confinement, as well as linearly polarizedpumping, seem to work for reaching the equilibrium BEC.

Sudden decrease in momentum distribution, position distribution andposition-momentum uncertainty product at BEC threshold.

Increase in position uncertainty and constant momentum uncertaintyare well reproduced by the inhomogeneous Gross-Pitaevskii equation.

First order coherence emerges at BEC threshold but decreases withpump rate.

Second order coherence measurement confirms the bosonic finalstate stimulation (photon bunching effect) and also shows the excesspopulation noise in the system.

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