Jacques Levrat, R. Butté, T. Christian, M. Glauser, E. Feltin, J.-F. Carlin, N.Grandjean,

Institute of Quantum Electronics and Photonics, Ecole Polytechnique Fédérale de Lausanne (Switzerland)

D. Read, A. V. Kavokin

School or Physics and Astronomy, University of Southampton (UK)

Y. G. Rubo

Centro de Investigaticion en Energia, Universidad Nacional Autonoma de México (Mexico)

PINNING AND DEPINNING OF THE POLARIZATION OF EXCITON-POLARITON

CONDENSATES AT ROOM TEMPERATURE

1

Outlines

Introductiono Motivation – Which material ?o Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs)o Emission properties of a GaN-based MC at threshold

Linear polarization behavior - Experimentso Experimental setupo Pinning of the linear polarizationo Power dependence

Linear polarization behavior - Theoryo Effect of magnetic field on the pseudospin evolutiono Modelo Stochastic evolution of the order parametero Model vs experimental datao Detuning dependence of the linear polarization degree

Conclusion and perspectives

2

Outlines

Introductiono Motivation – Which material ?o Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs)o Emission properties of a GaN-based MC at threshold

Linear polarization behavior - Experimentso Experimental setupo Pinning of the linear polarizationo Power dependence

Linear polarization behavior - Theoryo Effect of magnetic field on the pseudospin evolutiono Modelo Stochastic evolution of the order parametero Model vs experimental datao Detuning dependence of the linear polarization degree

Conclusion and perspectives

2

PARAMETERS III-arsenides II-tellurides III-nitrides

Exciton binding energy (meV)

Bulk: ~ 5QWs: ~ 10

Bulk: ~ 11QWs: ~ 22

Bulk: ~ 26QWs: ~ 50

Exciton oscillator strength (cm-2)

~ 5 1012 ~ 2.3 1013 ~ 5.1 1013

Motivation: Which materials ?

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 ~ 50 KT ~ 40 K T ~ 340 K

Efficient coupling to phonons (polar material) Efficient thermalization of hot carriers + limited bottleneck effect

VRS ~ 16 meV VRS ~ 26 meVVRS ~ 56 meV

3

k//

ELPB

k//

ELPB

Condensation phase diagram (,T,Pthr)

pol

rel

(meV)

Kinetic regime(pol <<rel)

Thermodynamic regime(pol >>rel)

Phonon efficiencyPol-pol interaction

Excitonic fraction

Intermediate regime

Thermodynamicsfavored

ThermodynamicsinhibitedTesc

T (K)opt(T)

Kineticregime

Thermodynamicregime

The system must face twoopposite constraints

J. Levrat et al., Phys. Rev. B 81, 125305 (2010)

k//

ELPB

polariton

polariton

phononphonon

4

340

- 120 0

4

0102030

40

50

60

70

80

90

100

-3-2.5

-2-1.5

-1-0.5

0

60

040

/VRS

340300

260220

180140

100

Temperature (K)

Pth

r (W

/cm

2)

Phase diagram (,T,Pthr)

Optimumdetuning

Kineticregime

Thermodynamic regime

Highly stable configurationPOLARIZATIONMEASUREMENTS

POSSIBILITY OF ROOM TEMPERATURE

MEASUREMENTS

R. Butté et al., Phys. Rev. B 80, 233301 (2009)

J. Levrat et al., Phys. Rev. B 81, 125305 (2010)

|X0|2 ~ 20% ~-40 meV

5

PhotonicDisorder

minimized

UV - Fourier spectroscopy

Bottleneck far below threshold Emission thermalized at threshold T = 300 ± 20 K

LASER

sample

ObjectiveNA = 0.55

BS plate UV-enhanced

CCD

f2f1

SIGNAL

J. Levrat et al., accepted for publication in Phys. Rev. Lett 6

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

-15-10

-5051015202530

Energy (eV)

An

gle

(d

egre

e)

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

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-5051015202530

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

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Energy (eV)

An

gle

(d

egre

e)

Polarization measurements at RT

Unpolarized emission Unpolarized emission below thresholdbelow threshold

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

1510

505

Energy (eV)

An

gle

(d

egre

e)

0

30

6090

120

150

180

210

240270

300

330

Angle (degree)

P = 0.98 PthrP = 1.03 Pthr

CX

Linearly polarized Linearly polarized emission above emission above

threshold:threshold:polarization degree >80%polarization degree >80%

max min

max minl

I I

I I

G. Christmann et al., Appl. Phys. Lett. 93, 051102 (2008)

7

Outlines

Introductiono Motivation – Which material ?o Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs)o Emission properties of a GaN-based MC at threshold

Linear polarization behavior - Experimentso Experimental setupo Pinning of the linear polarizationo Power dependence

Linear polarization behavior - Theoryo Effect of magnetic field on the pseudospin evolutiono Modelo Stochastic evolution of the order parametero Model vs experimental datao Detuning dependence of the linear polarization degree

Conclusion and perspectives

8

Polarization measurements at RT

-150 -100 -50 0 50 100 1503.50

3.75

4.00

4.25

4.50

4.75

5.00

UPB

En

erg

y (e

V)

k (m-1)

T = 300 K

VRS

= 56 meV

LPB

Non resonant excitation @ 4.66 eV

k// = 0

= 1°

LASER45°

6°

Tmeas.~ 25 ms500 ps

0.12 ms

Linear polarization averaged over 200realizations of the condensate <l>

MQW MC sample

9

Pinning of polarization at threshold

a-planem-plane

Polarization is pinned along crystal preferential axes (a- and m-planes)

Pinning of the polarization arising from bare mode splitting at k// = 0

Cavity mode Exciton

Local anisotropy due to thickness fluctuations of DBR layers

Local strain ( birefringence)

Lower symmetry of the QW interfaces

Exciton localization on islands of monolayer QW width fluctuations

10

a-plane

m-plane

Evolution of lvs power

<l > rapidly decreases well before reaching nsat

Opposite behavior for a SC laser

Henry et al., IEEE JQE 18, 259 (1982)

Blueshift of the mode < 1 meV

Broadening increase of the modes ~ 150 µeV

Below threshold:

FWHM ~15 meV

J. Levrat et al., accepted for publication in Phys. Rev. Lett 11

Outlines

Introductiono Motivation – Which material ?o Detuning and temperature dependence of polariton condensation threshold of GaN-based microcavities (MCs)o Emission properties of a GaN-based MC at threshold

Linear polarization behavior - Experimentso Experimental setupo Pinning of the linear polarizationo Power dependence

Linear polarization behavior - Theoryo Effect of magnetic field on the pseudospin evolutiono Modelo Stochastic evolution of the order parametero Model vs experimental datao Detuning dependence of the linear polarization degree

Conclusion and perspectives

12

Effect of magnetic field on pseudospin

Sint

LT

leads to beats between circularly polarized components of the photoemission

Arises from in-plane anisotropy

2 2

LT ex phk kk X k C k

Shelykh et al., Semicond. Sci. Technol. 25, 1 (2009)

Arises from anisotropic polariton-polariton interaction

TE-TM splitting of excitonic mode

TE-TM splitting of photonic mode

Intrinsic (LT)

Self-induced (int)

int 1 2 1 1~ V V N N

Shelykh et al., PSS(b) 242, 2271 (2005)

Spin-dependent polariton-polariton interaction

Population imbalance of circular polarization

leads to beats between linearly polarized components of the photoemission

Pseudospin (S)

Accounts for both spin (z) and dipole moment (x-y plane) orientation

Pseudospin changes due to effects of magnetic field and scattering with phonons, polaritons and defects rich and complex dynamics!

Self-inducedLarmor precession

13

Model

* *1 1 1 1

* *1 1 1 1

2 2

1 1

1

2

21

2

x

y

z

S

iS

S

Pinning of the order parameter of BECs: (t) , = ± 1

(2 component complex vector correlated with the Stokes vector of light emitted by polariton

condensates)

Question of interest

W(t)Incoherent

reservoir Nr(t)

( ) 1rr r

dNN t W t n t P t

dt

W(t) : income rate from reservoirNr (t) : reservoir occupation numberr -1 : polariton lifetime in the reservoir n(t) : condensate occupationP(t) : pumping rate

Condensate n(t)

2-level system

In the simplest-case of phonon-assisted relaxation:

( ) rW t r N t

W(t) determines the noise amplitude, responsible for the phase and polarization fluctuations in the condensate

E

k

D. Read et al., Phys. Rev. B 80, 195309 (2009)

14

Stochastic evolution of the order parameter

1( )

2 c

dW t

dt

2 2

1 2

i

1

2 xyi

t

Income rate

Escape ratec

-1 = pol ~ 0.2 ps Splitting betweenx- and y-polarizations

Relaxation parameter << c

Triplet polaritons 1 > 0)

Singlet polaritons 2 < 0)

Shot noise from the income of polaritons in the condensate

2 , , ,

2

i

i

S t dts i x y z

n t dt

n t S t

��������������

Time-integrated components

Once averaged over noise realizations:

<sy> = <sz> = 0<l> = <sx>

(fee energy minimized)

Averaged components

* *1 1 1 1

* *1 1 1 1

2 2

1 1

1

2

21

2

x

y

z

S

iS

S

Pseudospin components

D. Read et al., Phys. Rev. B 80, 195309 (2009)

x

y

15

<sx> ~ 0.8

<sx> ~ 0.4 <sx> ~ 0.18

<sx> ~ 0

Simulations

Far below threshold Weak condensate occupation Effect of disorder not pronounced Polariton-polariton interactions negligible

At threshold Pinning sx = -1 highly pronounced Polariton-polariton interaction negligible

Slightly above threshold Pinning and Larmor precession compete to be the dominant effect

Far above threshold Larmor precession dominates any remaining asymmetry in (sx,sy) plane

J. Levrat et al., accepted for publication in Phys. Rev. Lett 16

Model vs experimental results

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.00

30

60

90

120

150180

210

240

270

300

330 Pmin Pmax

< l>

P/Pthr

J. Levrat et al., accepted for publication in Phys. Rev. Lett 17

Detuning dependence

Minimum threshold powerat ~ - 60 meV

fast relaxationQuick build-up

of linear polarization

Reduced averaged linear polarization degree at ~ - 60 meV

No time to relax to the lowest energy state (linear polarization)

?

J. Levrat et al., accepted for publication in Phys. Rev. Lett 18

Perspectives

Control of the photonic disorder

Self-induced Larmor precession

Ultra-fast polarization switiching device

based on polariton condensates operating

at room temperature

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

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-5051015202530

3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65

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-5051015202530

Energy (eV)

Room temperature polariton

condensation

Pinning of the linear polarization degree

at threshold

+ +

+ =

19

Conclusions

• Full phase diagram of polariton condensation in GaN MCs (thermodynamic vs kinetic regimes)

• Pinning of the order parameter at threshold vs detuning

• Possibility of RT ultrafast polarization switch

• Depinning of the order parameter with pump power (pinning vs Larmor precession)

20

Acknowledgments

Thank you for your attention

21