Download - Jacques Levrat, R. Butté, T. Christian, M. Glauser, E. Feltin, J.-F. Carlin, N. Grandjean,
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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
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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
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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
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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
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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
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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
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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
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3.58 3.59 3.60 3.61 3.62 3.63 3.64 3.65
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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)
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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)
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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
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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
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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
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a-plane
m-plane
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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
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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
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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
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Model
* *1 1 1 1
* *1 1 1 1
2 2
1 1
1
2
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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)
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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
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<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
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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
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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
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Perspectives
Control of the photonic disorder
Self-induced Larmor precession
Ultra-fast polarization switiching device
based on polariton condensates operating
at room temperature
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Energy (eV)
Room temperature polariton
condensation
Pinning of the linear polarization degree
at threshold
+ +
+ =
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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)
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Acknowledgments
Thank you for your attention
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