probing the bogoliubov excitation spectrum of a polariton superfluid by heterodyne four-wave-mixing...
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PROBING THE BOGOLIUBOV EXCITATION SPECTRUM OF A POLARITON SUPERFLUID BY HETERODYNE FOUR-
WAVE-MIXING SPECTROSCOPY
Verena Kohnle, Yoan Leger, Maxime Richard, Michiel Wouters, Marcia Portella-Oberli,
Benoit Deveaud-Pledran
o Introduction
o strong coupling: polaritonso sample
o Motivation: excitation spectrum of a polariton superfluid
o Heterodyne Four Wave Mixing (FWM) experiment
o Experimental Results
o Conclusion
Outline
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Strong coupling regime: Polaritons• Polariton: quasi particle composed
by a photon coupled to an exciton• Microcavity 2D system for photons; Quantum well 2D system for excitons• Polaritons are the new eigenstates
of the system in the strong coupling regime
Picture: Kasprzak et al. Nature (2006)
Polaritons are composed bosons:
Photonic content: provides high degree of coherenceExcitonic content: interaction between polaritons
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Sample
Substrate (GaAs)
•••
•••
8nm QWIn0.04Ga0.96As
λ-cavity
bott
om D
BRto
p D
BR• AlAs/GaAs – cavity which contains a 8 nm In0.04Ga0.96As quantum well (QW)
• Bragg mirrors: contain 26.5 and 20 pairs of alternated /4 layers of AlGaAs and AlAs
• wedged cavity spacer layer the resonator frequency of
the resonator can be varied by moving the laser spot over the sample
• rabi splitting: 3.4 meV
1.491
1.490
1.489
1.488
1.487
1.486
1.485
1.484
1.483
en
erg
y (e
V)
43210-1-2 detuning (meV)
upper Polariton lower Polariton E_cavity (calculated) E_exciton (calculated)
space
Polariton superfluid: Bogoliubov dispersion
feature of interactions: blueshift of dispersion BOGOLIUBOV Dispersion:
• linear at small k• „ghost“ branch
In experiment: up to now nobody was able to show the „ghost“ branch
Polaritons : weakly interacting bose gas
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
State of the art
Utsunomiya et al. Nature, 4, 700 (2008)
No Bogoliubov ghost branch observed:
A proposal as an answer:
Wouters et al. Phys Rev B,79, 125311 (2009)
Wouters et al. Phys Rev B,79, 125311 (2009)
FWM I010 I0
en
erg
y
wavevector k
0-k0 +k0
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
our method:• using heterodyne Four-Wave-Mixing (FWM) setup • fs-laser broad energy spectrum (~12meV) normal and gohst branch are probed with the same laser pulse
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Heterodyne FWM setup
balanced detection
• best sensitivity• spectral interferometry
– amplitude & phase resolution
• balanced detection– background
suppression
Ref (0,0)
Pump (0,w1)
Trigger (k,w2)FWM(-k,2w1-w2)
Sample
AOM @ 2w1-w2
HeterodyneChannels: A (j=0)
B (j=p)
LensPinhole Miror
to CCD
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Bogoliubov: tracking the ghost branch
ghost branch
normal branch
k=0
k = 1 µm-1
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Dispersion of the Bogoliubov excitationsevolution in k of the different branches: (delay integration between 5 – 6 ps)
Gross-Pitaevskii equations:
Equation for excitons:
Equation for cavity photons:
Yx/p= exciton/photon wavefunctiong = exciton-exciton interaction potentialgx/p= decay rate of excitons/photons2WR= Rabi splittingF(r,t)= pump laser field
2 22x x
x x x x R px
Ψ iγi Ψ Ψ g Ψ Ψ Ω Ψ
t 2 2m
( )p pp p p R x
Ψ iγi Ψ ε Ψ Ω Ψ F(r,t)
t 2
k = 1 µm-1
Arb. Int. = 16
evolution in excitation power: (@ delay time t=5.7ps)
Bogoliubov: excitation power dependence
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
k = 1 µm-1
Arb. Int. = 16
ng
2 ng
evolution in excitation power: (@ delay time t=5.7ps)
Bogoliubov: excitation power dependence
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
k = 1 µm-1
Arb. Int. = 16
evolution in excitation power: (@ delay time t=5.7ps)
Bogoliubov: excitation power dependence
Introduction
Motivation
FWMexperiment
Experimentalresults
Conclusion/Outlook
conclusion & outlook Observation of the Bogoliubov excitation
spectrum of a polariton superfluid using heterodyne FWM spectroscopy
we demonstrate unambigously the excistence of the negative energy „ghost“ branch
Outlook: 2D FT allows to characterice th apperence of the different resonances
THANK YOU !
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