1. Spatial coherence and vortices of polariton condensates
Dmitriy Krizhanovskii
Sheffield University, United Kingdom

2. OUTLINE Background of semiconductor microcavities
Polariton condensation. Nonequilibrium system
Vortices in polariton condensates. Effect of interactions.
Comparison to atom BEC
Polariton condensates in acoustic lattices. Screening.

3. Collaborators Sheffield,UK K.Guda R.Bradley D.M.Whittaker J.S.Roberts
M.S.Skolnick
Berlin,Germany,PDI
Paulo Santos
E.Cerda
R.Hey
Madrid, Spain
Luis Vina
Daniele Sanvitto

4. A semiconductor microcavity
Top DBR
( CdMnTe/CdTe)
Cavity
QWs (CdTe)
Bottom DBR

5. A semiconductor microcavity
Upper polariton
Energy W
Lower polariton
Wavevector
Low mass (low density of state) times smaller than exciton mass
Ideal system to study interacting BEC. Few K critical temperature
Strong non-linearities
Rabi splitting ~13-26 meV and 5-10 meV for
CdTe and GaAs based microcavities, respectively

6. Atom BEC (3D)
Polariton condensate (2D)
Mass
105 me
4*10-5 me
Density
~1014 cm -3
~109 –1010
cm -2
Interactions ~ kN
10-7 meV
meV
Temperature
~nK
Up to 300 K

7. Optical parametric oscillator: resonant pumping
signal
idler
_High enough density of excitation close to the point of inflection of LP branch may lead to polariton pair scattering
_All 3 points (initial and 2 final states) can be simultaneously close to resonance with LP
_Population can efficiently build-up at “signal” and “idler” modes
Pump
signal emission
idler emission
Lower polariton
branch
Wavevector (104 cm-1)
Energy
Stevenson et al., PRL (2000)
Tartakovskii et al., PRB (2000)
Note: coherence of signal or
Idler is not inherited from the pump 7

8. Polariton condensation in CdTe: nonresonant pumping
Kasprzak et al, Nature 2006

9. Vortices of polariton condensates

10. Vortices in polariton condensates
Quantised spatial phase variation
(vortex) was observed for
polariton BEC
(Lagoudkais et al, Nature Physics, 2008)
The vortices arise from “interplay between disorder and the driven-dissipative nature of
the condensate”
In equilibrium condensates vortices do not form spontaneously in the limit of low temperature 10

11. Creation of vortices in OPO condensate by imprinting
Use of very weak probe carrying
vortex M=1 resonant with the
Signal
Probe is 40 times weaker than signal
Vortex in the signal is imprinted , phase of the signal
is being locked to that of very weak probe
Fork-like dislocation in signal self-interference pattern
confirms quantised phase variation
D.N Krizhanovskii et al, PRL (2010) 11

12. Vortex core is intrinsic property of signal
Vortex diameter created in the signal is
not determined by the spatial profile of the
probe.
Interactions produce a natural size for the vortex
determined by the strength of the interaction

13. Effect of particle density and interactions on vortex size
Intensity (Probe)~1/15 Intensity(Signal)
Kinetic term is compensated by the interaction term, which determines the natural vortex size (healing length) x:
Healing length
D.N Krizhanovskii et al, PRL (2010)

14. Vortices in atomic BEC are measured after expansion, which is
Atom BEC (3D)
Polariton condensate (2D)
Mass
105 me
4*10-5 me
Density
~1014 cm -3
~109 –1010
cm -2
Interactions ~ kN
10-7 meV
meV
Healing length
0.1 um
10 um
Vortices in atomic BEC are measured after expansion, which is
a destructive technique
Vortices in polariton system are measured in situ

15. Concept of healing length
Excitation spectrum
of equilibrium BEC
Also true for resonantly
pumped polaritons (Amo, NP 2009)
Excitation spectrum of
nonequilibrium condensate (Wouters, PRL 2007)
Sound-like (linear) dispersion at kx~0.5-1 in both cases
Healing length is inversely proportional to sound velocity cs~ x-1
Interactions increase sound velocity.

16. Vortex- Antivortex in signal and idler
Energy
Mi =1
Mp=0
Ms =-1
Wavevector (104 cm-1)
OPO involve 3 coherent fields.Signal, pump, and idler
Conservation of Orbital Angular Momentum in the
polartion-polariton scattering 2Mp=Ms+Mi
If a vortex Mi=+1 is created in idler then antivortex Ms=-1 must form

17. Condensates in disordered potential and acoustic lattices

18. Polariton condensation in CdTe: nonresonant pumping
Kasprzak et al, Nature 2006
Boltzman distribution for higher energy polaritons.
Polariton condensate is “nonequilibrium ”
M. Wouters et al, PRL 2007
Emission of polariton condensate is very broad ~0.3 meV . Short coherence time ~ 6 ps
=> reason is noisy pump 18

19. Polariton condensation using pump with reduced noise
Multiple condensates near the bottom of LP branch
~5-10μeV linewidth with CW noise free diode laser (at 1.81eV)
~0.3meV previously reported for multimode laser excitation (Kasprzak et al, Nature (2006), 0.55meV Balili, Snoke Science 2007)
~2 orders of magnitude reduction in linewidth reveals new physics
Momentum (mm-1)
A.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, (2008) D.N. Krizhanovskii et al, PRB (2009)

20. Generalised GP approach (theory by Michiel Wouters)
Gross-Pitaevskii equation 1 coupled to kinetic equation 2
for exciton reservoir
Coupling to reservoir
External potential
Interactions
Kinetic equation for exciton reservoir
D.N. Krizhanovskii et al, PRB (2009)

21. GP approach (theory by Michiel Wouters)
Experimental disorder potential
Without disorder there is only one solution.
With disorder multiple condensates observed=>result of nonequilibrium. Agreement with experiment
A.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, (2008); D.N. Krizhanovskii et al, PRB (2009)

22. Control of spatial coherence of condensates by SAW.
Surface acoustic wave
creates periodical potential (l ~ 8 mm)
SAW
x||[100]
z||[001] rf
Microcavity+QWs
Formation of Brillouin Zones
Energy gap ~ meV
Polariton confinement in real space.
Tool to manipulate condensates

23. Optical parametric oscillator: resonant pumping
signal
idler
Pump
signal emission
idler emission
Lower polariton
branch
Wavevector (104 cm-1)
Energy
Stevenson et al., PRL (2000)
Tartakovskii et al., PRB (2000) 23

24. OPO in periodical potential
SAW 5.2 dbm
SAW OFF: condensation at k=0
SAW ON: condensation at the maxima of the 1st BZ at k=+q/2 and k=-q/2
q- is the momentum of SAW
Energy (eV)
Momentum along SAW direction (mm-1)
SAW
x||[100]
z||[001] rf
Microcavity+QWs
f=0
f=p

25. Control of spatial coherence
First order spatial correlation function g1(-r,+r) vs SAW potential
SAW 1.2 dbm
SAW OFF
SAW 7.2 dbm
SAW direction
Suppression of polariton tunneling; Reduction of coherence length along SAW when tunneling time becomes comparable to coherence time (200 ps, D.Krizhanovskii et al, PRL 2006)
Coherence length along SAW wire L ~10 microns. Higher noise in 1D system.

26. Screening of SAW potential

27. Screening of SAW potential

28. Screening of SAW potential

29. Screening of SAW potential

30. Mechanism of screening
Both pump and signal are modulated
Pump population exhibits bistability
Above threshold there is more pump
polaritons in SAW minima
Pump –signal interactions screen SAW potential

31. Polariton condensates (BEC) under incoherent excitation in SAW potential
Energy
P-state
S-state
Momentum
In case of non-resonant pumping condensation into minima of 1st and 2nd BZs is observed
Narrow S and P states are observed
C. W. Lai et al., Nature 449, 529 (2007).

32. BEC: control of spatial coherence
Coherence of S-state (condensation
into minima of 1st BZ)
High power of SAW:
Tunnelling between minima is
suppressed
Coherence of S-state is reduced from
10 mm down to 5 mm at high power
of SAW
Coherence of P-state is about mm
at high power of SAW, longer than
that for S-state
P-state has energy above periodic
potential and hence long range
spatial coherence is established
Coherence of P-state (condensation
into minima of 2nd BZ)

33. Conclusion
Polariton condensate is a nonequilibrium, strongly interacting system
Control of spatial coherence of by periodical potential created by Surface of Acoustic Wave.
Transition from a single condensate with a long range spatial coherence into fragmented condensed state with reduced coherence length
4) Screening of SAW potnetial by strong interactions
5) Vortex can be imprinted onto condensate using very weak probe
6) Vortex core is determined by the interactions and decreases with population
7) Vortex and antivortex states are formed due to parametric scattering