dmitriy krizhanovskii
DESCRIPTION
Spatial coherence and vortices of polariton condensates. Dmitriy Krizhanovskii. Sheffield University, United Kingdom. OUTLINE. Background of semiconductor microcavities. Polariton condensation. Nonequilibrium system. Vortices in polariton condensates. Effect of interactions. - PowerPoint PPT PresentationTRANSCRIPT
PLMCN 2010, Mexica PLMCN 2010, Mexica
Dmitriy KrizhanovskiiDmitriy Krizhanovskii
Sheffield University, United Kingdom
Spatial coherence and vortices of Spatial coherence and vortices of polariton condensatespolariton condensates
Spatial coherence and vortices of Spatial coherence and vortices of polariton condensatespolariton condensates
PLMCN 2010, Mexica PLMCN 2010, Mexica
OUTLINEOUTLINE
Background of semiconductor microcavities
Vortices in polariton condensates. Effect of interactions. Comparison to atom BEC
Polariton condensation. Nonequilibrium system
Polariton condensates in acoustic lattices. Screening.
PLMCN 2010, Mexica PLMCN 2010, Mexica
Collaborators
Sheffield,UK
K.GudaR.BradleyD.M.WhittakerJ.S.RobertsM.S.Skolnick
Berlin,Germany,PDI
Paulo SantosE.CerdaR.Hey
Madrid, Spain
Luis VinaDaniele Sanvitto
PLMCN 2010, Mexica PLMCN 2010, Mexica
( CdMnTe/CdTe)
Bottom DBR
QWs (CdTe)
A semiconductor microcavityA semiconductor microcavityA semiconductor microcavityA semiconductor microcavity
Cavity
Top DBR
PLMCN 2010, Mexica PLMCN 2010, Mexica
Low mass (low density of state). 104-5 times smaller than exciton mass
Ideal system to study interacting BEC. Few K critical temperature
Strong non-linearities
A semiconductor microcavityA semiconductor microcavityA semiconductor microcavityA semiconductor microcavity
Upper polariton
Lower polariton
Ene
rgy
Wavevector0
Rabi splitting ~13-26 meV and 5-10 meV for CdTe and GaAs based microcavities, respectively
PLMCN 2010, Mexica PLMCN 2010, Mexica
Atom BEC (3D) Polariton condensate (2D)
Mass 105 me 4*10-5 me
Density ~1014 cm -3 ~109 –1010
cm -2
Interactions ~ N 10-7 meV 0.1-0.01 meV
Temperature ~nK Up to 300 K
PLMCN 2010, Mexica PLMCN 2010, Mexica
Optical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumping
_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
-4 -2 0 2 4
Pump
sig
nal em
issio
n idle
r em
issio
n
Lower polariton branch
Wavevector (104 cm-1)
En
erg
y
pumpsignal
idler
Stevenson et al., PRL (2000)Tartakovskii et al., PRB (2000)
Note: coherence of signal orIdler is not inherited from the pump
PLMCN 2010, Mexica PLMCN 2010, Mexica
Polariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumping
Kasprzak et al, Nature Kasprzak et al, Nature 20062006
PLMCN 2010, Mexica PLMCN 2010, Mexica
Vortices of polariton condensates
PLMCN 2010, Mexica PLMCN 2010, Mexica
Vortices in polariton condensatesVortices in polariton condensatesVortices in polariton condensatesVortices 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
PLMCN 2010, Mexica PLMCN 2010, Mexica
Creation of vortices in OPO condensate by imprintingCreation of vortices in OPO condensate by imprintingCreation of vortices in OPO condensate by imprintingCreation of vortices in OPO condensate by imprinting
Use of very weak probe carrying vortex M=1 resonant with theSignal
Probe is 40 times weaker than signal
Vortex in the signal is imprinted , phase of the signalis being locked to that of very weak probe
Fork-like dislocation in signal self-interference patternconfirms quantised phase variation
D.N Krizhanovskii et al, PRL (2010)
PLMCN 2010, Mexica PLMCN 2010, Mexica
Vortex core is intrinsic property of signalVortex core is intrinsic property of signalVortex core is intrinsic property of signalVortex core is intrinsic property of signal
Vortex diameter created in the signal isnot determined by the spatial profile of theprobe.
Interactions produce a natural size for the vortexdetermined by the strength of the interaction
PLMCN 2010, Mexica PLMCN 2010, Mexica
Effect of particle density and interactions on vortex sizeEffect of particle density and interactions on vortex sizeEffect of particle density and interactions on vortex sizeEffect of particle density and interactions on vortex size
Kinetic term is compensated by the interaction term, which determines the natural vortex size (healing length) :
shiftEm
h~
2 2
22
Healing length
D.N Krizhanovskii et al, PRL (2010)
Intensity (Probe)~1/15 Intensity(Signal)
PLMCN 2010, Mexica PLMCN 2010, Mexica
Atom BEC (3D) Polariton condensate (2D)
Mass 105 me 4*10-5 me
Density ~1014 cm -3 ~109 –1010
cm -2
Interactions ~ N 10-7 meV 0.1-0.01 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
PLMCN 2010, Mexica PLMCN 2010, Mexica
0.0 0.5 1.0 1.50
2
4
Ene
rgy
/ nU
0
k
Excitation spectrum of equilibrium BEC
Also true for resonantlypumped polaritons (Amo, NP 2009)
Excitation spectrum of nonequilibrium condensate (Wouters, PRL 2007)
•Sound-like (linear) dispersion at kin both cases
•Healing length is inversely proportional to sound velocity cs~
Interactions increase sound velocity.
Concept of healing length
PLMCN 2010, Mexica PLMCN 2010, Mexica
Vortex- Antivortex in signal and idler
OPO involve 3 coherent fields.Signal, pump, and idlerConservation 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
-4 -2 0 2 4
Mp=0
Ms =
-1
Mi =
1
Wavevector (104 cm-1)En
erg
y
PLMCN 2010, Mexica PLMCN 2010, Mexica
Condensates in disordered potential and acoustic lattices
PLMCN 2010, Mexica PLMCN 2010, Mexica
Polariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumpingPolariton condensation in CdTe: nonresonant pumping
Kasprzak et al, Nature Kasprzak et al, Nature 20062006
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
PLMCN 2010, Mexica PLMCN 2010, Mexica
A.P. D. Love, D. N. Krizhanovskii, et all Phys. Rev. Lett. 101, 067404 (2008)D.N. Krizhanovskii et al, PRB (2009)
20
25
30
351.674 1.675 1.676 1.677
x 12.5
EX6E
X5
EX4E
X3
EX2
EX1
EY6
EY5
EY4
EY3E
Y2
EY1
x10
X-polarised
Y-polarised
a)
Energy(eV)
Inte
nsi
ty (
arb
.units
)
-4 -2 0 2 41.675
1.676
1.677Y-polarisationb)
500.0906.313131719212525312938334437504156456349695375578161886594700074067813821986259031943898441.025E41.066E41.106E41.147E41.188E41.228E41.269E41.309E41.35E41.391E41.431E41.472E41.513E41.553E41.594E41.634E41.675E41.716E41.756E41.797E41.838E41.878E41.919E41.959E42E4
Momentum k (m-1)
Energ
y (m
eV
)
-4 -2 0 2 4
x12.5
Fig.1
X-polarisationc)
1
0
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 (m-1)
Polariton condensation using pump with reduced noisePolariton condensation using pump with reduced noisePolariton condensation using pump with reduced noisePolariton condensation using pump with reduced noise
PLMCN 2010, Mexica PLMCN 2010, Mexica
Generalised GP approach (theory by Michiel Wouters)
Gross-Pitaevskii equation 1 coupled to kinetic equation 2 for exciton reservoir
Coupling to reservoir
InteractionsExternal potential
Kinetic equation for exciton reservoir
D.N. Krizhanovskii et al, PRB (2009)
PLMCN 2010, Mexica PLMCN 2010, Mexica
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, 067404 (2008); D.N. Krizhanovskii et al, PRB (2009)
Experimental disorder potential
GP approach (theory by Michiel Wouters)
PLMCN 2010, Mexica PLMCN 2010, Mexica
Control of spatial coherence of condensates by SAW.
SAW
x||[100]
z||[001]
rf
Microcavity+QWs
Formation of Brillouin Zones
Energy gap ~0.1-0.2 meV
Surface acoustic wave creates periodical potential (m)
Polariton confinement in real space. Tool to manipulate condensates
PLMCN 2010, Mexica PLMCN 2010, Mexica
Optical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumpingOptical parametric oscillator: resonant pumping
-4 -2 0 2 4
Pump
sig
nal em
issio
n idle
r em
issio
n
Lower polariton branch
Wavevector (104 cm-1)
En
erg
y
pumpsignal
idler
Stevenson et al., PRL (2000)Tartakovskii et al., PRB (2000)
PLMCN 2010, Mexica PLMCN 2010, Mexica
OPO in periodical potential
Momentum along SAW direction (m-1)
Ene
rgy
(eV
)
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
SAW
x||[100]
z||[001]
rf
Microcavity+QWs
PLMCN 2010, Mexica PLMCN 2010, Mexica
Control of spatial coherenceFirst order spatial correlation function g1(-r,+r) vs SAW potential
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)
SAW OFF SAW 1.2 dbm SAW 7.2 dbm
Coherence length along SAW wire L ~10 microns. Higher noise in 1D system.
PLMCN 2010, Mexica PLMCN 2010, Mexica
Screening of SAW potential
-5 0 5 10 15
5
10
15
20
25
30C
oher
ence
leng
th (m
)
RF power (dBm)
68 mW
PLMCN 2010, Mexica PLMCN 2010, Mexica
Screening of SAW potential
-5 0 5 10 15
5
10
15
Coh
eren
ce le
ngth
(m
)
RF power (dBm)
140 mW
PLMCN 2010, Mexica PLMCN 2010, Mexica
Screening of SAW potential
-5 0 5 10 15
5
10
15
20
25C
oher
ence
leng
th (m
)
RF power (dBm)
200 mW
PLMCN 2010, Mexica PLMCN 2010, Mexica
Screening of SAW potential
-5 0 5 10 155
10
15
20
25
30
Coh
eren
ce le
ngth
(m
)
RF power (dBm)
300 mW
PLMCN 2010, Mexica PLMCN 2010, Mexica
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
PLMCN 2010, Mexica PLMCN 2010, Mexica
Polariton condensates (BEC) under incoherent excitation in SAW potential
Ene
rgy
MomentumS-state
P-state
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).
PLMCN 2010, Mexica PLMCN 2010, Mexica
BEC: control of spatial coherence
High power of SAW:
Tunnelling between minima issuppressed
Coherence of S-state is reduced from 10 m down to 5 m at high power of SAW
Coherence of P-state is about 10-12 mat high power of SAW, longer thanthat for S-state
P-state has energy above periodic potential and hence long range spatial coherence is established
40 44 48 52 56 60
0.0
0.2
0.4
0.6
g(y,
-y)
Y coordinate (m)
off 10 dBm
Coherence of S-state (condensation into minima of 1st BZ)
Coherence of P-state (condensation into minima of 2nd BZ)
35 40 45 50 550.0
0.2
0.4
0.6
g1(-
y, y
)
Position (microns)
PLMCN 2010, Mexica PLMCN 2010, Mexica
1) Polariton condensate is a nonequilibrium, strongly interacting system
2) Control of spatial coherence of by periodical potential created by Surface of Acoustic Wave.
3) 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
Conclusion