Dmitriy Krizhanovskii

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


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.


Collaborators

Sheffield,UK

K.GudaR.BradleyD.M.WhittakerJ.S.RobertsM.S.Skolnick

Berlin,Germany,PDI

Paulo SantosE.CerdaR.Hey

Madrid, Spain

Luis VinaDaniele Sanvitto


( CdMnTe/CdTe)

Bottom DBR

QWs (CdTe)

A semiconductor microcavityA semiconductor microcavityA semiconductor microcavityA semiconductor microcavity

Cavity

Top DBR


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


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


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


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


Vortices of polariton condensates


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


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)


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


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)


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


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


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


Condensates in disordered potential and acoustic lattices


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


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


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)


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)


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


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)


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


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.


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



-5 0 5 10 15

5

10

15

Coh

eren

ce le

ngth

(m

)

RF power (dBm)

140 mW



-5 0 5 10 15

5

10

15

20

25C

oher

ence

leng

th (m

)

RF power (dBm)

200 mW



-5 0 5 10 155

10

15

20

25

30

Coh

eren

ce le

ngth

(m

)

RF power (dBm)

300 mW


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


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).


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)


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

Dmitriy Krizhanovskii

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