• Indirect excitons in coupled quantum wells

• Exciton pattern formation and exciton transport

• Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials

• Spin transport of excitons

• Conveyers

• Vortices

In collaboration with:

Michael Fogler, Joe Graves, Martin Griswold, Aaron Hammack, Alex High, Jason Leonard, Andrew Meyertholen, Katya Novitskaya, Mikas Remeika, Averi Thomas, Alex Winbow, Sen Yang, Yuliya Kuznetsova (UCSD)

Tomas Ostatnick´y, Alexey Kavokin (Southampton), Yura Rubo (Cuernavaca)

Leonid Levitov (MIT), Ben Simons (Cambridge)

Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff)

Micah Hanson, Arthur Gossard (UCSB)

Transport and spin transport of excitonsLeonid V. Butov, UCSD

1 2

22~ 3 K

dB

dBB

n

T nmk

What temperature is “cold” for exciton gas?1/ 222dB

Bmk T

3D: 1 3

22 32

0.527

dB

dBB

BEC dB

n

T nmk

T T

2D:mexciton ~ 10 -6 matom Kelvin for excitons

is likemicroKelvin for atoms

transition from classical to quantum gas takes place when thermal de Broglie wavelength is comparable to interparticle separation

3D gas of Rb atoms: n = 1015 cm-3, matom = 105 me → TdB ~ 5×10-6 K

2D gas of excitons in GaAs QWn = 1010 cm-2, mexciton= 0.2 me → TdB ~ 3 K

n < nMott ~ 1/aB2 ~ 2×1011 cm-2

How to realize cold exciton gases ?

Tlattice << 1 K in He refrigerators

finite lifetime of excitons could result to high exciton temperature: Texciton > Tlattice

find excitons with lifetime >> cooling time Texciton ~ Tlattice

Challenges for realization of exciton condensates

To solve: Find or design semiconductor structures where

short lifetime excitons have long lifetimes >> cooling times

competing ground states, e.g. EHL excitons form the lowest energy state

exciton destruction, e.g. due to Mott transition

excitons have large binding energy

disorder disorder is weak

solving these challenges has led to studies ofvarious experimental systems

and various types of exciton condensate

Indirect excitons in coupled quantum wells

Electron-electron bilayers in magnetic fields at =1

Electron-hole bilayers with gate-induced carriers

Electron-hole bilayers with photoexcited carriers

_

_

+

+

h

e

e e

GaAs

AlxGa

1-xAs

z

E

K

E

excitondispersion

2D: coupling of E=0 state to continuum of energy states E > E

0

effective cooling of 2D excitons by bulk phonons

3D: coupling of E=0 state to single state E=E0exciton energy relaxation

by LA-phonon emission

E0=2M

xv

s

2

~ 0.05 meV

AlAs/GaAsCQW

GaAs/AlGaAsCQW

h

e

h

e

X

TX ~ 100 mKhas been realized experimentally

30 times below TdB

Why indirect excitons in CQW ?103-106 times longer exciton lifetime due to separation between electron and hole layers

103 times shorter exciton cooling time than that in bulk semiconductors

0 50 1000.1

1

TX

Time (ns)

A.L. Ivanov et al in PRL 86, 5608 (2001)

~ 10 ns to cool to 300 mK~ 100 ns to cool to 100 mK

realization of cold exciton gas in separated layers was proposed by Yu.E. Lozovik & V.I. Yudson (1975); S. I. Shevchenko (1976);T. Fukuzawa, S.S. Kano, T.K. Gustafson, T. Ogawa (1990)

Repulsive interaction between indirect excitons

_

_

+

+

h

e

indirect excitons are oriented dipoles

Repulsive dipole-dipole interaction● stabilizes exciton state against formation of metallic EHL

● results in effective screening of in-plane disorderA.L. Ivanov, EPL 59, 586 (2002)R. Zimmermann

D. Yoshioka, A.H. MacDonald, J. Phys. Soc. Jpn. 59, 4211 (1990)X. Zhu, P.B. Littlewood, M. Hybertsen, T. Rice, PRL 74, 1633 (1995)

the ground state is excitonic

1.54 1.55 1.56 1.57

PL

Int

ensi

ty

Wex

=4 W/cm2

Wex

=0.5 W/cm2

Energy (eV)

energy shift: E ~ n/C estimate for exciton density approximation for short-range 1/r3 interaction C = /4e2d

Repulsive interaction in experimentexciton energy increases with density L.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993)

C. Schindler, R. Zimmermann, PRB 78, 045313 (2008) C and n in experiments are higher

also high quality CQW samples with small initial disorder are required to overcome exciton localization

d

potential energy of indirect excitons can be controlled by voltage

the ability to control electron fluxes by an applied gate voltage

electronic circuit devices mesoscopicsthe field which concerns electron transport in a potential landscapes

in-plane potential landscapes can be created for excitons by voltage pattern e.g. traps, lattices, circuit devices

zE edF

the ability to control exciton fluxes by an applied gate voltage

excitonic circuit devices mesoscopics of bosons in semiconductors

e

h

condensation pattern formation

potential profilescan be created and in situ controlled

indirect excitons

energy can be controlled by gate voltage

can cool down to 0.1 K well below TdB ~ 3K

can travel over large distances

have built-in dipole moment ed

cold Bose gases in solid-state materials excitonic devices

transportspin transport

edFE

have long lifetimes

optical methods → local probe of excitons

d

Exciton pattern formation and exciton transport

external ring

ring fragmentation localized bright spots

Pattern Formation: Exciton Rings and Macroscopically Ordered Exciton State

same

spatial order on macroscopic lengths

0 20 400

400

800

Po

siti

on

on

th

e ri

ng

(m

)

Peak number

inner ring

410 m

T=1.8 K T=4.7 K

0 2 4 60

Am

plit

ud

e o

f th

eF

ou

rier

Tra

nsf

orm

T (K)

appears abruptly at low T

L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)

n

~ 0.1 meV

Kdrift

K0

E

K

K

0 40 80 120

1.546

1.547

1.548

1.549

0 40 80 120

flow of excitons out of excitation spot due to exciton drift, diffusion, phonon wind, etc.

r (m)

En

ergy

(eV

)

PL pattern spatial distribution of optically active low energy excitons

excitons can travel in a dark state after having been excited until slowed down to a velocity below photon emissionthreshold, where they can decay radiatively

PL

In

ten

sity

repulsive interaction → drift

excitation spothigh TX exciton drift

lower occupation of radiative zone

inner ringlower TX excitons relax to radiative zone

higher occupation of radiative zone

exciton transport over tensof microns

k k

E E

Inner ring

L.V. Butov, A.C. Gossard, D.S. Chemla, Nature 418, 751 (2002)

A.L. Ivanov, L. Smallwood, A. Hammack, Sen Yang, L.V. Butov, A.C. Gossard, EPL 73, 920 (2006)

inner ring forms due to exciton transport and cooling

Localization-delocalization transition for exciton transport in random potential

exp.

theory

exp.

theory

low densities:emission profile follows excitation spotexcitons are localized in random potential

high densities:emission extends well beyond excitation spotexcitons screen random potential, travel away from excitation spot and form inner ring

Kinetics of inner ring

formation time of inner ring ~ 30 ns

kinetics of inner ring

estimate of exciton transport characteristicsDX reaches ~ 20 cm2/s

PL jump vs r → excitons outside laser spotincluding inner ring region are cooled to Tlattice even during laser excitation

exp. theory

A.T. Hammack, L.V. Butov, J. Wilkes, L. Mouchliadis, E.A. Muljarov, A.L. Ivanov, A.C. Gossard, PRB 80, 155331 (2009)

External ring

above barrier laser excitation creates additional number of holes in CQW

heavier holes have higher collection efficiency to CQW

holes created at the excitation spot diffuse out this depletes electrons in the vicinity of the laser spot creating electron-free and hole rich region

electrons

excitons

holes

excess holes are photogenerated in the laser excitation spotelectron source is spread out over the entire plane due to current through the CQW from n-doped GaAs layers

same for e ↔ h

x

y

z

E

L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, PRL 92, 117404 (2004)

R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, PRL 92, 117405 (2004)

external ring forms at interface between electron-rich and hole-rich regions

0 1 2 3 4 5

Delay (s)

Rad

ius

(m

)

Rad

ius

(m

)

0

250

00 1 2 3 4 5

Delay time ( s)

c

40 cm2/s

Dh = 16 cm2/s

26 cm2/s

100m

- 9.5 s - 8.8 s - 6.5 s 0.2 s 1.5 s 2.5 s 3 s 4 s

-10s 0 5slaser pulse

e

h

external ring

LBS ringh

e

expansion of external ring collapse of external ring

a b c d e f g h

ij

50

80 cm2/sDe = 200 cm2/s

30 cm2/s

0

collapse of external ring expansion of LBS rings

kinetics of external and LBS rings

estimation of e and h transport characteristics

De ~ 80 cm2/s, Dh ~ 20 cm2/s

Kinetics of external ring and LBS ringstime

Sen Yang, L.V. Butov, L.S. Levitov, B.D. Simons, A.C. Gossard, PRB 81, 115320 (2010)

rings are far from hot spotsdue to long lifetimes of indirect excitons TX ≈ Tlattice

rings form is region where cold and dense exciton gas is created

macroscopically ordered exciton state (MOES)

localized bright spots have hot cores

no hot spots in external ring and LBS rings

indirect exciton PL direct exciton PL – pattern of hot spots

Spontaneous coherence

experimental method:Mach-Zehnder interferometry with spatial and spectral resolution

probing coherence far from laser both in space and energy: coherence is spontaneous

2 4 6 8 100

1

2

3

0

Co

her

enc

e L

eng

th (m

)

Temperature (K)

PL

Co

ntr

ast

alo

ng

th

e R

ing

left arm right arm

the increase of the coherence length is correlated with the macroscopic spatial ordering of excitons

~ 2 m >> the classical value ~ dB ~ 0.1 m

2 (1) ( )

~ 1

ikn d re g r

k

kr spontaneous coherence =

= condensation in k-space

Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, PRL 97, 187402 (2006)

MOES is a state with:● macroscopic spatial ordering and● large coherence length → a condensate in k-spacemodel: L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, 176404 (2005)

Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials

Exciton transport in potential landscapes • Lattices • Traps • Circuit devices • Random potentials

potential energy of indirect excitons can be controlled by voltage

in-plane potential landscapes for excitons can be created by voltage pattern

zE edF e

h

A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, JAP 99, 066104 (2006)

obstacle: in-plane electric field can lead to exciton dissociation

proposed design in which in-plane electric field is suppressed

allows creating virtually arbitrary in-plane potential landscape for excitons by voltage pattern

can be controlled in-situ by voltageson timescale much shorter than exciton lifetime

source

drain

gate

ONOFF5 m

Exciton Optoelectronic Transistor (EXOT)

photon input photon outputelectronic control

prototype EXOT performs switching at speeds > 1 GHz

prototype excitonic IC performs directional switching and merging

Time (ns)

xexciton flow is on

exciton flow is off

Gate

QWs

n

i

photonicsource

photonicdrain

opticalinputgate

opticaloutputgate

Ex

cit

on

en

erg

y

energy bump controlled by the Gate

similar in geometry and operation to electronic FET

0

1

0 20Distance (m)

Inte

nsi

ty

ON

OFF

A.A. High, A.T. Hammack, L.V. Butov, M. Hanson, A.C. Gossard, Opt. Lett. 32, 2466 (2007)

A.A. High, E.E. Novitskaya, L.V. Butov, M. Hanson, A.C. Gossard, Science 321, 229 (2008)

demonstrated operation up to ~ 100 K G. Grosso, J. Graves, A.T. Hammack, A.A. High, L.V. Butov, M. Hanson, A.C. Gossard, Nat. Photonics 3, 577 (2009)

delay between signal processing and optical communication is effectively eliminated in excitonic devices → advantage in applications where interconnection speed is important

A.A. High, A.K. Thomas, G. Grosso, M. Remeika, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 103, 087403 (2009)

5 m

eV

5 m

5 m 5 m

Width

Collection of exciton cloud to trap center with increasing density

density →

▲ exp▬ theory

excitation power (W)

repulsive interaction

screening of disorder

collection to trap bottom

cold exciton gas in trap

can be controlled in situ like traps for cold atoms

width of exciton cloud in trap

Elattice = 0

Elattice =

3.7 meV

M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, I. Bloch, Nature 415, 39, (2002)J.K. Chin, D.E. Miller, Y. Liu, C. Stan, W. Setiawan, C. Sanner, K. Xu, W. Ketterle, Nature 443, 961 (2006)

Excitons in lattices

Atoms in lattices

atoms in lattices – system with controllable parameters

use atoms in lattices to emulate solid state materials

controllable: exciton density, interaction, mass lattice amplitude, structure, constant

a tool with a number of control knobs for studying the physics of excitons

M. Remeika, J. Graves, A.T. Hammack, A.D. Meyertholen, M.M. Fogler, L.V. Butov, M. Hanson, A.C. Gossard, PRL 102, 186803 (2009)

Localization - delocalization transition (LDT)

estimate for the strength of disorder: Erand ~ 0.8 meV

Elattice >> Erand

interaction energy at LDT ≈ amplitude of unscreened lattice

model attributes LDT to interaction-induced percolation of exciton gas through external potential

Etotal = Elattice + Erand

Elattice << Erand

interaction energy at LDT ≈ amplitude of unscreened random potential

loc: emission profile follows excitation spotdeloc: emission extends well beyond excitation spot

Conveyers

A.G. Winbow, J.R. Leonard, M. Remeika, A.A. High, E. Green, A.T. Hammack L.V. Butov, M. Hanson, A.C. Gossard, unpublished

conveyer off conveyer on

Electrostatic conveyers for excitons

study dynamic LDT with varying conveyer amplitude conveyer speedexciton density

conveyers are created by applying AC voltages to lattice electrodes → traveling lattice

wavelength electrodesamplitude voltagespeed frequency

Transport of electrons, holes, excitons, and polaritons via SAW

C. Rocke, S. Zimmermann, A. Wixforth, J.P. Kotthaus, G. Böhm, G. Weimann, PRL 78, 4099 (1997)P.V. Santos, M. Ramsteiner, R. Hey, PSS B 215, 253 (1999)J. Rudolph, R. Hey, P.V. Santos, PRL 99, 047602 (2007)this conference

phonon wind in the conveyer framecrossing phonon velocity

Spin transport of excitons

Spin transport of excitons

exciton spin transport over substantial distances requires

• exciton transport over substantial distances

• long spin relaxation time

long r

high D

Spin-Flip Pathways

Tnnnnn

nwt

n

2112

,

he

S z

2

3,

2

11

he

S z

2

3,

2

11

he

S z

2

3,

2

12

he

S z

2

3,

2

12

ex

h

ee

r r 111 2 exheP

2/~ eP exP ~

2rex

optically activestates

dark states

hwewew

hw

ewh

wewexwrexw

hw

hwexw

hwewexwrew

hwew

hwew

w

0

1

1

0

polarization relaxation time

GaAs SQWdirect exciton

GaAs CQWindirect excitonwith small e-h overlap

fast depolarization within tens of ps

makes possibleexciton spin transport over substantial distances

ex is determined by exchange interaction between e and h

control p by changing e-h overlap

J.R. Leonard, Y.Y. Kuznetsova, Sen Yang, L.V. Butov, T. Ostatnick´y, A. Kavokin, A.C. Gossard, Nano Lett. 9, 4204 (2009)

M.Z. Maialle, E.A. de Andrada e Silva, L.J. Sham, PRB 47, 15776 (1993).

orders of magnitude enhancement of exciton spin relaxation time

II

IIP

exciton spin transport over substantial distances is problematic

100

101

102

103

0

30

100

101

102

103

0

5

10

0 5 10 150

10

20

30

108

109

1010

1011

10-3

10-1

101

100

101

102

103

0

30

108

109

1010

1011

0

5

10

10-3 10-1 101

0.1

1

10

<P

> (

%)

Pex

(W)

r clou

d (m

)

Pex

(W)

f

e

PH

WH

M (

%)

rcloud

(m)

D (

cm2/s

)N

b (cm-2)

ca

b

ExtractedResults

Fit ParametersFitted Data

Pr=

0 (%

)

Pex

(W)

d

p

(ns

)

Nb (cm-2)

P (

ns)

D (cm2/s)

mo

Density dependence

P of indirect excitons reaches several ns >> P of direct excitons

P and P drop with increasing density

decrease of P is correlated with the increase D → P drops when excitons become delocalized

loc

deloc21)(~ rcloud Dr

rP

pP

complies with DP spin relaxation mechanism

-20 0 20 -10 0 10

0

30

0

7

0

5

-20 0 20

Inte

nsity

(a.

u.)

Radius (m)

2.3

230 W

x100

x5.8

x1

Radius (m) Radius (m)

45

P (

%)

TheoryExperimentexperiment theory experiment and theory

Spin transport of excitons

extension of polarization profiles beyond excitation spot shows exciton spin transport

spin transport of indirect excitons originates from long spin relaxation time and long lifetime

Decrease of P and P with increasing density

AmeV 25

AmeV 20

complies with D’yakonov-Perel’ spin relaxation mechanism

exeBexT

Bex

e

ee

mmTkmk

TkDm

kΩ

Ωτ

212

21

2

timescattering momentum

precessionspin offrequency 2

timerelaxationspin

42211 162 DmeeP

experiment:

theoretical estimate:

spin splitting constant

Vortices

quantized atom vortices S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, W. Ketterle, PRL 87, 080402 (2001)F. Chevy, K.W. Madison, V. Bretin, J. Dalibard, PRA 64, 031601(R) (2001)Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006)

quantized optical vortices J. Scheuer, M. Orenstein, Science 285, 230 (1999)and references therein

quantized polariton vortices K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, Le Si Dang, B. Deveaud-Plédran, Nature Physics 4, 706 (2008)K.G. Lagoudakis, T. Ostatnický, A.V. Kavokin, Y.G. Rubo, R. André, B. Deveaud-Plédran, Science 326, 974 (2009)

quantized vortex is characterized by point (or line) around which phase of wave function varies by 2n

fork-like dislocation in phase pattern is signature of quantized vortex

Vortices

polariton half-vortices

Pex

Fork-like topological defects in interference pattern of indirect excitonsindicating the presence of quantized vortices

hor vert 1 2

topological defects in multicomponent spin systemsY.G. Rubo, PRL 99, 106401 (2007)

for different polarizations

A.A. High, A.T. Hammack, J.R. Leonard, L.V. Butov, T. Ostatnicky´, A. Kavokin, Y.G. Rubo, A.C. Gossard, unpublished

LBS ring region

external ring

region excitation and

inner ring

region

80 100 120 140 160 1800

5

10

15

20

25

hori vert sigma1 sigma2

num

ber

of f

orks

Excitation Power

80 100 120 140 160 180

0

2

4

6

8

10

12 hori vert sigma1 sigma2

num

ber

of f

orks

excitation power

number of forks in LBS ring region

number of forks in external ring region

no forks in excitation and inner ring region

Number of forks in various regions of exciton pattern formation

Acknowledgements

supported by ARO, NSF, DOE

UCSD:Aaron Hammack Alex HighAlex WinbowAnton MintsevAveri ThomasJames LohnerJason Leonard Joe GravesGabriele GrossoKatya NovitskayaMartin GriswoldMikas RemeikaSen YangYuliya Kuznetsova

Collaborators in studies of indirect excitons:Gerhard Abstreiter, WSIDaniel Chemla, UCB&LBNLValerii Dolgopolov, ISSP RASAlexander Dzyubenko, CSBMichael Fogler, UCSDNikolai Gippius, Blaise PascalArthur Gossard, UCSBAtac Imamoglu, UCSBAlexei Ivanov, CardiffAlexey Kavokin, SouthamptonLeonid Levitov, MITPeter Littlewood, CambridgeYuri Lozovik, IS RASYuri Rubo, CuernavacaBen Simons, CambridgeArthur Zrenner, WSI

In collaboration with: Tomas Ostatnick´y, Alexey Kavokin (Southampton)

Yuri Rubo (Cuernavaca)

Andrew Meyertholen, Michael Fogler (UCSD)

Leonid Levitov (MIT)

Ben Simons (Cambridge)

Lois Smallwood, Leonidas Mouchliadis, Joe Wilkes, Egor Muljarov, Alexei Ivanov (Cardiff)

Micah Hanson, Arthur Gossard (UCSB)