cold exciton gases in coupled quantum wells · michael fogler, martin griswold, aaron hammack, alex...
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Cold exciton gases in coupled quantum wellsLeonid V. Butov
UCSD Physics Department
Introduction● General overview of exciton condensation● Cold exciton gases in coupled quantum wells
Phenomena in cold exciton gases● Condensation, Coherence, and Pattern Formation
Trapping and control of exciton gases● Optical traps ● Electrostatic traps ● Excitonic Circuits
In collaboration with: Michael Fogler, Martin Griswold, Aaron Hammack, Alex High, Jason Leonard, Ekaterina Novitskaya, Averi Thomas, Alex Winbow, Sen Yang (UCSD)Alexei Ivanov, Leonidas Mouchliadis, Lois Smallwood (Cardiff University)
Ben Simons (Cambridge), Leonid Levitov (MIT)Micah Hanson, Arthur Gossard (UCSB)
presentations by
Aaron HammackAlex HighSen Yang
excitonic insulator (BCS-like condensate)
in dense electron-hole system (naBD >> 1)
excitons are similar to Cooper pairs
below Tc electrons and holes bind to pairs –excitons – forming BCS-like condensateL.V. Keldysh, Yu.E. Kopaev (1964)
electron-hole liquid
condensation in real space to electron-hole droplets forming degenerate Fermi gas of electrons and holesL.V. Keldysh (1968)
Bose Einstein condensate
in dilute exciton gas (naBD << 1)
excitons are (interacting)Bose particles similar to hydrogen atoms
below Tc thermal distribution of excitons leads to their condensation in k-spaceL.V. Keldysh, A.N. Kozlov (1968)
n
T
BEC BCS
exciton gas
electron-hole plasma
pairing of fermions
k-spacecondensation of bosons
transition from BEC to BCS can occur with increasing density transition from BEC or BCS to laser can occur with increasing coupling of excitons to photonsP.B. Littlewood, P.R. Eastham, J.M.J. Keeling, F.M. Marchetti, B.D. Simons, M.H. Szymanska, J. Phys. 16, S3597 (2004)
naBD ~ 1
e&h Fermi-surfacesmatched
mismatched
polariton laser
macroscopic occupation of coupled exciton-photon mode
thermal equilibrium is not requiredA. Imamoglu, R.J. Ram, S. Pau, Y. Yamamoto (1996)
Different types of exciton condensate
+_
+_
+_
+_
electron-hole liquid
GeSi
Bose Einstein condensate
Cu2OIndirect excitons in CQW
polariton laser
Microcavity polaritons
Experimental systems
excitonic insulator (BCS-like condensate)
Electron-electron bilayers in high magnetic fields at n =1
1 2
22 ~ 3 K
dB
dBB
n
T nmk
λ
π
−=
=
What temperature is “cold” for exciton gas?1/222dB
Bmk Tπλ
⎛ ⎞= ⎜ ⎟
⎝ ⎠
3D: 1 3
22 32
0.527
dB
dBB
BEC dB
n
T nmk
T T
λ
π
−=
=
=
2D:mexciton ~ 10 -6 matomKelvin 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
estimates for characteristic temperatures for cold 2D Bose gases
nmTMkB
dB 16022/12
≈⎟⎟⎠
⎞⎜⎜⎝
⎛=
πλ
thermal de Broglie wavelength22 3dBB
nT KMkπ
= ≈
λdB is comparable to interexcitonic separation
( )1 0.3
lncS dBT T KnS
= ≈ for N=nS~105
BEC in finite 2D system
for n = 1010 cm-2 per spin state ( < nMott ~ 1/aB2 ~ 1011 cm-2), M = 0.22 m0
at T=1 K
V.N. Popov, Theor. Math. Phys. 11, 565 (1972)D.S. Fisher, P.C. Hohenberg, PRB 37, 4936 (1988)
0 3dBT T K= ≈temperature of quantum degeneracy
( )0 exp 1E dBN T T= = −
Yu.M. Kagan, lecturesW. Ketterle, N.J. van Drutten, PRA 54, 656 (1996)
Kosterlitz-Thouless temperature2
2
ln ln (1 / ) 11 ln ln (1 / )K T d B
n aT T Kn a
≈ ≈+
pairing of vortices =onset of macroscopic superfluidity which is not destroyed by vortices
21 1.7
ln ln(1/ )c dBT T Kna
= ≈
lnln(1/na2)=1–3 for 1/na2=10-108 for lnln(1/na2)=1.5
temperature of onset of local superfluidityBogoliubov temperature onset of nonzero order parameter
2 1dBnλ =
N. Prokof’ev, O. Ruebenacker, B. Svistunov, PRL 87, 270402 (2001)
1
supe
rfuid
den
sity
ns /
n
TBEC=0 TBTKT
A.L. Ivanov, P.B. Littlewood, H. Haug, PRB 59, 5032 (1999)
2
1 0 .6ln ( 4 ) ln ln (1 / )c dBT T K
n aξ π≈ ≈
+
for not so dilute gas
ξ≈380
How to realize cold exciton gas ?Tlattice << 1 K in He refrigeratorsfinite lifetime of excitons could result to high exciton temperature: TX > Tlattice
find excitons with lifetime >> cooling time → TX ~ Tlattice
GaAsAlxGa1-xAs
zE
KE
excitondispersion
2D: coupling of E=0 state to continuum of energy states E > E0effective cooling of 2D excitons by bulk phonons
3D: coupling of E=0 state to single state E=E0exciton energy relaxationby LA-phonon emission
E0=2Mxvs2
~ 0.05 meV
AlAs/GaAsCQW
GaAs/AlGaAsCQW
h
e
h
e
XΓ
TX ~ 100 mKhas been realized experimentally
30 times below TdB
Why indirect excitons in CQW ?
high quality CQW samples with small in-plane disorder are required to overcome exciton localization
103-106 times longer exciton lifetime due to separation between electron and hole layers
103 times shorter exciton cooling timethan 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)
A.L. Ivanov, P.B. Littlewood, H. Haug (1990)
Repulsive interaction between indirect excitons
_
_
+
+
h
e
indirect excitons are oriented dipoles
Dipole-dipole repulsive interactionstabilizes exciton state against formation of metallic electron-hole droplets
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 of the system is excitonic
1.54 1.55 1.56 1.57
PL In
tens
ity
Wex=4 W/cm2
Wex=0.5 W/cm2
Energy (eV)
energy shift: δE ~ 4πne2d/ε → estimate for exciton densityapproximation for short-range 1/r3 interaction
Repulsive interaction in experiment: Exciton energy increases with densityL.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993).
C. Schindler, R. Zimmermann, arXiv:0802.3337 [PRB 78, 045313 (2008)]→ density is higher
presentation byLeonidas Mouchliadis
What is observed when the gas of indirect excitons is cooled ?
Enhancement of exciton scattering rate to low energy statesL.V. Butov, A.L. Ivanov, A. Imamoglu, P.B. Littlewood, A.A. Shashkin, V.T. Dolgopolov, K.L. Campman, A.C. Gossard, PRL 86, 5608 (2001)
Phenomena observed in cold gases of indirect excitons
2 34 5 6
0
4
8
12
0.02
0.04
0.06
0.08
0.10
0.12
Magnetic Field ( T)
τ- 1 ( ns-1
)
Temperature (K)2 3 4 5 6
0
4
812
0.000
0.005
0.010
0.015
0.020
Magnetic Field (T)
τ r-1 ( n
s-1)
Temperature (K)
50 100 150
Modulation of exciton density in ring, formation of ordered exciton stateL.V. Butov, A.C. Gossard, D.S. Chemla, cond-mat/0204482 [Nature 418, 751 (2002)]
800.4 801.0 801.6
Enhancement of the exciton coherence length, beyond classical valueSen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, cond-mat/0606683 [PRL 97, 187402 (2006)].
Enhancement of exciton radiative decay, mobility, emission fluctuationL.V. Butov, A. Zrenner, G. Bohm, G. Weimann, J. de Physique 3, 167 (1993); L.V. Butov, A. Zrenner, G. Abstreiter, G. Bohm, G. Weimann, PRL 73, 304 (1994); L.V. Butov, A.I. Filin, PRB 58, 1980 (1998).
Narrowing of exciton emission linewidthT. Fukuzawa, E.E. Mendez, J.M. Hong, PRL 64, 3066 (1990); J.A. Kash, M. Zachau, E.E. Mendez, J.M. Hong, T. Fukuzawa, PRL 66, 2247 (1991).
Appearance of narrow line(s) in PLA.V. Larionov, V.B. Timofeev, P.A. Ni, S.V. Dubonos, I. Hvam, K. Soerensen JETP Letters, 75, 570 (2002).
Enhancement of polarization degree A.V. Larionov, V.B. Timofeev, J. Hvam, K. Soerensen, JETP 90, 1093 (2000).
before this conference
anticipated phenomenon in the cold exciton gas - exciton BEC
http://physics.ucsd.edu/~lvbutov/ maintained by Aaron Hammack
experimental evidence for phenomena expected for exciton BEC are observed below TdB
enhancement of exciton
consistent with onset ofradiative decay rate superradiance
mobility superfluidity
scattering rate with stimulatedincreasing density scattering
coherence length coherence
Butov et al. PRL 73, 304 (1994) PRB 58, 1980 (1998) PRL 86, 5608 (2001)Sen Yang et al.PRL 97, 187402 (2006)
expected specific properties of exciton BEC:● macroscopic occupation of one state
● macroscopic phase coherence
● exciton superfluidity● bosonic stimulation of exciton scattering
experiment:measurement of the state occupations by spatially and angularly resolved PLexciton condensate superradiance (macroscopic dipole) interference of condensates coherence of emitted light
exciton transport
exciton kinetics
23
45 6
0
4
8
12
0.02
0.04
0.06
0.08
0.10
0.12
Magnetic F ield (T )
τ- 1 (
n s-1)
Temperature (K)
50 100 150
800.4 801.0 801.6
2 3 4 5 6
0
4
812
0.000
0.005
0.010
0.015
0.020
Magnetic Field (T)
τ r- 1 (n
s-1)
Temperature (K)
_
_
+
+
h
e
recombination of excitons tunneling of electrons?
for both: exciton in the initial state, no exciton in the final state
coupled electron and hole layers electron-electron bilayers in high magnetic fields at ν =1
J.P. Eisenstein, A.H. MacDonald, Nature 432, 691 (2004)
2 3 4 5 6
0
4
812
0.000
0.005
0.010
0.015
0.020
Magnetic Field (T)
τ r- 1 ( n
s-1)
Temperature (K)
enhancement of radiative decay rate of excitons
particle-hole transformation1 2 1 2 1 2 1 2
collective electron state exciton condensatee e e hν ν ν ν= + = ⇒ = + =
⇒
I.B. Spielman, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, PRL 84, 5808 (2000)
L.V. Butov, A.I. Filin,PRB 58, 1980 (1998)
collective electron state in QH bilayers at ν=1J.P. Eisenstein, G.S. Boebinger, L.N. Pfeiffer, K.W. West, S. He, PRL 68, 1383 (1992)
enhancement of tunneling rate of electrons
particle –hole transformation implies similarity
exciton superradiance(ξ < λ )
1 2~rτ ξ−
new phenomena which were not anticipated
spatially localized exciton cloud
Butov et al. Nature 417, 47 (2002)
exciton ringsmacroscopically ordered exciton state
Butov et al. Nature, 418, 751 (2002)
pattern formation
new phenomena which were not anticipated
spatially localized exciton cloud (LBS)
Butov et al. Nature 417, 47 (2002)
pattern formation
800.4 801.0 801.6
spontaneous coherenceSen Yang et al.PRL 97, 187402 (2006)arXiv:0804.2686v1
1.24 1.26 1.28
0.02
0.03ν = 5
Gate Voltage (V)
ν = 6
presentation bySen Yang
commensurability of exciton density wave
kinetics of inner ring kinetics of external ring & LBS rings
presentation byAaron Hammack
presentation bySen Yang
presentation bySen Yang
exciton ringsmacroscopically ordered exciton state
Butov et al. Nature, 418, 751 (2002)
Trapping and control of cold exciton gasesoptical traps for excitons
A. Hammack et al.PRL 96, 227402 (2006)PRB 76, 193308 (2007)
A. High et al.Science 321, 229 (2008)
excitonic devicesA. High et al.arXiv:0804.4886v1
cooling, localization, & interaction
1.563 1.567
180 μeV
presentation byAaron Hammack
electrostatic traps for excitons
presentation byAlex High
presentation byAlex High
presentation byAlex High
spin transport of excitons
J.R. Leonard et al.arXiv:0808.2402v1
external ring
ring fragmentation localized bright spots
Pattern Formation
same
exciton state with spatial order on macroscopic lengths –
Macroscopically Ordered Exciton State (MOES)
0 100 200 300 400 5000
0 20 400
400
800
Posi
tion
on th
e rin
g (μ
m)
Peak number
PL in
tens
ity
position on the ring (μm)
inner ring
L.V. Butov, A.C. Gossard, and D.S. Chemla, cond-mat/0204482 [Nature 418, 751 (2002)]
410 μm
Temperature dependence of ring fragmentation
ring fragmentation into spatially ordered array of beads appears abruptly at low T
T=4.7 K
0 2 4 60Ampl
itude
of t
heFo
urie
r Tra
nsfo
rm
T (K)
T=1.8 K
low-T phenomenonobserved below a few Kwhere exciton gas is degenerate
high-T phenomenaobserved up to tens of Kwhere exciton gas is classical
their origin is classical
● inner rings ← exciton transport and coolingL.V. Butov, A.C. Gossard, and D.S. Chemla, cond-mat/0204482 [Nature 418, 751 (2002)]A.L. Ivanov, L. Smallwood, A. Hammack, Sen Yang, L.V. Butov, A.C. Gossard, cond-mat/0509097 [EPL 73, 920 (2006)]
● external rings and LBS ← in-plane charge separation L.V. Butov, L.S. Levitov, B.D. Simons, A.V. Mintsev, A.C. Gossard, D.S. Chemla, cond-mat/0308117 [PRL 92, 117404 (2004)]R. Rapaport, G. Chen, D. Snoke, S.H. Simon, L. Pfeiffer, K.West, Y.Liu, S.Denev, cond-mat/0308150 [PRL 92, 117405 (2004)]
observed features in exciton PL pattern ● inner ring● external ring● localized bright spots● MOES
presentation by Sen Yang
presentation by Aaron Hammack
presentation by Sen Yang
high T low T
external ring is far from hot excitation spotdue to long lifetimes of indirect excitons TX ≈ Tlattice
external ring is the region where the cold and dense exciton gas is created
macroscopically ordered exciton state
localized bright spots have hot cores
no hot spots in the ring
indirect exciton PL direct exciton PL – pattern of hot spots
Coherence
presentation by Sen Yang
Probe of spontaneous coherence (not driven by laser excitation)
left arm
right arm
Spontaneous coherence for the MOES ?far from laser in space and in energy: coherence is spontaneous
experimental method:Mach-Zehnder interferometrywith spatial and spectral resolution
Sen Yang, A. Hammack, M.M. Fogler, L.V. Butov, A.C. Gossard, cond-mat/0606683 [PRL 97, 187402 (2006)].
2 4 6 8 100
1
2
3
0800.4 801.0 801.6
2 4 6 8 10
0.1
0.2
0.3
0 10 20 300.1
0.2
0.3
Coh
eren
ce L
engt
h (μ
m)
Temperature (K)
Inte
rfer
ence
Vis
ibili
ty
PL C
ontr
ast a
long
the
Rin
g
Temperature (K) Mξ (μm)
a condensate in k-space
Emergence of spontaneous coherence of excitons at low temperatures
2 (1) ( )
~ 1
ikn d re g r
kδ ξ
−= ⋅
⋅∫ kr
ξ ~ 2 μm → spread of the exciton momentum distribution δk ~ 104 cm-1
is much smaller than that for a classical exciton gas 5 1~ 2 ~ 3 10 cm at 2cl Bk mk T T Kδ −× =
an enhancement of the exciton coherence length is observed at temperatures below a few Kelvin
the increase of the coherence length is correlated with the macroscopic spatial ordering of excitons
at T=2 K the exciton coherence length ξ ~ 2 μm strongly exceeds the classical value ~ λdB ~ 0.1 μm
0 100 2000
9.1 K
3.8 K
2.2 K
800 8020
9.1 K3.8 K2.2 K
x (μm)
PL in
tens
ity
Wavelength (nm)
Puzzle of broad linewidth
800 8020
9.1 K3.8 K2.2 K
Wavelength (nm)
Δ ~ 1.2 meV
2
2
~ 2 μm phase-breaking time
~ a few ns
for ~ 10 cm s
D
Dφ
ξ
τ ξ
⇒
=inverse
linewidth~ 1 pscτ
⇒
?~ 40 nsrecτ
indirectexcitons in CQW
polaritons in MC
spatial correlation measurementsusing a Michelson interferometer
J. Kasprzak et al., Nature 443, 409 (2006)
Sen Yang et al, cond-mat/0606683 [PRL 97, 187402 (2006)]
broad linewidth for polariton condensate above threshold suggested explanation: due to density fluctuations D.N. Krizhanovskii et al, this conference
I.B. Spielman, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, PRL 84, 5808 (2000)e-e bilayers
width of tunneling peak Δ > kBT
2 4 6 8 100
1
2
3
10
Coh
eren
ce L
engt
h (μ
m)
Temperature (K)
1Q
1
DM
@ L. Mouchliadis, A. L. Ivanov, arXiv:0802.4454 [PRB 78, 033306 (2008)]* M.M. Fogler, Sen Yang, A.T. Hammack, L.V. Butov, A.C. Gossard, arXiv:0804.2686 [PRB 78, 035411 (2008)]
NA=sinα
22
1x Q
ξ ξ= +
ξ optical coherence length
ξx exciton coherence length
Effect of finite spatial resolution
01 Abbe limit2Q NA
λπ π
= =
Finite spatial resolution * = k-filtering effect @
spatial resolution
without taking into account spatial resolutiontaking into account spatial resolution
What we know about the macroscopically ordered exciton state
observed in external ring● on interface between hole-rich area
and electron-rich area
observed in a cold exciton gas● at low temperatures below a few K● in a system of indirect excitons● in the external ring far from hot excitation spot
MOES is a state with:● macroscopic spatial ordering● large coherence length → a condensate in k-space
spread of the exciton momentum distribution is much smaller than that for a classical exciton gas
characterized by repulsive interaction(→ not driven by attractive interaction)
_
_
+
+
h
erepulsive interaction of oriented dipolesSen Yang et al., PRB 75, 033311 (2007)
0 2 4 60
Am
plitu
de o
f the
Four
ier T
rans
form
T (K)not observed for inner ring
instability requires positive feedback to density variations
instability can result from quantum degeneracy in a cold exciton system due to stimulated kinetics of exciton formation
Theoretical model for MOES consistent with the experimental observations
2
2
2
ee e e h e
hh h e h h
XX X e h X opt
n D n wn n Jt
n D n wn n Jt
n D n wn n nt
τ
∂= ∇ − +
∂∂
= ∇ − +∂
∂= ∇ + −
∂
L.S. Levitov, B.D. Simons, L.V. Butov, PRL 94, 176404 (2005)
22
0~ 1dB x
B
T nmgk TT
Ew N e eπ
=+ = =
Trapping and control of cold exciton gases
● with laser light
● with laterally modulated gate voltage
Excitonic devices
presentation byAaron Hammack
methods which allow fast controlon timescale much shorter than exciton lifetime
Laser induced traps for excitons
100 μm
x
E
laser laser
trap ● can be switched on and off● no heating in the trap center→ excitons are cold in the trap
● ability to form various potential patterns
low density
high density
A. Hammack, M. Griswold, L.V. Butov, A.L. Ivanov, L. Smallwood, A.C. Gossard, cond-mat/0603597 [PRL 96, 227402 (2006)]
experimentalimplementationof this idea
trap profile
Exciton collection to the laser induced trap
Vg = -1.2 VPex = 75 µW
δ = 4 ns
x
y50
(ns)
experiment theory
PL in excitation ringPL at trap center
observed hierarchy of times (exciton cooling time) < (trap loading time) < (exciton lifetime in the trap)
is favorable for creating a dense and cold exciton gas in the traps and its control in situ
τlifetime ~ 50 ns – 10 μsτloading ~ 40 nsΤcooling to 1.5 K < 4 ns
A. Hammack, L.V. Butov, L. Mouchliadis, A. L. Ivanov A.C. Gossard, PRB 76, 193308 (2007)
Trapping and control of cold exciton gases
● with laser light
● with laterally modulated gate voltage
Excitonic devicespresentation byAlex High
methods which allow fast controlon timescale much shorter than exciton lifetime
potential energy of indirect excitons can be controlled by an applied gate voltage
the ability to control electron fluxes by an applied gate voltage
electronic devices mesoscopicsthe field which concerns electron transport in a potential relief
virtually any in-plane potential reliefcan be created for excitons by the appropriately designed voltage pattern, e.g. traps, quantum point contacts, lattices
this relief can be rapidly controlled in-situby varying the electrode voltages zE eF dδ =
the ability to control exciton fluxes by an applied gate voltage
excitonic devices mesoscopics of bosons in semiconductors
no exciton dissociation
r ex exeF a E<<
CQW far from top gate reducesin plane field, Fr
First electrostatic traps for indirect excitonsS. Zimmermann, A. Govorov, W. Hansen, J. Kotthaus, M. Bichler, W. Wegscheider, PRB 56, 13414 (1997)T. Huber, A. Zrenner, W. Wegscheider, M Bichler. Phys. Stat. Sol. (a) 166, R5 (1998)
Experimental obstacle in early works → in-plane electric field dissociated excitons
Solution: to position CQW layers closer to the homogeneous bottom electrode1999 – calculations2005 – experimentA.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, cond-mat/0504045 [JAP 99, 066104 (2006)]
dissociation rate vs Fr
D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood, C.A. Burrus, PRB 32, 1043 (1985)
A.G. Winbow, A.T. Hammack, L.V. Butov, and A.C. Gossard, Nano Letters 7, 1349 (2007)A.G. Winbow, L.V. Butov, and A.C. Gossard, arXiv:0807.4920v1
prototype of storage device reaches sub-ns switching time and several μs storage time
Photon storage
store photons in the form of indirect excitons
storage and release of photons is controlled by gate voltage pulses
source
draingate
ONOFF5 μm
Exciton Optoelectronic Transistor (EXOT)
photon input photon outputelectronic control
prototype of EXOT reaches a contrast ratio > 30 between ON and OFF state with operation at speeds > 1 GHz
7.0 7.50
τ~160 psτ90/10~400 ps
Time (ns)x
exciton flow is on
exciton flow is off
Gate
QWs
n
i
photonicsource
photonicdrain
opticalinputgate
opticaloutputgate
Exci
ton
ener
gy
energy bump controlled by the Gate
similar in geometry and operation to electronic FET
0
1
0 20Distance (μm)
Inte
nsity
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)
excitons in the trap
10 μm1
2 3
g1
g2 g3
4image of gates
excitonic circuits perform operations on excitons that can be also viewed as operations on photons using excitons as intermediate media
both paths openleft path openright path open
two paths open one path openthree paths open
Poutput=Pleft+PrightPoutput=PrightPoutput=Pleft
Directional SwitchFlux of excitons photoexcited at is directed by gate control.
Star SwitchFlux of excitons photoexcited at is directed by gate control.
Flux mergerTwo fluxes of excitons photoexcited at are combined by gate control. The device can implement sum operation and logic AND gate with 1 set at Poutput=Pleft+Prightand 0 at Poutput<Pleft+Pright
Control of Exciton Fluxes. Excitonic circuits.
0 20
left+rightleftright
left onright onleft offright off
l, μm
Inte
nsity
directional switch
flux merger
0
1
0
1
0
1
A.A. High, E.E. Novitskaya, L.V. Butov, M. Hanson,A.C. Gossard, Science 321, 229 (2008)
Application of electrostatic traps formed by laterally modulated gate voltage
● cooling
● localization
● interactionpresentation byAlex High
Elevated trap cooling
Photoexcited hot excitons lose kinetic energy as they travel up potential energy hill → cooling of excitons
Trap at potential energy that is higher than potential energy at excitation
E
x
laser laser
Evaporative coolingExcitons with higher energy easier escape trap. This increases relative occupation of lower energy states → cooling of exciton gas
A.T. Hammack, N.A. Gippius, Sen Yang, G.O. Andreev, L.V. Butov, M. Hanson, A.C. Gossard, cond-mat/0504045 [JAP 99, 066104 (2006)]
Cooling excitons beyond temperature, which can be reached by phonon cooling
somehow similar to Sisyphus cooling used to cool atoms below the Doppler limit
0 50 1000.1
1
Time (ns)
T (K
) ~ 100 phononT mK
~ 3dBT K<<
1.548 1.552
1.564 1.568
1.563 1.567
12
34
e
h
s1
s2 s3
g1
g2 g3
t
10 μm
Energy (eV)
PL In
tens
ity-5 0
1.52
1.56
Ener
gy (e
V)
Electrode Voltage (V)
yx
real trap
elevated trap
Using elevated trap for studying individual exciton states in disorder potentialdisorder is an intrinsic feature of CM materials
in-plane disorder potential in QWs forms mainly due to QW width and alloy fluctuations
emission of individual exciton states localizedin local minima of disorder potential (2-4)and delocalized exciton states (1)
E
xintermediate regime
180 μeV
0
1
Et - Eg (meV)
I 2/I 1
sharp lines emerge at the transition from the real trap to elevated trap
elevated trap technique
( )introduce effective temperature
~ expdeloc loc B
T
n n k Tδ ε= −
( )'cooling efficiency'
1 1 lnnorm elev
elev norm BT T k
γ δ δ
ε γ
=
= +
1 1 1
estimate: rate equations1 , +
is small for DX can be large for IX
esc loc optγ τ τ τ τ τ
γγ
− − −
⇒
= + =
-10 0 10 200
1
real trap elevated
trap
real trap elevated trap
t surr
t surr
E EE E
<
>
experiment: ~ 10; ~ 10 ;
~ 3 ~ 1.8B
norm elev
k K
T K T K
γ ε
⇒
A.A. High, A. T. Hammack, L.V. Butov, L. Mouchliadis, A. L. Ivanov, M. Hanson, and A.C. Gossard, arXiv:0804.4886v1
0 100.0
2.5
-0.7 -0.51.560
1.5671.562 1.567 1.562 1.568
Inte
nsity
(arb
. uni
ts)
Temperature (K)
I 2/I1
Ene
rgy
(eV)
Trap voltage (V)
4
321
4 3 2
Energy (eV)
1
Inte
nsity
(arb
. uni
ts)
2.7K
4.5K
5.1K
7.0K
T=10K
1x
2x
2x
2x
2xVt= -.70V
-.65V
-.60V
-.55V
-.50V
2 1
Energy (eV)relative intensity of lines 2-4 in the elevated trap regime reduces with increasing Tbath
nominal10.7 d nm d≈ ≈
zE eF dδ =
0
600
1200
1800
sum
hom
inhom
0.0 0.5 1.00
100
200
sum
elastic
inelastic
1.562 1.569
1234
1140 μW
470 μW
150 μW
36 μW
9.1 μW
1.65 μW 450x
60x
38x
9x
2x
1x
200
800
1400
1.565
1.566
1.567
100 101 102 103
102
103
104
105
108 7x1092x109
FWHM
(μeV
)
8 μm
1.562 1.569
yE
Pex (μW)Energy (eV)Energy (eV)
PL
Inte
nsity
Ener
gy (e
V)
n (cm-2)
200
800
1400
n (1010 cm-2)
FWHM
(μeV
)FW
HM (μ
eV)
FWHM
(μeV
)
loc
deloc
deloc
loc
(1) Energy increases due to repulsive ex-ex interaction.
(2) Intensity saturates: no more than one exciton can occupy potential minimum due to dipole blockade
(3) Disorder potential is effectively screened due to ex-ex interaction.
(4) Homogeneous broadening due to ex-ex interaction increases with density and dominates thelinewidth at high densities.
(5) Homogeneous broadening is lower for localized excitons. Localization suppresses scattering.
Density dependence
(1)
(2)
(3)
(4)
(5)
exp theory
3 μm circle trap 20 μm circle trapCircle Trap
•single electrode trap•potential parabolic for small radii (<3μm)•potential box-shaped for large radii
Concentric Rings Trap
•Multiple electrodes allow versatile shaping of radially symmetric potential profile
Diamond-shaped traps
Diamond-Shaped Trap•Single electrode creates parabolic trapping potential even for large lengths •can collect many excitons to the trap center•can be operated by a single electrode
20 μm diamond trap
Conical Trap Elevated Trap
Hammack et al., J. Appl. Phys. 99, 066104 (2006).
D
D
Distance from trap center (μm)
Distance from trap center (μm)
Ener
gy (m
eV)
low density high densityx (μm)
Elevated Diamond Trap: Density Dependence
Exciton spin transport
J.R. Leonard, Sen Yang, L.V. Butov, A.C. Gossard, arXiv:0808.2451v1
he
S z
23
,21
1
−+
−=
he
S z
23,
21
1
+−
+=
he
S z
23
,21
2
++
+=
he
S z
23
,21
2
−−
−=
τex
τh
τeτe
+σ−σ
τr τr
<P>
(%)
10
0
0 5 10
<τp>
(ns)
0
5
Tbath (K)
10Tbath (K)
0
10
c
τex is short for direct excitons → fast spin relaxation
due to small exchange interactionτex is much larger for IX
long spin relaxation time for IX
+ long-range transport of IX
spin transport of IX
τp is large
τp drops with T
1000Pex (μW)
0.5
0
<P>
(%)
1 10 100 1000Pex (μW)
10
30 a
<τp>
(ns)
0
5
15
1 10 100nr=0 (109/cm2)
b
r clo
ud(μ
m)
0
10
20
1 10 100
c
P HW
HM (%
)
0
10
30
0 10 20rcloud (μm)
0 10 20rcloud (μm)
1
P HW
HM/ P
max e
d
10
20
20
τp drops with n
ltravel increases with n
polarization is observedup to several μm away from the excitation spot
↨spin transport of excitons
( ) 11 1
emission polarization
polarization relaxation time
2
1
p
p r
p e h ex
p r
P
PP
ττ τ
τ τ τ τ
τ τ
−− −
=+
= + +
=−dark states
optically active states
Status of experiments on cold excitons in CQW nanostructures
● Cold exciton gases with T << TdB were realized experimentally
● Experimental evidence for phenomena expected for exciton BEC was observed below TdB :
● A new low-temperature state – the macroscopically ordered exciton state was observed
enhancement of exciton
consistent with onset of
● radiative decay rate superradiance
● mobility superfluidity
● scattering rate with stimulated increasing density scattering
● coherence length spontaneous coherence
PRL 73, 304 (1994) PRB 58, 1980 (1998)
PRL 97, 187402 (2006)
Nature 418, 751 (2002)
23
4 56
0
4
8
12
0.02
0. 04
0. 06
0 .08
0 .10
0.12
Ma g
net ic Fi eld (T)
τ-1 (n
s-1)
Te mp era ture (K)
23
45
6
0
4
812
0.000
0.005
0.010
0.015
0. 020
Mag net ic F
i eld (T)
τ r-1 ( ns- 1 )
Tempe rat ure (K)
50 100 150
800.4 801.0 801.6
PRL 86, 5608 (2001)
Status of control of excitons● Trapping of excitons in laser induced traps was demonstratedObserved hierarchy of times is favorable for in situ control of cold exciton gases
● Excitonic storage device was demonstratedPrototype reaches ns switching time and several μs storage time
● Exciton optoelectronic transistor (EXOT) was demonstratedPrototype performs switching with contrast ratio > 100 between ON and OFF state with operation at speeds > 1 GHz.
● Simple excitonic integrated circuits (EXIC) were demonstratedPrototype performs operations with exciton fluxes such as directional switching and merging
For building devices operating with excitons in place of electronsThe direct coupling of the photons, used in communication, to excitons, used as the device operation media, may lead to the development of efficient optoelectronic devices that utilize excitons
For studying physics of cold excitons –cold bosons in CM materials
Possible future applications for control of excitons
cooling loading recτ τ τ<< <<
ONOFF
Application: Traps were used for studying individual exciton states in disorder potential
Nano Lett. 7, 1349 (2007)
PRL 96, 227402 (2006)PRB 76, 193308 (2007)
1.563 1.567
Science 321, 229 (2008)
arXiv:0804.4886v1
Acknowledgements
supported by ARO, NSF, DOE
UCSD Group:Aaron Hammack Alex HighJason Leonard Mikas RemeikaAlex WinbowSen YangMartin GriswoldJames LohnerKatya NovitskayaAveri ThomasJoe Graves
Visiting scientists:Nikolai GippiusAnton Mintsev
Collaborators:Gerhard Abstreiter, WSI, GermanyDaniel Chemla, UCB&LBNLValerii Dolgopolov, ISSP RASAlexander Dzyubenko, CSBMichael Fogler, UCSDArthur Gossard, UCSBAtac Imamoglu, UCSBAlexei Ivanov, Cardiff University, UKLeonid Levitov, MITPeter Littlewood, Cambridge, UKYuri Lozovik, IS RASBen Simons, Cambridge, UKArthur Zrenner, WSI, Germany