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CollisionCollision--induced processesinduced processeswith superwith super--cooled excitonscooled excitons
Makoto Makoto KuwataKuwata--GonokamiGonokami
Department of Applied Physics, University of TokyoDepartment of Applied Physics, University of TokyoSORST, Japan Science and Technology Agency (JST)SORST, Japan Science and Technology Agency (JST)
http://www.gono.t.uhttp://www.gono.t.u--tokyo.ac.jptokyo.ac.jp
The 10The 10thth USUS--Japan Joint Seminar Japan Joint Seminar –– Fundamental Issues and Fundamental Issues and ApplocationsApplocations of Ultracold and Molecules of Ultracold and Molecules --
1.1. Introduction Introduction 2.2. Excitation and detection of cold excitons in CuExcitation and detection of cold excitons in Cu2OO
Direct excitation of Direct excitation of supersuper--cooledcooled excitons byexcitons by pulsed twopulsed two--photon photon resonant excitation of 1sresonant excitation of 1s--ortho excitons ortho excitons Collision induced Collision induced orthoortho to to parapara transformationtransformation
3.3. QuasiQuasi--steady state excitonic Lyman spectroscopy steady state excitonic Lyman spectroscopy ParaexcitonsParaexcitons at quasiat quasi--equilibrium conditionequilibrium conditiondetected by CW detected by CW excitonicexcitonic Lyman spectroscopy with COLyman spectroscopy with CO22 laserlaser
Evaluation of densityEvaluation of density--dependent particle lossdependent particle loss4. Future Prospects4. Future Prospects
OutlineOutline
CoworkersCoworkers
AcknowledgementAcknowledgementN. Naka (Univ. Tokyo)
R. Shimano (Univ. Tokyo)
M. Kubouchi(Univ. Tokyo)
K. Yoshioka(Univ. Tokyo)
A. Mysyrowicz (ENSTA,Ecole Polytechnique, France)
Y. Svirko(Joensuu Univ.Finland)
T. Tayagaki(Univ. Tokyo)
T. Ideguchi(Univ. Tokyo)
BEC of ExcitonsBEC of Excitons
87Rb:Cu2O 1s-exciton:
~105×me
~3×me
mass Tc
10-7 K
1.9 K
nc
~1012 cm-3
1017 cm-3
2 / 32
cB
2 nTmk 2.612π ⎛ ⎞= ⎜ ⎟
⎝ ⎠h
quasi Bose particles
electron(s=1/2)
hole(s=1/2) h
e
heh
e
Excitons in Semiconductors
excitonphoton
Small mass (less or comparable with the free electron) →high TcDensity is easily controlled by light: boson-fermion crossover
biexciton
1960
1970
1980
1990
2000
L. V. Keldysh and A. N. Kozlov, Sov. Phys. JETP 27, 521 (1968).R. C. Casella, J. Phys. Chem. Solids 24, 19 (1963).S. A. Moskalenko, Fiz. Trerd. Tela. 4, 276 (1962) [Sov. Phys. Solid State 4, 199 (1962)].I. M. Blatt, K. W. Böer, and W. Brandt, Phys. Rev. 126, 1691
Theoretical PredictionTheoretical Prediction
Early Experiments on CuEarly Experiments on Cu22OO
D. Hulin, A. Mysyrowicz, and C. Benoît à la Guillaume, Phys. Rev. Lett. 45, 1970 (1980).Bose statistics of Cu2O orthoexcitons
D. Snoke, J. P. Wolfe, and A. Mysyrowicz, Phys. Rev. Lett. 59, 827 (1987).Quqntum saturation of Cu2O orthoexcitons
D. W. Snoke, J. P. Wolfe, and A. Mysyrowicz, Phys. Rev. B 41, 11171 (1990).BEC of Cu2O paraexcitons
T. Fukuzawa, E. E. Merdez, and J. M. Hong, Phys. Rev. Lett. 64, 3066 (1990).Phase transition to ordered state of indirect excitons in coupled quantum well
E. Fortin, E. Benson, and A. Mysyrowicz, Phys. Rev. Lett. 70, 3951 (1993). Excitonic superfluidity in Cu2O
Rb,Na BEC(95)
History of exciton BECHistory of exciton BEC
biexciton BEC in CuClbiexciton BEC in CuCl
Atom BECAtom BEC
Finite life timethermal relaxation versusrecombination lifetimekBTc versus η/τlife excitation
diffuse
excitation
hot excitons
Heating photo excitationnonradiative recombination
Open systemdiffusion of exciton
lifeτ relaxτRadiativedecay
Interaction withphonon
Difficulties in Exciton BECDifficulties in Exciton BEC
1s-excitons: electric dipole transition forbidden2Γ6
+x 2Γ7+ xΓ1
+=3Γ5++Γ2
+
Γ5+ orthoexciton: electric quadrupole transition allowed
Γ2+ paraexciton: pure spin-triplet
→ optical transition is strictly forbidden,extremely long life time
Γ6+
Γ7+
valence
conduction
Γ8+
2.17eV
Excitons in CuExcitons in Cu22OO
Yellow-series exciton
yex g 2
RE E
n= −
Cu2O (4.2K)
n 2= 3 4e e,↑ ↓
H H,↑ ↓
Cu 3-d
Cu 4-s
10 secnτ =
τ=10μsec
( 0 sec)30rad nτ >
Paraexcitons in CuParaexcitons in Cu22OO
e H1:zJ = ↑ ↑
( ) ( )
( ) ( )
H h h
H h h
1 yz zx xy3
1 yz zx xy3
i
i
⎡ ⎤↑ = − + ↓ + ↑⎣ ⎦
⎡ ⎤↓ = − − ↑ − ↓⎣ ⎦
note;
( ) ( ) ( )e H e H e h e h e h e h1 yz zx yz zx xy3
i i⎡ ⎤↑ ↓ − ↓ ↑ = − − ↑ ↑ − + ↓ ↓ − ↑ ↓ + ↓ ↑⎣ ⎦
J=1: ortho J=0: para
( )e H e H10 :2zJ = ↑ ↓ − ↓ ↑
G. M. Kavoulakis, Yia-Chung Chang, and Gordon Baym, Phys. Rev. B 55, 7593 (1997).
( )
( ) ( )
ex
22 , * , d d3
E K
eε∞
Δ
′ ′ ′= Ψ Ψ′−∫ K Kx x x x x x
x x
paraortho
K
E
ΔEex(K=0)=12meV
electron-hole exchange interaction
Para exciton state is purely spin-triplet state-> no direct optical processes
(Γ5+) (Γ2
+)he
he
( )e H e H10 :2zJ = ↑ ↓ + ↓ ↑
e H1:zJ = − ↓ ↓
D. W. Snoke et al., Phys. Rev. Lett. 59, 828 (1987).
Phonon-assisted luminescence spectrum of orthoexciton (Xo-Γ3
-) are well fitted with Bose-Einstein distribution function
Experiments in CuExperiments in Cu22O so far: luminescence spectrum analysisO so far: luminescence spectrum analysis
However, orthoexcitons remain in normal region.
Paraexciton BEC ?
BEC
How to detect optically forbidden paraexcitons?How to detect optically forbidden paraexcitons?
D. W. Snoke et al., Phys. Rev. B 41, 11171 (1990).
Very weak luminescence of paraexcitons.ηXo-Γ3 : ηXp-Γ5~ 500:1
ortho
paraDetailed quantitative analyses forintrinsic and extrinsic processes are necessary to measure the number of excitons.
Phys. Rev. B 42,7876 (1990).Paraexcitons were
detected by field ionization (Schottky barrier) .
E. Fortin, E. Benson, and A. Mysyrowicz, Phys. Rev. Lett. 70, 3951 (1993).
Ballistic transport of paraexcitons: super fluidity ?
Spectroscopic information was lost.
1) Luminescence spectrum can be reproduced by MB distribution with spatial inhomogeneity : not BE statistics
2) TA-phonon mediated ortho-para conversion rate:τo-p=3 ns (T=2 K)
→ too slow conversion rate to accumulate paraexcitons
3) Large Auger recombination rate(nonradiative two-body decay)
A=10-16cm3/ns : Excitons decay before reaching the critical density nc=1017 cm-3
K. E. O’Hara and J. P. Wolfe, Phys. Rev. B 62, 12909 (2000).
2ddn Ant
= −
Objection to exciton BEC in CuObjection to exciton BEC in Cu22OO
Quantitative analysis of luminescence measurement
No BEC of ortho nor paraexcitons!
he
he
h
e ionization due to recombination energy
e
h
MB
BE
h
e
J. I. Jang et al. Phys. Rev. B 70, 195205 (2004).
Probing 1s-2p induced absorption• electric dipole transition allowed
for both ortho- and spin-triplet para-excitons• distinguish paraexcitons from
orthoexcitons• m1s >m2p → induced absorption
spectrum reflects the distribution of excitons
Optical detection of paraexcitons by 1sOptical detection of paraexcitons by 1s--2p transition2p transition
Our approach:Time resolved Excitonic Lyman Spectroscopy
K
2.7m0
E1.7m0
n(E) , Δα
2p2p--orthoortho
2p2p--parapara
1s1s--orthoortho
1s1s--parapara
ωh
Exchange energyExchange energy
J. Phys. Soc. Jpn. 73, 1065 (2004).Solid State Comm.134, 127 (2005).Phys. Rev. Lett. 94, 016403 (2005).
Theoretical Prediction;H. Haken, Fortschr. Phys. 38, 271 (1958).S. Nikitine, J. Phys. Chem. Solids 45, 949 (1984).K. Johnsen and G.M.Kavoulakis, Phys. Rev. Lett. 86, 858 (2001).
CW probe experiments; (1) M. Jorger & C.Klinghirn, (2) K. Karpinska & P.H.M. von Loosdrecht (Groningen)
Evaluation of Exciton density from 1sEvaluation of Exciton density from 1s--2p induced absorption2p induced absorption
( )( ) ( )2, ,ex b exn E N N Eε χ= + %%
( ) ( )
2
1 21 22 2
0 1 2
2, s ps p
ex exs p
EN E N
E E i E
μχ
ε−−
−
= ⋅− − Γ
%
( ) ( ){ }1 Im ,exb
EE N Ec
α χε
Δ = %h
( )2
1 2 1 2
0
s p s pex
b
ES E dE N
c
π μα
ε ε− −≡ Δ = ⋅∫ h
02
1 2 1 2
bex
s p s p
cN S
E
ε ε
π μ− −
= ⋅h
S
SampleSample
Cu2Onaturaly grown single crystal3×5mmThickness 200 μm
phonon
Mid-infrared linear absorption spectrum
transparent window near 1s-2p transition!
6
4
2
0
αl
160140120100energy [meV]
13 12 11 10 9 8wavelength [μm]
Ortho1s-2p
Para1s-2p
phonon
αL
energy [meV]
Ti:Sapphire Regen.(1 kHz, 150 fs)
OPA + DFG(AgGaS2, GaSe)
OPA +SHG(BBO)
delay
pinhole
Sample (liq.He)
probe:~10 μm
pump:1220 nm, 600 nm(widht;14meV, 2μJ)
chopper
monochromator
HgCdTe detectordelay
λ/2@1220nm
PC
PD
I/O Boxcar Integrator
trigger
Spot size;300μmφ
Experimental setup : midExperimental setup : mid--infrared pumpinfrared pump--probe spectroscopyprobe spectroscopy
120
100
80
60
40
20
0
Δα (c
m-1
)
130120110Energy (meV)
-10 ps
10 ps
30 ps
200 ps
800 ps
Induced absorption spectra Induced absorption spectra byby oneone--photon (photon (orthoexcitonorthoexciton--phononphonon--sideband) excitationsideband) excitation
paraortho1) Strong signal at para exciton resonance.2) Spectrum narrowing with time.3) Red shift of the absorption maximum.
excitation
Initially hot excitons
Tex>>Tlattice
Thermalizationwith lattice
Two-photon electric dipole transition of orthoexcitons is allowed.
Γ4−xΓ4
−=Γ1++Γ3
++Γ4++Γ5
+
orthoexcitons ko~ 0
1s ortho
1s para
KInstantaneous preparation of Quantum degenerate ortho-excitons
Phase space compression of laser photonsby resonant two-photon excitation
M. Kuwata-Gonokami, et al., J. Phys. Soc. Jpn., 71, (2002) 1257
Large phase space density of photons in ML-fs laser
76MHz repetition, δλ 2nm, 1mWPhoton number per mode; 500nν =
Direct excitation of cold orthoexcitons by TPADirect excitation of cold orthoexcitons by TPA
No peak shift -> No excess heating
cold distribution around K=0
Tex< TlatticeNortho~1015 cm-3
Ortho;1s-2p
excitation
Ortho;1s-3p
Para;1s-2p
Rapid production of paraexcitons
100
75
50
25
0
Δα
(cm
-1)
135130125120115Energy (meV)
20 ps
200 ps
400 ps
800 ps
Resonant twoResonant two--photon excitation of orthoexcitonphoton excitation of orthoexciton
12345
200
2
2
0
Δα(c
m)
135130125120115Energy (meV)
400
300
α(c
m-1
)
217021652160215521502145Energy (meV)
6
4
0ττdelaydelay== 4 4 nsns 11ss--2p para2p para
4.2 4.2 KK
12 12 meVmeV
11ss--2p2p11ss--3p3p
11ss--4p4p
11ss--5p5p
2p2p 3p3p 4p4p 5p5p
KK
12 meV12 meV
EE
2p2p
1s1s--orthoortho
1s1s--parapara
22ωω=2033 meV=2033 meV
3p3p4p4p npnpττdelaydelay=5 ps=5 ps orthoortho--excitonexciton
129 129 meVmeV 116 116 meVmeV
129 129 meVmeV
Low density regime: Low density regime: NNexex<10<101515 cmcm--33
Observation of Excitonic Lyman seriesObservation of Excitonic Lyman series
6
5
4
3
2
1
0T
(K)
2 3 4 5 60.1
2 3 4 5 6
Time (ns)
Cu2O4.2 K
n~10n~101515
6420
Δα(c
m-1) 11ss--2p2p 11ss--3p3p
11ss--4p4p
135130125120115Energy (meV)
BoltzmannBoltzmann fittingfittingSuper cooled stateSuper cooled state
4.2 K
ThermalizationThermalization dynamics of superdynamics of super--cooled 1s orthoexciton (4.2K)cooled 1s orthoexciton (4.2K)
8
6
4
2
0
Δα (c
m-1
)
135134133132Energy (meV)
50 ps
800 ps
400 ps
200 ps
T=4.2 K
((ΔΔEE1s1s--4p4p))22~(~(γγ4p4p))22+ ((+ ((mm1s1s//mm44pp--1)1)ff1s1s))22
Line shape analysis:Line shape analysis:
20
15
10
5
0
Δα (c
m-1
)
135130125120115Energy (meV)
20 ps
400 ps
1.6 ns
800 ps
20
15
10
5
0
Δα (c
m-1
)
135130125120115Energy (meV)
20 ps
400 ps
1.6 ns
800 ps
20
15
10
5
0
Δα (c
m-1
)
135130125120115Energy (meV)
20 ps
400 ps
1.6 ns
800 ps
1.0
0.8
0.6
0.4
0.2
0.0
n ex
(cm
-3)
1.61.41.21.00.80.60.40.20.0
Time (ns)
total exciton
orthoexciton
paraexciton
Extraction of orthoExtraction of ortho--para conversionpara conversion
nex(t~0)= 8x1014 cm-3
• Total exciton density conserves
OrthoOrtho--parapara conversion: conversion: ττoo--pp=3 ns=3 nsTA-phonon assisted spin transformation
1.8 K
:Nonlinear ortho-to-paraexciton conversion
:: Linear orthoLinear ortho--para conversion: para conversion: ττoo--pp=3 ns=3 ns
100
75
50
25
0
Δα
(cm
-1)
135130125120115Energy (meV)
20 ps
200 ps
400 ps
800 ps100
75
50
25
0
Δα
(cm
-1)
135130125120115Energy (meV)
20 ps
200 ps
400 ps
800 ps
ortho1s-2p
1s-3p 1s-4p
100
75
50
25
0
Δα
(cm
-1)
135130125120115Energy (meV)
20 ps
200 ps
400 ps
800 pspara1s-2p
n(t~0)~4x1015 cm-31.8 K
Temporal evolution of excitonsTemporal evolution of excitons;;High density excitationHigh density excitation
5
4
3
2
1
0
n (1
015cm
-3)
0.80.60.40.20.0
Time (ns)
G. M. Kavoulakis and A. Mysyrowicz, Phys. Rev. B 61, 16619 (2000).
2ddn Cnt
= −
p p
-p
kk
-k
q
-p-q
-k-q
Collision induced Collision induced orthoortho--parapara conversionconversion
16 35 10 /C cm ns−≈ ×
Temporal evolution of nTemporal evolution of northoortho, n, nparapara, , nntotaltotal
0
0
( )1
nn tAn t
=+
2tt Ann
dtd
−=
2 2
2 2
324
124
( )
O o p o o t t o
p o p o p t t o
t o p
d n n An n An Cndtd n n An n An Cndtn n n
−
−
= −Γ − + −
= Γ − + +
= +
Model:Model:
A: Dissociation process A: Dissociation process C: SpinC: Spin--flip processflip process
If C >> A, we can accumulate paraexcitons before we lose excitons by Auger recombination.
5
4
3
2
1
0
n (1
015cm
-3)
543210
n (1015cm-3)
5
4
3
2
1
0
n (1
015cm
-3)
543210
n (1015cm-3)
Extraction of collisionExtraction of collision--induced spininduced spin--flip processflip process
t= 200 pst= 200 ps
2orthopara Cnn
dtd
−=collisioncollision--inducedinducedspinspin--flipflip
C=2.6x10C=2.6x10--1616 cmcm33/ns/nsKaovulakisKaovulakis et al.et al. PRB PRB 61, 16619 (2000).61, 16619 (2000).
C=5C=5××1010--1616 cmcm33/ns/ns
C=0C=0
5
4
3
2
1
0
n (1
015cm
-3)
543210
n (1015cm-3)nnorthoortho(t~0) (10(t~0) (101515 cmcm--33))
orthoortho
parapara
totaltotal
5
4
3
2
1
0
n (1
015cm
-3)
0.80.60.40.20.0Time (ns)
orthoortho
parapara
totaltotal
C C > A> A
2totaltoral Ann
dtd
−= (A=10(A=10--1616 cmcm33/ns)/ns)OO’’Hara and Wolfe, PRB 62, 12909 (2000).Hara and Wolfe, PRB 62, 12909 (2000).
Enhanced collision induced spinEnhanced collision induced spin conversion of excitonsconversion of excitons ::Virtual Virtual biexcitonbiexciton mediated resonant scattering ?mediated resonant scattering ?
F. Bassani and R. Rovere, Solid State Commun., 19, 887 (1976).
h
e
h e
e h
exchange
h
e
h
e
h
e
paraortho
virtual biexciton
Jz=1
Jz=-1
ortho para
para
Biexciton state in Cu2O;Large e-h exchange makes Biexciton state unstable
ortho
virtual biexciton state
(nearly zero binding energy)
(Energy)
Resonant scattering enhances collision cross section
12meV(140K)
200
2
2
0
Δα
(cm
)
135130125120115Energy (meV)
400
300
α(c
m-1 )
217021652160215521502145Energy (meV)
6
4
0ττdelaydelay== 4 4 nsns
11ss--2p para2p para
4.2 4.2 KK
12 12 meVmeV
11ss--2p2p11ss--3p3p
11ss--4p4p
11ss--5p5p
2p2p 3p3p 4p4p 5p5p
ττdelaydelay=5 ps=5 ps orthoortho--excitonexciton
ParaexcitonsParaexcitons generated via TPA of generated via TPA of orthoexcitonsorthoexcitons
Summary of femtosecond experiments
We obtain paraexciton density of 1015 cm-3
under orhtoexciton excitation of 4x1015 cm-3
Tpara< 20KC ~ 2.6x 10-16 cm3/nsec
We need to
- Accumulate paraexcitons with continuous feeding at low lattice temperature.
- Precisely estimateAuger rate and paraexciton life time
CW based experiment
Questions:Mechanism of giant collision cross-section ?Why did we obtain cold paraexcitons ?
Excitonic 1Excitonic 1ss--npnp transitions and COtransitions and CO22 laser lineslaser lines
Accidental coincidence – Single mode tunable CO2 laserto probe 1s paraexcitons
Quasi-steady state measurements for long lived paraexcitons
Experimental SetExperimental Set--up: Steadyup: Steady--state excitonic Lyman spectroscopystate excitonic Lyman spectroscopy
Simplified schematic
probe
pump(exciton)
time
probetransmitted
2f
2f, modulated at f
f
Induced absorption (-ΔT/T)can be obtained by measuringf & 2f components of the probebeam using lock-in amplifier(s)
power stabilization
Pump: single-mode dye laser (orthoexcitons)Probe: single-mode tunable CO2 laser
f=5 kHz
φ 200 μm
11ss--22pp absorption spectra of quasiabsorption spectra of quasi--steady state paraexcitonssteady state paraexcitons
2.5x10-2
2.0
1.5
1.0
0.5
0.0
-ΔT/
T
134132130128126124Photon energy (meV)
5.1 K
8.1 K
11.0 K
16.0 K
21.2 K
25.1 K
T =30.5 KL
Due to the relative stability of the probe light,we are currently able to detect
a transmission variation as small as 0.001 %(corresponds to <1012 cm-3)
Temperature dependence of differentialtransmission spectra at 1s-2p paraexcitonresonance
Exactly match theoretical curvesassuming Maxwell-Boltzmann distributionfunctions
We successfully detected 1s paraexcitonsin a steady state regime!
Life time measurement of paraexcitonsLife time measurement of paraexcitons
probe
pump
time
probetransmitted
frep=5 kHz
We measure the probepulse transmission and evaluatethe induced transmission change.
Reported value of paraexciton lifetime:Several hundred nanoseconds to millisecondswith luminescence measurements*
Timing controlled pulses
Lifetime measurement of 1s paraexcitons by CW Lyman spectroscopy
*S. Denev et al., Phys. Rev. B 65, 085211 (2002).A. Jolk et al., Phys. Rev. B 65, 245209 (2002).J. P. Wolfe et al., Solid State Commun. 134, 143 (2005).
Excitation intensity dependence of paraexciton densityExcitation intensity dependence of paraexciton density
Sublinear dependence on excitation intensity
linear
Auger effect is also observed in this steady-state regime
sublinear
*
* T. Tayagaki et al., J. Phys. Soc. Jpn. 74, 1423 (2005).
Temperature dependence of Auger recombination rateTemperature dependence of Auger recombination rate
Temperature-dependent diffusionof excitons (2D)
plus
Nonlinear rate equations(Auger recombination)
Numerical simulation
Temperature dependence ofthe nonlinear particle loss rate
T=5 K
*Collision-induced spin-frip processes are not included
Independent of temperature
The density-dependent particle loss ratecannot be explained by a classical hard-sphere model:
exnvστ ⋅=−th
1
ex
Bth mπ
Tkv 8=
ConclusionConclusion
1) We proposed and demonstrated a scheme to detect paraexcitons by using the 1s-2p transition of excitons. This allows us to quantitatively study the temporal and spatial behavior of paraexcitons.
2) Excitonic Lyman series of super-cooled orthoexciton was observed.We found that high density cold paraexcitons are efficiently created by resonant two-photon excitation of orthoexcitons.
3) To examine the dynamics of long lived paraexcitons, we developedCW CO2 laser-based Lyman spectroscopy. We measured a paraexciton lifetime longer than 20 micro seconds. We also obtained information on the collision-induced loss of paraexcitonsunder quasi-equilibrium condition.
Optical Trapping with Resonant Dressed FieldOptical Trapping with Resonant Dressed Field
dressed field
2p
g
1sδE
( )2 21 2
21 2
1 ( )21 ( )
2
s p
s p
E E
E I
δ μ
μ
−
−
= Δ + − Δ
≈ ∝Δ
μ1s-2p (transition dipole moment) = 4.2 eÅΔ (detuning) = 1 meVI (Intensity) =20MW/cm2
δE = 0.8 meV (corresponds to 2K)
Exciton gas can be trapped by the Stark potential .
Sympathetic cooling under high-density excitation
E1s-ortho
k k
E
E
k
Phonon scattering
E
k
E
k
1s-para
1s-ortho
1s-para
Sympathetic cooling
1s-ortho
1s-para
Hot paraexciton
Phonon scattering rate:γLA
-1=5 ns at 2K
hot para ehsuper-cooled ortho
eh
eh
eh
ortho-to-paraexciton conversion
experimental:τ~300 ps
How to cool paraexcitons ?How to cool paraexcitons ?
• Sympathetic cooling with super cooled orthoexciton gas
• Heat exchange with the lattice
336T Jm-3K-4
3kB/2 Nex
Energy to be extracted from excitons (1016 cm-3)at T=2 K in a (100 μm)3 boxto cool down to T=1 K: 4.12×10-13 J
1016 excitons in V=(100 μm) 3
V=(100 μm) 3 lattice
T=0 K
T=0.98 K
T=1 K
T=1 K
*L. V. Gregor, J. Phys. Chem. 66, 1645 (1962)., K. E. O’Hara and J. P. Wolfe, Phys. Rev. B 62, 12909 (2000).
(100 μm)3
T=2 K T=1 K
1016 cm-3
4.12×10-13 J
*classical gas
Specific heat
*Specific heat
Heat capacity of a phonon field is two-orders of magnitudelarger than that of a cold exciton gas
We need to cool down the crystal.
n=1x10n=1x101717 cmcm--3 3 TTCC=2.3 K=2.3 Kn=1x10n=1x101616 cmcm--3 3 TTCC=500mK=500mK
he
exciton gas
3He refrigerator
How to reach excitonic BEC phase ?How to reach excitonic BEC phase ?
Phase
boun
dary
0.1
1
10
Tem
pera
ture
(K)
1015 1016 1017 1018
Density (cm-3)
liq. 4He T=1.6 K
liq. 3He T=300 mK
((mmexex=2.7m=2.7mee.).)
Ene
rgy
Biexciton
Wave number
10 2 cm-1
2k0
Em(2k0)2
12meV
2.4μeV
k0
<Phase space compression scheme>
(10 µm)3
Spatial confinement of ultracold excitonsby polarization and wavevectrorcontrolled optical pulses(Spatial Control)
Excitonic BECEfficient creation of ultracold excitonsby chirp-controlled optical pulses(Frequency Control)
0.01
0.1
1
10
Tem
pera
ture
(K)
1013 1015 1017 1019
Density (cm-3)
BEC
T~0 K
Macroscopic Coherence
・
Excitonic BEC Excitonic BEC created by spatialcreated by spatial--temporal controlled optical pulsestemporal controlled optical pulses
CREST-JST: Oct. 2006~
Next:Next:
Confinement of paraexcitons: Optical Trap by MIR field (1s-2p resonant exciton transition)
Accumulation of para-excitons below 1K region;Cooling of para-excitons with super cooled ortho-excitons;
…. Sympathetic cooling of excitons
CW –based Experiment: poster by Kousuke Yoshioka