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