StudyonBose-EinsteinCondensationofPositronium

1

K.Shu1,T.Murayoshi1,X.Fan1,A.Ishida1,T.Yamazaki1，T.Namba1，S.Asai1,

K.Yoshioka2,M.Kuwata-Gonokami1,N.Oshima3,B.E.O’Rourke3,R.Suzuki3

1Dept.ofPhysics,GraduateSchoolofScience,andInternationalCenterforElementaryParticlePhysics(ICEPP),TheUniversityofTokyo,

2PhotonScienceCenter(PSC),GraduateSchoolofEngineering,TheUniversityofTokyo,

3NationalInstituteofAdvancedIndustrialScienceandTechnology(AIST)

14thInternationalWorkshoponSlowPositronBeamTechniques&Applications2016.05.24@Matsue,JAPAN

Critical Temperature (K)9−10 7−10 5−10 3−10 1−10 10 210

)3D

ensi

ty (/

cm

410

810

1210

1610

2010

BECphaseoverthelines

Ps - BEC• Ps:Thelightestatom

AdvantageVeryhighcriticaltemperatureofBEC

• e.g.)14K @1018 /cm3

Ø PsisthebestcandidateforthefirstBECwithanti-matter

NovelapplicationsofPs- BEC:pPrecisemeasurementsof

anti-mattergravitypRealizationof511keV laser

usingdecayinggammarays

Goal

87Rb 1H Ps

2

1995

1998

Critical Temperature (K)9−10 7−10 5−10 3−10 1−10 10 210

)3D

ensi

ty (/

cm

410

810

1210

1610

2010

BECphaseoverthelines

Challenges:HighDensityandCooling

3

u DifficultbecauseofShortlifetimeas142ns

TwoChallengesinlifetimep Highdensity1018 /cm3

p Cooling10K

Currently1015 /cm3*1,150K*2

Bothneedmuchimprovement!

Goal

Current87Rb 1H

Ps

*1:S.Mariazzietal. Phys.Rev.Lett.104,243401(2010).*2:D.B.Cassidy etal. physica statussolidi 4,3419(2007).

Ourstrategy:Two-StageCoolingThermalization andLaserCooling

4

Usingtwocoolingprocesses:efficientindifferentPstemperatureregion

Magnifiedview

Positronbeam

107 spin-polarizedpositrons/bunchfocusedinto100nm

Laserbeamsfromsixdirections

Internalvoid100nm× 100nm×100nm

1Kcavitymadebysilica(SiO2)whichistransparenttothelaser

4000spin-polarizedPscreated

4x1018 /cm3e+

DescribedinK.Shuetal. J.Phys.B49,104001(2016).

1. Downto300K:Energyexchangebycollisionswithcoldsilica(thermalization process)2. Downto10K:Lasercooling (Dopplercooling)

ModeloftheSimulation

5

Ps

Ps

VariablesforeachPs• Velocity• Internalstate

1. 1s2. 2p3. decayed

1. Collisionswiththesilicawalls(Thermalization)

3. Photonabsorptions/emissions

2. Ps-Pstwo-bodyelasticscatterings

• VariablesofeveryPsaretrackedatthesametime• 3interactionsareintegrated• DetailsareinapostersessionbyA.Ishidatoday

Coldsilicawall

Thermalization ModelandParameters

6

• TheclassicalmodelbyNagashima etal.←well-testedforPsinlargeporesfromY.Nagashima etal.Phys.Rev.A,52,258(1995)

dEav

dt= − 2

LM

!2mPsEav

"Eav −

3

2kBT

#Eav : Ps average kinetic energy, mPs : Ps mass,

L : Mean free path of scatterings,

M : Effective of mass of scatteing bodies,T : Temperature

Measuredvaluessuperimposed

M dependsonkineticenergyofPsEstimatedbyvariousexperiments

Legends:DBS(1987):T.Changetal. Phys.Lett.A126,189ACAR（1995）:Y.Nagashima etal. Phys.Rev.A52,258ACAR（1998）:Y.Nagashima etal. J.Phys.B31,3292γ/3γ(2013)： K.Shibuyaetal. Phys.Rev.A52,258

• Estimationofthedependence：𝑀(𝐸) = 𝑝( + 𝑝* exp

./0

Energy (eV)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

(a.m

.u)

MSi

lica

Effe

ctiv

e M

ass

210

310DBS(1987)ACAR(1995)ACAR(1998)

(2013)γ/3γ2

UncertaintyofM

Time (ns)0 100 200 300 400 500 600

Tem

pera

ture

(K)

1

10

210

310Slow

Best fit

Fast

EvaluationofPsThermalization

7

Timeevolution ofPstemperature

300Kin100ns

Veryslowforfullthermalization

Included• ClassicalmodelwiththreeM

estimation• Thetwobodyelasticscatterings

AninitialconditionØ Psinitialkineticenergy： 0.8eV

fromY.Nagashima etal. Phys.Rev.A52,258(1995)

Ø AninitialnumberofPs： 4000Ø Silicacavity：

100nmx100nmx100nm，1K

• Cooledto300Kin100ns• Coolingto10KistooslowØ Lasercoolingisimportantafter300K

UncertaintyofM

ü Precisemeasurementisnecessary

LasercoolingofPs

8

PsPs

1s

2p(τ=3.2ns)

Psinternalstate

E

5.1eV=243nm=1.23PHz(UV)

Resonancebetween1s – 2pwillbeusedCooledinevery3.2nsx2=6.4nsinaverage

Time (ns)200− 0 200 400 600

Inte

nsity

(Arb

.)

0

0.2

0.4

0.6

0.8

1

RequirementsfortheLaser:Longpulse

9

TworequirementsforefficientcoolingespeciallyforPs:

e+ injectionatt=0

• Pscoolingtakestheorderofthelifetime(>100ns)

• Lasershouldbepulsedwith300nswidth(muchlongerthanusual)

• Pulseenergyis40µJ tosaturatecoolingcycle

LaserintensityvsTime

300ns

① Longpulse

40µJ pulse

Laser Frequency Detune (GHz)600− 500− 400− 300− 200− 100− 0

Inte

nsity

(Arb

.)

0

0.2

0.4

0.6

0.8

1

1.2

RequirementsfortheLaser:Broadbandwidth &Frequencyshift

10

②Broadbandwidth&Frequencyshift

t=0ns

1s-2pResonance

ForhotPs

ForcoldPs

140GHz

FrequencyProfileoftheCoolingLaser

• DopplerbroadeningforPsisquitelargebecauseofitslightmassc.f.500GHzat300K

BroadbandwidthTocoolPswithvariousvelocities

FrequencyshiftTofollowsmallerDopplershiftofcoldPs

TworequirementsforefficientcoolingespeciallyforPs:

Laser Frequency Detune (GHz)600− 500− 400− 300− 200− 100− 0

Inte

nsity

(Arb

.)

0

0.2

0.4

0.6

0.8

1

1.2

RequirementsfortheLaser:Broadbandwidth &Frequencyshift

11

TwospecialrequirementsforefficientPscooling:

② Broadbandwidth&Frequencyshift

• DopplerbroadeningforPsisquitelargebecauseofitslightmassc.f.240GHzat300K

BroadbandwidthTocoolallofPswithvariousvelocities

FrequencyshiftTofollowsmallerDopplershiftofcooledPs

t=300ns

1s-2pResonance

FrequencyProfileoftheCoolingLaser

60GHzshiftin300ns

LaserSpecifications

12

Veryspecialspecs!Especially:fastandwell-controlledfrequencyshiftinginpulsedmode

Newtrialforoptics!!!

Pulseenergy 40µJCenterfrequency 1.23PHz- D(t)Frequencydetune

（D(t)）D(0ns)=300GHz

D(300ns)=240GHzBandwidth（2σ） 140GHz

Timeduration（2σ） 300nsBeamwaist（2σ） 200µm

Summaryofrequiredspecifications

DesignoftheLaserSystem

13

NewlydesignedforPscooling

SHG THG

EOM2Sideband Generator

Ti:Sapphire

EOM1Frequency Shifter

1.23PHz(byTHG)410THz820THz

injectionseededTi:sapphire laser

40µJ

10mJ

Q-switchedPump Laser

(a)(b) (c)

10mW

SHG THG

EOM2Sideband Generator

Ti:Sapphire

EOM1Frequency Shifter

1.23PHz(byTHG)410THz820THz

injectionseededTi:sapphire laser

40µJ

10mJ

Q-switchedPump Laser

(a)(b) (c)

10mW

DesignoftheLaserSystem

14

NewlydesignedforPscooling

Ideaofthedesign:1. Controling frequencyinContinuousWavemodewithathirdfrequency

☆BothofshiftingandbroadeningarepossiblebyEOMs

(b) 20GHz (a)

f f410THz

CW

f

(c)20GHz

(b) (a)20GHz

1

SHG THG

EOM2Sideband Generator

Ti:Sapphire

EOM1Frequency Shifter

1.23PHz(byTHG)410THz820THz

injectionseededTi:sapphire laser

40µJ

10mJ

Q-switchedPump Laser

(a)(b) (c)

1mW

DesignoftheLaserSystem

15

NewlydesignedforPscooling

Ideaofthedesign:2. SeedingtheCWlaserintoTi:Sapphire togeneratepulsedlaser

☆ Generatepulsedlaserwithcontrolledfrequency

2

Developmentofthecoolinglaser

16

Theinitialpart(CWseedlaser)

Home-madeExternalCavityDiodeLaser☆Compact

8cm

Gratings

410THzOutput

LaserDiodeopnextHL7301MG(InGaAsP)

• Oscillatingatdesired~410THz• Powerfulenough(~10mW)

ECDL-Box

Tocontroller

410THz(red)light

Developmentofthecoolinglaser

17

Theinitialpart(CWseedlaser)

Home-madeExternalCavityDiodeLaser☆Compact

8cm

Gratings

410THzOutput

LaserDiodeopnextHL7301MG(InGaAsP)

• Oscillatingatdesired~410THz• Powerfulenough(~10mW)

ECDL-Box

Tocontroller

410THz(red)light

Time (s)0 1000 2000 3000 4000 5000

Tem

pera

ture

drif

t (K)

0.006−

0.004−

0.002−

0

0.002

Time (s)0 1000 2000 3000 4000 5000

LD fr

eque

ncy

drift

(GH

z)

1.2−

1−

0.8−

0.6−

0.4−

0.2−

0

0.2

Next:Ø DesigningTi:Sapphire

oscillatorfor300nspulseandinjectionseeding

Velocity (km/s)60− 40− 20− 0 20 40 60

Arb.

EvaluationoftheCooling

18

Time (ns)0 100 200 300 400 500 600

Tem

pera

ture

(K)

1

10

210

310

TimeevolutionofPstemperature

t=380ns

70K

• Withoutthelaser,coolingistooslow(byBestfitestimationofM)

Without thelaser

Psvelocitydistribution(Calculatedbysimulatedtemperature)

Time (ns)0 100 200 300 400 500 600

Tem

pera

ture

(K)

1

10

210

310

Velocity (km/s)60− 40− 20− 0 20 40 60

Arb.

EvaluationoftheCooling

19

TimeevolutionofPstemperature Psvelocitydistribution(Calculatedbysimulatedtemperature)

t=380nst=380ns

70K

11KWithlaserWithout thelaser

Withthelaser

• Withoutthelaser,coolingistooslow(byBestfitestimationofM)• Withthelaser,coolingfrom~300Kisaccelerated

Velocity (km/s)60− 40− 20− 0 20 40 60

Arb.

Time (ns)0 100 200 300 400 500 600

Tem

pera

ture

(K)

1

10

210

310

EvaluationoftheCooling

20

TimeevolutionofPstemperature

t=380nst=380nst=450ns

• Withoutthelaser,coolingistooslow(byBestfitestimationofM)• Withthelaser,coolingfrom~300Kisaccelerated• Comparedwiththecriticaltemperature,BECtransitionwillhappenat

400ns!

70K11K

Without thelaser

WiththelaserCriticaltemperature

7K(broad)+30%condensate(peak)

Psvelocitydistribution(Calculatedbysimulatedtemperature)

Roadmap1. PrecisePsDopplerspectroscopy(in2years)

l EstablishmentofamethodologyforcoldPsl SolvinguncertaintyofPsthermalization processwithsilica

2. Pslasercooling(in4years)l Developmentofthelasersystemwithlongpulse,widebandwidth,

frequencyshift

3. Developingadensepositronsysteml 107 e+ into100nmdiameterinananosecondsbunch

4. PsBECl Combingallthetechnologies!

21

PrincipleofDoppler-sensitivetwo-photonspectroscopyofPs

1. Excitedto3s byabsorbingco-propagatingtwophotons

2. Ionize3s-Pstofreee+ ande-3. Thee+ annihilatesintoγ-rays

• Conventionaltechniqueisnotprecisefor10KPsorBEC• WewilluseDoppler-sensitivetwo-photonspectroscopy (NewforPs)

• Dopplereffectisdoubledbecausetwo-photon:sensitivetoPstemperature• ResonancecanbemeasuredviaSSPALS

(D.B.Cassidyetal. App.Phys.Lett.88,194105(2006)) 22

E

-6.8eV

-0.76eV-1.7eV

1s

3s

Twophotonsof410nmwavelengthPs

410nmpulsedlasere+e-

Frequency (GHz)50− 0 50

Exci

ted

Ps ra

tio

0

0.05

0.1

0.15

0.2 / ndf 2χ 3.105 / 4

Constant 0.007273± 0.118 Mean 1.669± 0.3335 Ps Temperature (K) 1.648± 11.82

/ ndf 2χ 3.105 / 4Constant 0.007273± 0.118 Mean 1.669± 0.3335 Ps Temperature (K) 1.648± 11.82

Wavelength 410nm

Pulseenergy 1mJ

Timeduration Afewns

Bandwidth（FWHM） 25GHz

Freq. tunable range 150GHz

beamwaist(2σ) 850µm

Repetitionrate 100Hz

Laserspec.fortemperaturemeasurement

23

LaserRequirementsforDopplerSpectroscopy

Planton Confirmfeasibilityofthemethodn Measurethermalization processofPswithcoldsilica

Expectedresonancecurvefor10KPswith107 Psintotal,att=300ns

◯ Visiblewavelength◯ EasilyachievablebandwidthØ Designofthelaserisunderstudy

(SHGofTi:Sapphire laserisapromisingcandidate)

GoalforDensePositron

Numberofpositrons 107 e+/bunchBeamwaist <100nmPulsewidth <5ns

Positron Energy <5keV

GoalforPs-BEC

Numberofpositrons 104 e+/bunchBeamwaist 25µmPulsewidth ~µs

Positron Energy 0.5~30 keV

CurrentatAIST microbeam1stagebrightness-enhancement-system

24

Principleofpositronfocusing(brightnessenhancement):

Focusinglens

Re-moderator

Re-moderatedpositronsare• Perpendiculartosurface• MonochromaticEnergy• Withfocusedwaist

bunchede+ beam

N.Oshimaetal. J. Appl.Phys. 103,094916(2008).

PlannedUpgradeofPositronBeam

Ø Buncher andbeamopticsarenowunderdetailedconsideration 25

Twonecessaryimprovements:State-of-the-art Goal

Buncher forspin-polarizedpositron 108 e+/bunch 2x109 e+/bunchBeamcompressionratio byFocusinglens 1/10 1/20- 1/30

With20%re-moderationefficiency,107 e+ in100nmby3-stagebrightness-enhancement-system

Silicatarget

n=2x109 e+φ=15mm

4x108 e+750µm

8x107 e+40µm

2x107 e+2µm

2x107 e+100nmAttarget

①

Summary

26

• WeproposedandevaluatedanewexperimentalschemeshowntobepossibletorealizePs-BECby:1. Thermalizationprocesswithcoldsilica(downto300K)2. Lasercooling(downto10K)

• TheCoolinglaserisspecialfor:1. Longpulse– 300nstimeduration2. Broadbandwidth– 140GHz3. Frequencyshift– 60GHz← NewopticsforefficientcoolingCWseedECDLisreadyNext:Ti:Sapphire injectionseedinglaserincludingfrequencyshift

• Severaltasksareunderdetailedstudyandpreparation:1. Doppler-enhanced1s - 3s spectroscopyusingtwo-photonexcitation2. Designingabuncher andbeamopticsfor107 spin-polarizede+/bunch

in100nmwaistby20timesmoree+ &factor2strongfocusing