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