P rob ing att os eco nd pul ses by XU V st im ula ted dy na mic s
J.MarcusDahlstr¨om PhD:Lund[LTH]->Post-doc:Stockholm[SU]->Guestres.:Hamburg[CFEL/MPGPKS] -------------------* 2015-05-27Nordita,Stockholm,Sweden. AlbaNovaMPG-PKS J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulatedOutlineoftalk: Introductionto“attophysics” Detailsoncomputationalmethod(SU:MBPT) Newproposal: Attosecondinterferometrybasedonstimulatedholedynami J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
In tr o duc tio n to “a tto ph ysics ”
Overviewofpumpandprobesetups (a) (b) (c)Pump and probe!
Probe/Dump!Pump! (1as=10−3 fs=10−18 s)
Traditionalpumpandprob withfemto-pulsescontrolof Born-Oppenheimerdynamics: J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
In tr o duc tio n to “a tto ph ysics ”
Overviewofpumpandprobesetups (a) (b) (c)Pump and probe!
Probe/Dump!Pump! (1as=10−3 fs=10−18 s)
Traditionalpumpandprobe withfemto-pulsescontrolof Born-Oppenheimerdynamics: -Tannor-Rice:(t-domain) -Brumer-Shapiro:(ω-dom.) J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
In tr o duc tio n to “a tto ph ysics ”
Overviewofpumpandprobesetups (a) (b) (c)Pump and probe!
Probe/Dump!Pump! (1as=10−3 fs=10−18 s)
Traditionalpumpandprob withfemto-pulsescontrolof Born-Oppenheimerdynamics: -Tannor-Rice:(t-domain) -Brumer-Shapiro:(ω-dom.) Attosecondstreak-camera: photoionizationbyXUVatto- pulseandanIRfsprobefield. Controlofe− wavepacket. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
In tr o duc tio n to “a tto ph ysics ”
Overviewofpumpandprobesetups (a) (b) (c)Pump and probe!
Probe/Dump!Pump! (1as=10−3 fs=10−18 s)
Traditionalpumpandprobe withfemto-pulsescontrolof Born-Oppenheimerdynamics: -Tannor-Rice:(t-domain) -Brumer-Shapiro:(ω-dom.) Attosecondstreak-camera: photoionizationbyXUVatto- pulseandanIRfsprobefield. Controlofe− wavepacket. RABBITTmethod: photoionizationbytrainof atto-pulsesandanIRfsprobe field→interferenceinω- domain. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
In tr o duc tio n to “a tto ph ysics ”
ReconstructionofAttosecondBeatingbyInterferenceofTwo-photonTransitio Attosecondpulsetrain→oddXUVharmonics:(2q+1)ω. 0 (a)(e) Experiment:Pauletal.Science(2001)2921689 Theory:Muller(2002)Appl.Phys.B74s17-21 J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulatedA tom ic dela y in sing le io niz at io n
SketchoftheRABBITTsetup Atome–
meTi
fo
sptighfl
trec
meto er
APT-laserdelay(inlaserperiods)
Pho toel ectr on en erg y
(in ha rm on ic ord er)
XUV
IR
τ t2q: Time delay measurement ~ group delay Time-of-flighttubedeterminestheenergyoftheelectron. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
A tom ic dela y in sing le io niz at io n
SketchoftheRABBITTsetup Atome–
meTi
fo
sptighfl
trec
meto er
APT-laserdelay(inlaserperiods)
Pho toel ectr on en erg y
(in ha rm on ic ord er)
XU
IR
τ t2q: Time delay measurement ~ group delay Time-of-flighttubedeterminestheenergyoftheelectron. Informationaboutthedelayofthewavepacketisfoundin modulationsofthesidebandsoverpump-probedelay. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
A tom ic dela y in sing le io niz at io n
SketchoftheRABBITTsetup Atome–
meTi
fo
sptighfl
trec
meto er
APT-laserdelay(inlaserperiods)
Pho toel ectr on en erg y
(in ha rm on ic ord er)
XUV
IR
τ t2q: Time delay measurement ~ group delay t 2q Time-of-flighttubedeterminestheenergyoftheelectron. Informationaboutthedelayofthewavepacketisfoundin modulationsofthesidebandsoverpump-probedelay. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
In ter -sp ecies pho toi on iz at io n dela y ex p eri men t
(inattoseconds,1as=10−18 s) Sideband202224 τ(Ar)−τ(Ne)68±1570±1252±25 Theory605140 τ(Ar)−τ(He)82±1583±2271±21 Theory725945 τ(Ne)−τ(He)23±412±410±8 Theory1284 Thedelayisrelativetothesamesidebandorder. ArhasalargerdelaythanbothNeandHe. Theoryshowsslightlysmallerdelays. [Gu´enotetal2014J.Phys.B:At.Mol.Opt.Phys.47245602]: J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulatedIn ter -sp ecies pho toi on iz at io n dela y ex p eri men t
(inattoseconds,1as=10−18 s) Sideband202224 τ(Ar)−τ(Ne)68±1570±1252±25 Theory605140 τ(Ar)−τ(He)82±1583±2271±21 Theory725945 τ(Ne)−τ(He)23±412±410±8 Theory1284 Thedelayisrelativetothesamesidebandorder. ArhasalargerdelaythanbothNeandHe. Theoryshowsslightlysmallerdelays. TheRABBITTmethodisnotperfectforattosecondmetrology becausewemeasuredifferentdelaysfordifferenttargetatoms. [Gu´enotetal2014J.Phys.B:At.Mol.Opt.Phys.47245602]: J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddyM eth o d
DiagrammaticMany-BodyPerturbationTheorywithPhotons IndependentelectronHamiltonian: h�(r)=−1 2d2 d2 r+�(�+1) 2r2−Z r+uHF(r)+uQ(r) RestrictedHartree-Fock(sumorbitalsbwithoccupancyq b): u HF(r)=� bq b[J b(r)−1 2K b(r)], LindgrenandMorissonAtomicMany-BodyTheory,Springer(1982) J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulatedM eth o d
DiagrammaticMany-BodyPerturbationTheorywithPhotons IndependentelectronHamiltonian: h�(r)=−1 2d2 d2 r+�(�+1) 2r2−Z r+uHF(r)+uQ(r) RestrictedHartree-Fock(sumorbitalsbwithoccupancyq b): u HF(r)=� bq b[J b(r)−1 2K b(r)], J b(r)Pa(r)=� kc(abk)1 rY k(bb,r)Pa(r), K b(r)P a(r)=−2� kd(abk)1 rY k(ab,r)P b(r), Y k(ab,r)=r� ∞ 0dr�rk < rk+1 >P a(r� )P b(r� ) LindgrenandMorissonAtomicMany-BodyTheory,Springer(1982) J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddyM eth o d
ProjectedpotentialuQ(r)altersexcitedelectronorbitals Excitedelectronsshouldseealongrange−1/rpotential: u Q=−ˆ Q1 rJ0(aa,r)ˆ Q,ˆ P=
occ � a|Pa��Pa|
ˆ Q=
exc � p|P p��P p|, TheprojectedpotentialensuresRydbergseriesandCoulom asymptoticwavefunctionsforexcitedstates. Seealso:Dahlstr¨omandLindrothJ.Phys.B(2014)47124012 J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
M eth o d
ProjectedpotentialuQ(r)altersexcitedelectronorbitals Excitedelectronsshouldseealongrange−1/rpotential: u Q=−ˆ Q1 rJ0(aa,r)ˆ Q,ˆ P=
occ � a|Pa��Pa|
ˆ Q=
exc � p|P p��P p|, TheprojectedpotentialensuresRydbergseriesandCoulombi asymptoticwavefunctionsforexcitedstates. Fermivacuum(secondquantization):1=
ˆ P+
ˆ Q. Holes(↓∈
ˆ Poccupied)andelectrons(↑∈
ˆ Qexcited). Seealso:Dahlstr¨omandLindrothJ.Phys.B(2014)47124012 J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
Di ag ra mma tic p er tu rb at io n the or y
Setupofuncorrelatedperturbedwavefunctionp a
Time
p a
(forward)(backward) ρfwd(a)=� p
� ...|p��p|d Ω|a� � a+Ω−� p ρbwd(a)=� p
� �a|d Ω|p��p|... �a−Ω−�p [M˚artensson-PendrillJ.Phys.France46,1949(1985);Dahlstr¨ometal.Phys.Rev.A86,061402(2012) J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
RP AE- ty p e effe cts in XUV- IR pro ces ses :
(RPAE=RandomPhaseApproximationwithExchange) +++ +++(a)(b)(c) (d)(e)(f)(g) Figure:XUVphotonabsorbedfirstincludingRPAE-typecorrelation andtheninteractionwiththeIRfieldlast:(a)“Hartree-Fock”;(b) Direct;(c)Exchange;and(d)-(g)Ground-statecorrelations.Final-stat correlationisnotincluded. [Dahlstr¨al.Phys.Rev.A(2012)][Dahlstr¨al.Phys.Rev.A(2012)]J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
“W or st ca se ”: Co rr el at io n effect s in Ar 3s
−1 RABBITTdelaydependsstronglyoncorrelationeffects: -400-300-200-1000
100
200
300 354045505560 Sidebandenergy(eV)
Ato mic
del ayf
ro m3 s(a s)
RPAE3s{3p,3s} Forward-onlyRPAE3s{3p,3s} RandomPhaseApp.(RPA)3s{3p,3s} Tamm-DancoffApp.(TDA)3s{3p,3s} [Dahlstr¨om&LindrothJ.Phys.B47(2014)124012] J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
Ov er vi ew of in te rf er om et ri c sc heme s
IR-drivenelectrondynamics→XUV-stimulatedholetransition Fano res. ?XUVHARMONICS + IR PROBE:
XUVPUMP ANDXUVHARMONICPROB J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
Con sid er at io ns fo r a rea l pr ob e sche me
Probephotoelectronorremainingholeintarget?Time
p
a q
(Probe hole)(Probe electron)
p a b
M(e) qa(ω1,ω2)=lim ε→0+� n� �q|O 2|p��p|O 1|a� (� a+ω 1−� p+iε)∈CX J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
Con sid er at io ns fo r a rea l pr ob e sche me
Probephotoelectronorremainingholeintarget?Time
p
a q
(Probe hole)(Probe electron)
p a b
M(e) qa(ω1,ω2)=lim ε→0+� n� �q|O 2|p��p|O 1|a� (� a+ω 1−� p+iε)∈CX M(h) pb(ω1,ω2)=�a|O2|b��p|O1|a� (� a−� b−ω 2) ���� −δω
∈R,√ J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
Ca rt o on of en er gy- sh ea ri ng mech anism
Spectralshearofphotoelectronduetoenergysharingwithhole Ne: 2p 2s(a)(b)(c)(d) J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
S et up of XU V fie lds
XUVfieldisdividedintwopartsaspump:E1andprobe:E2 0.00.51.01.52.02.53.0 Energy[au:1au=27.2eV]02
46
810
1214
16 E-field[au]
Probe (E_2) relative phase is controlled Pump (E_1) phase is unknown
Hole-hole resonance ThepumpE1:broadbandwidthwithunknownphase,φ(ω). TheprobeE2:hastwocomponents:aboveandbelow resonance[Ne2p−1 ↔Ne2s−1 ]withrelativephase,ϕ. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
XU V pr ob e fie ld in th e time -do ma in
Evelope-modulationontheattosecondtimescale. -2.0x10-3-1.5x10-3-1.0x10-3-5.0x10-40.0x1005.0x10-41.0x10-31.5x10-32.0x10-3 010203040506070 Time(fs)probefield (e) E 2(t)+E 3(t)∼cos[δωt−1 2(φ−φ)]cos[ωt− 32ab
1 2(φ+φ 32 J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
P ho to io ni za tio n fr om out er or bita l
Time-DependentConfiguration-InteractionSingles TDCIScalculationusingTSURFFfor1Dneonmodel 10-1410-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1Pho toel ectro
ny iel dfro ma
=2p
(1)
(2)(3) (S−) (P2 ) (P3 ) 01020304050 Photoelectronkineticenergy[eV]
Pump
Probe Pump-Probe [CalculationbyJhih-AnYouinthegroupofNinaRohringer] J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
P ho to io ni za tio n fr om in ner or bit al
Time-DependentConfiguration-InteractionSingles TDCIScalculationusingTSURFFfor1Dneonmodel 01020304050 Photoelectronkineticenergy[eV]10-1010-910-810-710-610-510-410-310-210-1
Pho toel ectro
ny iel dfro mb
=2s
(1) (S+)
(P2 )
Pump Pump+Probe [CalculationbyJhih-AnYouinthegroupofNinaRohringer] J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
Ov er vi ew of pro p osa l
CoherentcontrolofXUVpumpandprobefields Reaction microscope APT (2, 3)IRfs LASER
SAP (1) IsolatedattosecondpulseandXUVprobefieldsaregeneratedby high-orderharmonicgeneration(HHG). IRphase,φIR,isusedtocontrolXUVprobefield. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
Is ol at ed atto se con d pu lse s in th e ti me- do ma in
Thespectralphasechangesthetemporalstructureofthepulses. -2.0x10-2-1.5x10-2-1.0x10-2-5.0x10-30.0x1005.0x10-31.0x10-21.5x10-22.0x10-2 343536373839 Time(fs)β=100 -1.0x10-2-8.0x10-3-6.0x10-3-4.0x10-3-2.0x10-30.0x1002.0x10-34.0x10-36.0x10-38.0x10-31.0x10-2 343536373839 Time(fs)
α=100
-2.0x10-2-1.5x10-2-1.0x10-2-5.0x10-30.0x1005.0x10-31.0x10-21.5x10-22.0x10-2 343536373839 Time(fs)
α=10 -2.0x10-2-1.5x10-2-1.0x10-2-5.0x10-30.0x1005.0x10-31.0x10-21.5x10-22.0x10-2 343536373839 Time(fs)
α=0 (a)(b) (c)(d)
Elec tri cfi eld am plitu de
arg[E1(ω)]=φ1(ω)=α(ω−ω1)2 +β(ω−ω1)3 J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
P ho to io ni za tio n fr om in ner or bit al: (S +) p ea k
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Res ult s fo r in dep end ent -pa rt icl e mo del of neo n (3D )
Responsetimesandyields. 708090100110120020
40
60
80100
120
140 Responsetime[as]
s-wave d-wave k-state 708090100110120 Photonenergyofpumpfield,ω1[eV]
10-3
10-2
10-1
100
101
102
Yiel d(s qu ared matri
xel emen
ts)
2s
2p
kdks(a) (b) 2s
2p
kdks k'p
(c) (d)
hole only s-wave:d-wave:hole holeelectron electron Wγ(k)=|Aγ|−|Bγ|cos[2δω(τ(GD) 1−τ(GD) 3,2−τγ(k))] J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulated
Thecomplexamplitudeforatransitionfromαtoγbyfirst absorptionofaphotonfromthepumpfield,E1(ω1),andthena photonfromeitherprobefield,E fwheref=[2,3],is S γ≈1 2πi
3 � f=2E fE 1(ω pc−ω f)M pc(ω pc−ω f,ω f),(1) wherethetwo-photonmatrixelementcontainstwoterms, Mpc(ω1,ωf)=M(h) pc(ω1,ωf)+M(e) pc(ω1,ωf) =� �
b�
z b� cz pb� ω f−ω b� c−lim ξ→0+�� p�z pp�z p� c ω f−ω pp�−iξ
� ,(2) correspondingtostimulatedhole(h)andelectrondynamics(e), respectively.Totalenergyconservationrequiresthat ω1+ωf=�p−�c.InwritingEq.(2)wehaveusedsecond quantizationtoapproximatetheN-bodymatrixelementsby single-particletransitions, Z β� α≈z p� b�,Z γβ�≈−z b� cδ p,p�+z pp�δ c,b�. J.MarcusDahlstr¨omProbingattosecondpulsesbyXUVstimulateddy
