Antoine Browaeys Ins/tut d’Op/que, CNRS Interac(ng Cold Rydberg atoms: A Toy Many‐Body System + e ‐ Séminaire Poincaré 7 décembre 2013
AntoineBrowaeysIns/tutd’Op/que,CNRS
Interac(ngColdRydbergatoms:
AToyMany‐BodySystem
+
e‐
SéminairePoincaré7décembre2013
Many‐bodysystemsandcomplexity
Microscopic
Quantumlaws…
Many‐bodysystemsandcomplexity
Microscopic Macroscopic
?
Quantumlaws…
quantumorclassicallaws
Many‐bodysystemsandcomplexity
Microscopic Macroscopic
Complexity:forN>30–40,ab‐ini/ocalcula/onsimpossible!!SizeofHilbertspace~2Ntoolarge
Oneidea(Feynman1982):engineerquantumsystemsinthelab.Measuretofindproper/esyoucan’tcalculate!
?
Quantumlaws…
quantumorclassicallaws
QuantummetrologyMany‐bodyphysics
Transi(onquantum/classicalQuantuminforma(on
Message
Dura/
on
sizeL
Ln
ExpL
Applica(onsofquantumstateengineering
Quantumstateengineering=controlinterac(onsbetweenpar(cles
TrappedcoldionsAtomsandphotons
Coldatoms
Quantumstateengineering=controlinterac(onsbetweenpar(cles
TrappedcoldionsAtomsandphotons
Coldatoms
Ar(ficialatoms
NVcenter Supra.circuit
Quantumstateengineering=controlinterac(onsbetweenpar(cles
TrappedcoldionsAtomsandphotons
Coldatoms
Ar(ficialatoms
NVcenter Supra.circuit
Many‐bodytoysystems
Quantumstateengineering=controlinterac(onsbetweenpar(cles
TrappedcoldionsAtomsandphotons
Ar(ficialatoms
NVcenter Supra.circuit
Many‐bodytoysystems
ColdRydbergatoms
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
Rydbergatoms(alkalicase)
continuum
Ene
rgy
Rydbergstates
+
e‐
JohannesRydberg1854‐1919
Rydbergatoms(alkalicase)
continuum
Ene
rgy
Rydbergstates
+
e‐
JohannesRydberg1854‐1919
Alkaliatoms(Rb,Cs)⇒hydrogenoid
Rydbergatoms(alkalicase)
continuum
Ene
rgy
Rydbergstates
+
e‐
JohannesRydberg1854‐1919
Screeningeffectofelectroniccore:
Quantumdefect:
Alkaliatoms(Rb,Cs)⇒hydrogenoid
Proper(esofRydbergatoms
~ 100nm
+
e‐Bohrmodel:size
Proper(esofRydbergatoms
~ 100nm
+
e‐Bohrmodel:size
1. Largedipoleelementsbetweenand
for
Proper(esofRydbergatoms
~ 100nm
+
e‐Bohrmodel:size
1. Largedipoleelementsbetweenand
Ex:n≈50⇒3000×d(H20)!
for
Proper(esofRydbergatoms
~ 100nm
+
e‐Bohrmodel:size
1. Largedipoleelementsbetweenand
2. Largepolarizability ⇒largeAC&DCStarkshig
Ex:n≈50⇒3000×d(H20)!
for
Proper(esofRydbergatoms
~ 100nm
+
e‐Bohrmodel:size
1. Largedipoleelementsbetweenand
2. Largepolarizability ⇒largeAC&DCStarkshig
3. Longlife/me ⇒n>60,τ>100μs
Ex:n≈50⇒3000×d(H20)!
for
+ + R
A B
Twoatombasis:
Interac(onbetweenRydbergatoms
+ + R
A B
ns,ns
ETwoatombasis:
Interac(onbetweenRydbergatoms
+ + R
A B
ns,ns
np,(n‐1)p
Δ(n)
ETwoatombasis:
Interac(onbetweenRydbergatoms
+ + R
A B
ns,ns
np,(n‐1)p
Δ(n)
ETwoatombasis:
Interac(onbetweenRydbergatoms
+ + R
A B
np,(n‐1)p
Δ(n)
ETwoatombasis:
ns,ns
Interac(onbetweenRydbergatoms
+ + R
A B
Twoatombasis:
VanderWaals:⇒
np,(n‐1)p
Δ(n)
E
ns,ns
Interac(onbetweenRydbergatoms
+ + R
A B
Twoatombasis:
VanderWaals:⇒
np,(n‐1)p
Δ(n)
E
ns,ns
Interac(onbetweenRydbergatoms
Scaling:
+ + R
A B
Twoatombasis:
VanderWaals:⇒
Resonantregime:⇒
np,(n‐1)p
Δ(n)
E
ns,ns
Interac(onbetweenRydbergatoms
Scaling:
Ex:for87Rbresonance59d3/2+59d3/2↔57p1/2+61f5/2
Tuningtheinterac(on:Försterresonance
np,(n‐1)p
Δ(n)
E
ns,ns
TuneΔ(n):Starkshig
Ex:for87Rbresonance59d3/2+59d3/2↔57p1/2+61f5/2
Tuningtheinterac(on:Försterresonance
dd
pf
F(V/cm)
E
gg
np,(n‐1)p
Δ(n)
E
ns,ns
TuneΔ(n):Starkshig
Interac(onbetween”real”Rydbergatoms
Ex:87Rbatomsin62d3/2
Rydberginterac/on:1011xgroundstate+switchable
(L.Béguin)
”Early”experimentsandthe“need”forcoldatoms
J‐MRaimond,J.Phys.B14,L655(1981)The“denseRydberggas”
DenseCsbeam
ωL
Broadeningofexcita/on
”Early”experimentsandthe“need”forcoldatoms
J‐MRaimond,J.Phys.B14,L655(1981)
kBT<<Interac(onenergy⇒T<1mK⇒coldatoms
The“denseRydberggas”
DenseCsbeam
ωL
Broadeningofexcita/on
”Early”experimentsandthe“need”forcoldatoms
J‐MRaimond,J.Phys.B14,L655(1981)
kBT<<Interac(onenergy⇒T<1mK⇒coldatoms
Mourachko,PRL80,253(1998)Manybodyin“frozengas”
p+p↔s+s’p+s↔s+p
Diffusionofexcita/onfasterthanmo/on⇒correla/ons
betweenallatoms
The“denseRydberggas”
DenseCsbeam
ωL
Broadeningofexcita/on
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
D.Jaksch,etal.,PRL85,2208(2000)M.D.Lukin,etal.,PRL87,037901(2001)
Rydbergblockadeandcollec(veexcita(on
RA B
D.Jaksch,etal.,PRL85,2208(2000)M.D.Lukin,etal.,PRL87,037901(2001)
Rydbergblockadeandcollec(veexcita(on
RA B
Rydbergblockadeandcollec(veexcita(on
D.Jaksch,etal.,PRL85,2208(2000)M.D.Lukin,etal.,PRL87,037901(2001)
RA B
If :noexcita/onof⇒BLOCKADE
Rydbergblockadeandcollec(veexcita(on
RA B
Collec/veoscilla/onbetweenandwithcoupling
Rydbergblockadeandcollec(veexcita(on
with
RA B
BlockadesphereandN‐atomcollec(veexcita(on
Onlyoneatomexcitedwithinasphereof“blockade”radiusRb
BlockadesphereandN‐atomcollec(veexcita(on
Onlyoneatomexcitedwithinasphereof“blockade”radiusRb
BlockadesphereandN‐atomcollec(veexcita(on
Onlyoneatomexcitedwithinasphereof“blockade”radiusRb
Coherentexcita/on:
Ex:62d3/2,Ω/2π=1MHz⇒Rb=10μm
BlockadesphereandN‐atomcollec(veexcita(on
Natomswithintheblockadesphere⇒collec/veoscilla/on
Onlyoneatomexcitedwithinasphereof“blockade”radiusRb
Ex:62d3/2,Ω/2π=1MHz⇒Rb=10μm
Coherentexcita/on:
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
Non‐resonantatom‐laserinterac/on⇒light‐shia
|g〉
|e〉
I ~ I
Microscopicop(caldipoletrap
Dipoletraplight
Non‐resonantatom‐laserinterac/on⇒light‐shia
|g〉
|e〉
I ~ I
HighNAlens
Dichroicmirror
Size ~ 1 µmVolume ~ 1 µm3
Depth≈1mK⇒lasercooledatoms
Microscopicop(caldipoletrap
Laser‐cooledatomsT~100µK
Fluorescencephotoncounter,
camera
Dipoletraplight
Non‐resonantatom‐laserinterac/on⇒light‐shia
|g〉
|e〉
I ~ I
Resonantlaser
HighNAlens
Dichroicmirror
Microscopicop(caldipoletrap
Schlosseretal.,Nature411,1024(2001)Sortaisetal.,PRA75,013406(2007)
Loadingrate
Loadingthetrapwithindividualatoms
Light‐assistedlossinthetrap
Loss~1/trapsize
v w
Coolinglasers
Prevents2trappedatomswhenloss>>loading
8.5 9.0 9.5 10.0 10.5 11.0 11.5 0 20 40 60 80 100
Time (s)
Cou
nt /
10 m
s Fluorescence@780nminducedbythecoolinglasers
Trappingasingle(cold)atom
Schlosseretal.,Nature411,1024(2001);Sortaisetal.,PRA75,013406(2007)
8.5 9.0 9.5 10.0 10.5 11.0 11.5 0 20 40 60 80 100
Time (s)
Cou
nt /
10 m
s
Schlosseretal.,Nature411,1024(2001);Sortaisetal.,PRA75,013406(2007)
0atom
1atom
NONdeterminis(csingle‐atomsource
Fluorescence@780nminducedbythecoolinglasers
Trappingasingle(cold)atom
Coherentexcita(onofatomstoRydbergstate(ex:87Rb)
795nm
475nm
2‐photonexcita/on:
Coherentexcita(onofatomstoRydbergstate(ex:87Rb)
795nm
475nm
2‐photonexcita/on:
Prepare:
Coherentexcita(onofatomstoRydbergstate(ex:87Rb)
Resultofasinglemeasurement:
OR
795nm
475nm
2‐photonexcita/on:
Prepare:
⇒mustrepeattocalculatePr(x100)
Coherentexcita(onofatomstoRydbergstate(ex:87Rb)
58d3/2
Resultofasinglemeasurement:
⇒mustrepeattocalculatePr(x100)
OR
795nm
475nm
2‐photonexcita/on:
Ω/2π =0.9MHz
Prepare:
P r
10μmA B
Addressableexcita/on
Demonstra(onoftheRydbergblockade:U.Wisconsin
E.Urbanetal.,Nat.Phys.5,110(2009)
Oscilla/onofatomB
90d5/2
10μmA B
Addressableexcita/on
Demonstra(onoftheRydbergblockade:U.Wisconsin
E.Urbanetal.,Nat.Phys.5,110(2009)
P g
Demonstra(onoftheRydbergblockade:U.Wisconsin
Oscilla/onofatomB
90d5/2
10μmA B
Addressableexcita/on
Excita/onofatomBcondi/onnedbythestateofatomA⇒Demonstra/onofC‐NOTgateandentanglement
P g
Isenhoweretal.,PRL104,010503(2010)
Rydbergblockadeandcollec(veexcita(on:Ins(tutd’Op(que
474nm
795nmA
Exc.probaatomAonly
58d3/2
Gaëtanetal.,Nat.Phys.5,115(2009)
BLOCKADE
474nm
795nmA
BR=5μm
Exc.probaatomAonlyExc.probaatomA&B
58d3/2
Rydbergblockadeandcollec(veexcita(on:Ins(tutd’Op(que
Gaëtanetal.,Nat.Phys.5,115(2009)
Exc.probaatomAonlyExc.probaatomA&BExc.probaatomAORB
Freq.ra/o=1.41474nm
795nmA
B
Rydbergblockadeandcollec(veexcita(on:Ins(tutd’Op(que
R=5μm
58d3/2
Gaëtanetal.,Nat.Phys.5,115(2009)
Freq.ra/o=1.41474nm
795nmA
B
Rydbergblockadeandcollec(veexcita(on:Ins(tutd’Op(que
R=5μm
58d3/2
Fromfullblockadetopar(alblockade…
Non‐addressableexcita/on
VanderWaalsregime
R
A
B
Fromfullblockadetopar(alblockade…
Non‐addressableexcita/on
Par(alblockade:dynamicsinvolvesΩandUvdW
VanderWaalsregime
R
A
B
Fromfullblockadetopar(alblockade…
Non‐addressableexcita/on
VanderWaalsregime
R
A
B
P rr
time(µs)
V=Ω=1MHz
Schrödinger’sequa/on:
Fromindependentatomstoblockade(62d3/2)
1
0 1
0
1
0
1
0
1
0
2π 4π 6π 0 8π Pulse area Ωt
1
0 1
0
1
0
1
0 2π 4π 6π 0 8π Pulse area Ωt
R (µm)
15
10
9
4
53D3/2 62D3/2 82D3/2
MeasurementoftheVanderWaalsenergybetween2atoms
53D3/2 62D3/2 82D3/2
x50
MeasurementoftheVanderWaalsenergybetween2atoms
Theorycurves:directdiagonaliza/on(dipole‐dipoleinterac/on)Noadjustableparameter!
Béguinetal.,Phys.Rev.Le~.110263201(2013)
MeasurementoftheVanderWaalsenergybetween2atoms
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
Rydbergblockadeincoldatomiccloud:theU.Connec(cutexpt.
297nm
nL
5s
Pulsed,incoherentlaserexcita/onofaMOT⇒ expectNRyd∝Intensity
D.Tongetal.,PRL93,063001(2004)
Rydbergblockadeincoldatomiccloud:theU.Connec(cutexpt.
297nm
nL
5s
Pulsed,incoherentlaserexcita/onofaMOT⇒ expectNRyd∝Intensity
D.Tongetal.,PRL93,063001(2004)
Rydbergblockadeincoldatomiccloud:theU.Connec(cutexpt.
297nm
nL
5s
Pulsed,incoherentlaserexcita/onofaMOT⇒ expectNRyd∝Intensity
Increasen⇒increaseC6⇒increaseRb
D.Tongetal.,PRL93,063001(2004)
Rydbergblockadeindensecoldatomiccloud:theStulgartexpt.
H.Heidemannetal.,PRL99,163601(2007)
Useadenseultracoldcloudof87Rb+coherent2‐ph.excita/on
⇒reachsatura/on
Rydbergblockadeindensecoldatomiccloud:theStulgartexpt.
H.Heidemannetal.,PRL99,163601(2007)
Useadenseultracoldcloudof87Rb+coherent2‐ph.excita/on
Inhomogeneousdistribu/onofN
⇒reachsatura/on
Rydbergblockadeindensecoldatomiccloud:theStulgartexpt.
H.Heidemannetal.,PRL99,163601(2007)
Useadenseultracoldcloudof87Rb+coherent2‐ph.excita/on
Inhomogeneousdistribu/onofN
⇒Incoherentbehavior
⇒reachsatura/on
Collec(veRabioscilla(onsinensemble
Y.O.Dudinetal.,Nat.Phys.8,790(2012)
Excita/onvolume<Rb3
Expect:
102s,Rb=15μm
Op(callamces
1D 2D
Singlesiteresolu/on(<1µm)
16µm
Bakretal.,Nature462,74(2009)Shersonetal.,Nature467,68(2010)
Fluorescenceimageofindividualatoms
Planeofatoms
Spa(alobserva(onoftheblockade(MPQ,Garching)
500nmP.Schaussetal.,Nature491,87(2012)
Posi/onresolveddetec/on
Spa(alobserva(onoftheblockade(MPQ,Garching)
500nmP.Schaussetal.,Nature491,87(2012)
Correla/onfunc/on
Rb
Posi/onresolveddetec/on
Outline
1. Rydbergatomsandtheirinterac/on
2. Rydbergblockade:theore/calaspects
3. Observa/onoftheRydbergblockadeandcollec/veexcita/onfor2atoms
4. Rydbergblockadeincoldatomicensembles
5. Applica/onofRydbergblockadeinquantumop/cs
Adreamfora“quantuminternet”
J.H. Kimble (2005)
InterconnectQ.processorandQ.memoryusingphotons
Adreamfora“quantuminternet”
Interac/onbetweenphotons!
J.H. Kimble (2005)
InterconnectQ.processorandQ.memoryusingphotons
Requirements: 1. Singlephotonondemand2. Photonstorage3. Photonicgate
control
target
π
Single‐photonsourceandphotonstorage
D.Maxwell,etal.,PRL110,103001(2013)
D.Maxwell,etal.,PRL110,103001(2013)
Single‐photonsourceandphotonstorage
D.Maxwell,etal.,PRL110,103001(2013)
Momentumconserva/on:
Single‐photonsourceandphotonstorage
D.Maxwell,etal.,PRL110,103001(2013)
2ph
oton
proba.
Momentumconserva/on:
Suppressionof2photonevents
Single‐photonsourceandphotonstorage
D.Maxwell,etal.,PRL110,103001(2013)
μW
Momentumconserva/on:
Photonstorageusingmicrowave
writing Storage in |r’〉 release
t
Single‐photonsourceandphotonstorage
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
T1
Atomiccloud
ωprobeω0
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
Atomiccloud
1
ωprobeω0
T
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
probe
control
EIT+Rydbergblockade:Tcontrolledby1ph.!
1
Atomiccloud
1
ωprobeω0
T
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
probe
control
EIT+Rydbergblockade:Tcontrolledby1ph.!
1
Atomiccloud
1
ωprobeω0
T
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
probe
control
EIT+Rydbergblockade:Tcontrolledby1ph.!
1’
Atomiccloud
1
ωprobeω0
T
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
probe
control
EIT+Rydbergblockade:Tcontrolledby1ph.!
2
Atomiccloud
1
ωprobeω0
T
1’
Non‐linearityatthesingle‐photonlevel
Electromagne/callyInducedTransparency(EIT)
probe
control
probe
control
EIT+Rydbergblockade:Tcontrolledby1ph.!
2’
1’
2issca~ered
Atomiccloud
1
ωprobeω0
T
Non‐linearityatthesingle‐photonlevel
PhotodiodeB
PhotodiodeA
Probe+Control
Atomicsample
T.Peyroneletal.,Nature488,57(2012).
Nocontrol
Strongcontrol
Non‐linearityatthesingle‐photonlevel
PhotodiodeB
PhotodiodeA
Probe+Control
Atomicsample 1’
Prevents2ndph.during:
Non‐linearityatthesingle‐photonlevel
PhotodiodeB
PhotodiodeA
Probe+Control
Atomicsample 1’
Prevents2ndph.during:
Non‐linearityatthesingle‐photonlevel
PhotodiodeB
PhotodiodeA
Probe+Control
Atomicsample
Photonordering!
1’
Prevents2ndph.during:
Mechanismforphotonicgate
Conclusiononinterac(ngRydberggases
Playgroundforsemi‐classicalarguments(Bohrmodel)
Basicdemonstra/onsOK
Conclusiononinterac(ngRydberggases
Playgroundforsemi‐classicalarguments(Bohrmodel)
Basicdemonstra/onsOK
Quantuminforma(on
Improvefidelity
Simula(onofcondensedmalerSystems
Spinsystems,newphaseswithtailoredinterac/ons…
Conclusiononinterac(ngRydberggases
Playgroundforsemi‐classicalarguments(Bohrmodel)
Basicdemonstra/onsOK
Quantuminforma(on
Improvefidelity
Backto“old”ideas:coupletosolidstatesystems(surface,cavity)
Simula(onofcondensedmalerSystems
Spinsystems,newphaseswithtailoredinterac/ons…
Largeαtoprobesurfacefield,
electrometry
Ryd.beam
μwave
Hogan,PRL108063004(2012)
THANKYOU!
+
e‐
Rydbergblockadeindensecoldatomiccloud:theStulgartexpt.
Ω0/2π=210kHz
Ω0/2π=42kHz
ng0=7x1013at/cm3
ng0=3x1013at/cm3
H.Heidemannetal.,PRL99,163601(2007)
Checkscalinglaws
ExpectrateofRydbergproduc/onwith
Find:
Also,expect:andfind:
Demonstra(onofaC‐NOTgate:U.Wisconsin
D.Jackschetal.,PRL85,2208(2000)
Sequence:πA–2πB–πA
control target
Usethecondi/onnallogicofblockade
Demonstra(onofaC‐NOTgate:U.Wisconsin
D.Jackschetal.,PRL85,2208(2000)
11 → 10 10 → 1101 → 0100 → 00
Sequence:πA–2πB–πA
control target
Tableoftruth:
Usethecondi/onnallogicofblockade
Demonstra(onofaC‐NOTgate:U.Wisconsin
Isenhoweretal.,PRL104,010503(2010)
D.Jackschetal.,PRL85,2208(2000)
11 → 10 10 → 1101 → 0100 → 00
Sequence:πA–2πB–πA
control target
Tableoftruth:
Usethecondi/onnallogicofblockade
Fromfullblockadetopar(alblockade…
Blockaderegime:Prr=0andProscillates√2faster
Non‐addressableexcita/on
VanderWaalsregime
R
A
B