Interacng Cold Rydberg atoms: A Toy Many‐Body System · 2. Rydberg blockade: theorecal aspects 3....

AntoineBrowaeysIns/tutd’Op/que,CNRS

Interac(ngColdRydbergatoms:

AToyMany‐BodySystem

+

e‐

SéminairePoincaré7décembre2013

Many‐bodysystemsandcomplexity

Microscopic

Quantumlaws…


Microscopic Macroscopic

?

Quantumlaws…

quantumorclassicallaws


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



Coldatoms

Ar(ficialatoms

NVcenter Supra.circuit



Coldatoms

Ar(ficialatoms


Many‐bodytoysystems



Ar(ficialatoms


Many‐bodytoysystems

ColdRydbergatoms

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


continuum

Ene

rgy

Rydbergstates

+

e‐


Alkaliatoms(Rb,Cs)⇒hydrogenoid


continuum

Ene

rgy

Rydbergstates

+

e‐


Screeningeffectofelectroniccore:

Quantumdefect:

Alkaliatoms(Rb,Cs)⇒hydrogenoid

Proper(esofRydbergatoms

~ 100nm

+

e‐Bohrmodel:size


~ 100nm

+

e‐Bohrmodel:size

1.  Largedipoleelementsbetweenand

for


~ 100nm

+

e‐Bohrmodel:size


Ex:n≈50⇒3000×d(H20)!

for


~ 100nm

+

e‐Bohrmodel:size


2.  Largepolarizability ⇒largeAC&DCStarkshig

Ex:n≈50⇒3000×d(H20)!

for


~ 100nm

+

e‐Bohrmodel:size


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:


+ + R

A B

ns,ns

np,(n‐1)p

Δ(n)

ETwoatombasis:


+ + R

A B

np,(n‐1)p

Δ(n)

ETwoatombasis:

ns,ns


+ + R

A B

Twoatombasis:

VanderWaals:⇒

np,(n‐1)p

Δ(n)

E

ns,ns


+ + R

A B

Twoatombasis:

VanderWaals:⇒

np,(n‐1)p

Δ(n)

E

ns,ns


Scaling:

+ + R

A B

Twoatombasis:

VanderWaals:⇒

Resonantregime:⇒

np,(n‐1)p

Δ(n)

E

ns,ns


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


J‐MRaimond,J.Phys.B14,L655(1981)

kBT<<Interac(onenergy⇒T<1mK⇒coldatoms

The“denseRydberggas”

DenseCsbeam

ωL



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


Outline






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)

RA B

If :noexcita/onof⇒BLOCKADE


RA B

Collec/veoscilla/onbetweenandwithcoupling


with

RA B

BlockadesphereandN‐atomcollec(veexcita(on

Onlyoneatomexcitedwithinasphereof“blockade”radiusRb



Coherentexcita/on:

Ex:62d3/2,Ω/2π=1MHz⇒Rb=10μm


Natomswithintheblockadesphere⇒collec/veoscilla/on


Ex:62d3/2,Ω/2π=1MHz⇒Rb=10μm

Coherentexcita/on:

Outline






Non‐resonantatom‐laserinterac/on⇒light‐shia

|g〉

|e〉

I ~ I

Microscopicop(caldipoletrap

Dipoletraplight


|g〉

|e〉

I ~ I

HighNAlens

Dichroicmirror

Size ~ 1 µmVolume ~ 1 µm3

Depth≈1mK⇒lasercooledatoms


Laser‐cooledatomsT~100µK

Fluorescencephotoncounter,

camera

Dipoletraplight


|g〉

|e〉

I ~ I

Resonantlaser

HighNAlens

Dichroicmirror


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:


795nm

475nm


Prepare:


Resultofasinglemeasurement:

OR

795nm

475nm


Prepare:

⇒mustrepeattocalculatePr(x100)


58d3/2

Resultofasinglemeasurement:

⇒mustrepeattocalculatePr(x100)

OR

795nm

475nm


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



E.Urbanetal.,Nat.Phys.5,110(2009)

P g


Oscilla/onofatomB

90d5/2

10μmA B


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



Exc.probaatomAonlyExc.probaatomA&BExc.probaatomAORB

Freq.ra/o=1.41474nm

795nmA

B


R=5μm

58d3/2


Freq.ra/o=1.41474nm

795nmA

B


R=5μm

58d3/2

Fromfullblockadetopar(alblockade…

Non‐addressableexcita/on

VanderWaalsregime

R

A

B



Par(alblockade:dynamicsinvolvesΩandUvdW

VanderWaalsregime

R

A

B



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


Theorycurves:directdiagonaliza/on(dipole‐dipoleinterac/on)Noadjustableparameter!

Béguinetal.,Phys.Rev.Le~.110263201(2013)


Outline






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




Inhomogeneousdistribu/onofN

⇒reachsatura/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






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)


Momentumconserva/on:



2ph

oton

proba.


Suppressionof2photonevents



μW


Photonstorageusingmicrowave

writing Storage in |r’〉 release

t


Non‐linearityatthesingle‐photonlevel

Electromagne/callyInducedTransparency(EIT)

probe

T1

Atomiccloud

ωprobeω0



probe

control

Atomiccloud

1

ωprobeω0

T



probe

control

probe

control

EIT+Rydbergblockade:Tcontrolledby1ph.!

1

Atomiccloud

1

ωprobeω0

T



probe

control

probe

control


1’

Atomiccloud

1

ωprobeω0

T



probe

control

probe

control


2

Atomiccloud

1

ωprobeω0

T

1’



probe

control

probe

control


2’

1’

2issca~ered

Atomiccloud

1

ωprobeω0

T


PhotodiodeB

PhotodiodeA

Probe+Control

Atomicsample

T.Peyroneletal.,Nature488,57(2012).

Nocontrol

Strongcontrol


PhotodiodeB

PhotodiodeA

Probe+Control

Atomicsample 1’

Prevents2ndph.during:


PhotodiodeB

PhotodiodeA

Probe+Control

Atomicsample

Photonordering!

1’

Prevents2ndph.during:

Mechanismforphotonicgate

Conclusiononinterac(ngRydberggases

Playgroundforsemi‐classicalarguments(Bohrmodel)

Basicdemonstra/onsOK




Quantuminforma(on

Improvefidelity

Simula(onofcondensedmalerSystems

Spinsystems,newphaseswithtailoredinterac/ons…




Quantuminforma(on

Improvefidelity

Backto“old”ideas:coupletosolidstatesystems(surface,cavity)

Simula(onofcondensedmalerSystems

Spinsystems,newphaseswithtailoredinterac/ons…

Largeαtoprobesurfacefield,

electrometry

Ryd.beam

μwave

Hogan,PRL108063004(2012)

THANKYOU!

+

e‐


Ω0/2π=210kHz

Ω0/2π=42kHz

ng0=7x1013at/cm3

ng0=3x1013at/cm3


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



11 → 10 10 → 1101 → 0100 → 00


control target

Tableoftruth:



Isenhoweretal.,PRL104,010503(2010)


11 → 10 10 → 1101 → 0100 → 00


control target

Tableoftruth:



Blockaderegime:Prr=0andProscillates√2faster


VanderWaalsregime

R

A

B

Interacng Cold Rydberg atoms: A Toy Many‐Body System · 2. Rydberg blockade: theorecal aspects 3....

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Transcript of Interacng Cold Rydberg atoms: A Toy Many‐Body System · 2. Rydberg blockade: theorecal aspects 3....