Controlling light and ma.er using coopera4ve radia4on Part I: … · 2019-03-13 · Controlling...

Controllinglightandma.erusingcoopera4veradia4on

PartI:Dickestates,coopera4veeffects,entanglement

SusanneYelin

UniversityofConnec4cutHarvardUniversity

Herrsching,March6,2019 �1

�2

Roy Glauber, 1925 - 2018

Goalsofthelectures

• Use2Darray…

�3

�4

• …toreflectlight…

• …emitincontrolledway…

Increase(impurity)crosssec4on?

Increase(impurity)crosssec4on?

• …edgestateswithphotons?

wikipedia

• 2DmaterialslikegrapheneorTMDs

• …toswitch(singlephotons)

• …toswitch(singlephotons)

Quantummirror:Refrac4onsuperposi4on

�10whyquantumphysicists.com

Why “cooperative effects”??

Coopera4veradia4on:superradiance

�12

For want of a better term, a gas which is radiating strongly because of coherence will be called “superradiant.”

— Robert H Dicke, 1954.

Dicke, Phys. Rev. 93, 99 (1954).

What is an atom?

levels

What is an atom?

levels

(sub)levels

How does it couple to light?

photon energy: hνatomic transition energy: Eup-Edown

hνEup

Edown

How does it couple to light?

photon energy: hνatomic transition energy: Eup-Edown

hνEup

Edown

time

inte

nsity

Cooperative effects in radiation

single atom

time

inte

nsity

Cooperative effects in radiation

two far-away atoms

time

inte

nsity

Cooperative effects in radiation

two close atoms

time

inte

nsity

Cooperative effects in radiation• Superradiance∝N2

duetoconstruc4veinterference

• Build-upof“collec4vedipoles”

many close atoms

Coopera4veEffects

• Twoimportantaspects:– collec4veeffects(manypar4cles)

�27

Coopera4veEffects

• Twoimportantaspects:– collec4veeffects(manypar4cles)

• e.g.,muchhigherchanceforphotonstointeractwithmanyatomsthanone

– “exchange”duetodipole-dipoleinterac4on• excita4onsareexchanged

• “Coopera4ve”ismorethanjust“collec4ve”!

�27

Collective effects: Example of quantized field

• Interaction Hamiltonian with classical light (Rabi frequency Ω)

• Interaction Hamiltonian with quantized light (coupling element g, annihilation operator a, number of atoms N)

!28

H/~ = g

pN�|eihg| a+ a

+ |gihe|�

H/~ = ⌦ (|eihg|+ |gihe|)

Coopera4veeffects

• simplestformof“exchangeinterac4on”

�29

Coopera4veeffects

• Tradi4onalexample:superradiance

�30

time

inte

nsity

Cooperative effects in radiation• Superradiance∝N2

duetoconstruc4veinterference

• Build-upof“collec4vedipoles”

many close atoms

Whatissuperinsuperradiance?

�32

man(Clark)

manymen(Clarks)

Whatissuperinsuperradiance?

�32

man(Clark)

manymen(Clarks)

SUPERMAN

Whatissuperinsuperradiance?

�32

man(Clark)

manymen(Clarks)

SUPERMAN

�33

Examples

Superradiantlaser

�34

Bohnet,Chen,Weiner,Meiser,Holland,Thompson,Nature484,78(2012)

JILA

#Atoms ≫ #Photons

⟱

much more coherent lasing

�35

Super- radiance in BECs

Inouye, Chikkatur, Stamper-Kurn, Stenger, Pritchard, KetterleScience  23 (1999)

momentum conservation

+interference of matter waves

�36Torres, Patrick, Coutant, Richartz, Tedford, WeinfurtnerNature Physics 13, 833 (2017).

Physics World

rotation energy amplifies waves if Ωrot > ωwave

Black hole superradiance

�37Pani, Brito, Cardoso, Class. Quantum Grav. 32 134001 (2015)

(basically same as for water waves)

spinning black hole….

… amplifies graviational waves

Subradiance

�38Guerin, Araujo, Kaiser, PRL 116, 083601 (2016)

pulseno pulse

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors

‣ Collec4ve(Lamb)levelshifs

‣ Subradiance

‣ Entanglement

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors‣ Coopera4veresonances

‣ Applica4ons:

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors‣ Coopera4veresonances

‣ Applica4ons:

• topologywithphotons• nonlinearquantumop4cs

• Quantummetasurfaces

Superradiance:recentexperiment

Grimes, Coy, Barnum, Zhou, Yelin, Field, PRA 95, 043818 (2017)

Superradiance:recentexperiment

Grimes, Coy, Barnum, Zhou, Yelin, Field, PRA 95, 043818 (2017)

Ba

SuperradianceinBaRydbergs

typical superradiance

time profile

shift from red…

Collective shift

SuperradianceinBaRydbergs

typical superradiance

time profile …to blue

Collective shift

�45

|ee⇥ � |1, 1⇥

|gg⇤ ⇥ |1,�1⇤

Coopera4veradia4on:twoatoms

|egi |gei

atoms distinguishable

�47

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥ 1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

atoms indistinguishable

Coopera4veradia4on:twoatoms

|ee⇥ � |1, 1⇥

�47

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥ 1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

atoms indistinguishable

Coopera4veradia4on:twoatoms

|ee⇥ � |1, 1⇥

�47

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥ 1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

atoms indistinguishable

Coopera4veradia4on:twoatoms

|ee⇥ � |1, 1⇥

destructive interference

�48

|ee⇥ � |1, 1⇥

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥

1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

dipole-dipole exchange interaction

atoms indistinguishable

Coopera4veradia4on:twoatoms

�49dipole-dipole exchange interaction

|ee⇥ � |1, 1⇥

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥

1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

atoms indistinguishable

Coopera4veradia4on:twoatoms

�51dipole-dipole exchange interaction

|ee⇥ � |1, 1⇥

|gg⇤ ⇥ |1,�1⇤

1⇤2

(|eg⇥+ |ge⇥) � |1, 0⇥

1⌅2

(|eg⇤ � |ge⇤) ⇥ |0, 0⇤

atoms indistinguishable

Coopera4veradia4on:twoatoms

exchange interaction:• usually dipole-dipole mediated• creates shift and broadening

(Kramers-Kronig) •

Whatis“superradiance”?

�52

1.EverythingthatinvolvesDickestates- (e.g.,collec4ve√Neffects,-bad-cavitylimit,

-…)

Dickestates

�53

Fullysymmetricstateofnexcita4onsinNpar4cles,forexample

N-par4cleDickestatesdecaywithuptoN2speedup

|2i4 =1p6

(|1100i+ |1010i+ |1001i+

|0110i+ |0101i+ |0011i)

Dickestates

• Ques4on:WhendowehaveasystemthatconsistsonlyofDickestates?

• Answer1:Whenthereexistsnomechanismtodis4nguishatoms.Example:

• Problem:interac4ons(dip-dip)drivesystemoutofpurelysymmetricstate!Howtodeal?

• (Answer2:Whentheexchangeinterac4onisinfinitelyhigh.Inthiscase,otherstatescannotbereached.Example:“many-bodyprotectedmanifolds”)

�54

λ

�55

Describingsuperradiance

�55

Describingsuperradiance

Useangularmomentumform:｜J,mdenotessystemwithmexcita4ons,m=-J…J.

Angularmomentumstates

• Formof3-atomDickestate?

• Whataretheotherstates?

• 4atoms?

• 40?

�56

Popula4onofsymmetricstates

• Whatpossiblepathcouldasystemstar4ngin|11111…>take,

• withonlydecay?

• whenthereisdipole-dipoleinterac4on?

�57

Stateconnec4ons

�58

J =N

2J =

N

2� 1 J = 0

Spontaneous superradiant decay

Stateconnec4ons

�58

J =N

2J =

N

2� 1 J = 0

Spontaneous superradiant decay

dipole-dipole interaction

Formofdipole-dipoleinterac4on

�59

Hdip�dip =X

i 6=j

Vij �+i �

�j

“Exchange”term• Howwouldthisshowupinamasterequa4on?

�60

Formofdipole-dipoleinterac4on

�61

dipole-dipole interaction: ‣distance dependence‣angle dependence‣ real + imaginary part

real virtual photon exchange

flip-flop“exchange”

shift/dephasing

Atom-atomcorrela4onsinsuperradiance:Classicexample

•Superradiance λ

Gross,Haroche,Phys.Rep.93,301(‘82) �62

�63

inte

nsity

/ at

om

t/γ-1

Same parameters as before: C=10

with exchange

no exchange(“amplified spontaneous emission”)

Fleischhauer, Yelin, PRA 59, 2427 (99); Lin, Yelin, Adv. Atom. Mol. Opt. Phys. 61, 295 (2012)

Whatis“superradiance”?

�64

1.EverythingthatinvolvesDickestates- (e.g.,collec4ve√Neffects,-bad-cavitylimit,

-…)2.Onlysystemsinvolvingcoopera4ve(andnonlinear)effects

- i.e.,effectofexchangeinterac4on-morethansingleexcita4on

Whatis“superradiance”?

�64

1.EverythingthatinvolvesDickestates- (e.g.,collec4ve√Neffects,-bad-cavitylimit,

-…)2.Onlysystemsinvolvingcoopera4ve(andnonlinear)effects

- i.e.,effectofexchangeinterac4on-morethansingleexcita4on

only for purists

Fulldynamics(alldegreesoffreedomofatoms,fields)

Dynamicsofatomsindensemedia-Schwinger-Keldysh&DysonEq.

twoprobeatoms+

surroundingatoms

Twoatoms+field

effec4vetwo-atomdescrip4on�65

Fleischhauer, Yelin, PRA 59, 2427 (99); Lin, Yelin, Adv. Atom. Mol. Opt. Phys. 61, 295 (2012)

Fulldynamics(alldegreesoffreedomofatoms,fields)

Dynamicsofatomsindensemedia-Schwinger-Keldysh&DysonEq.

Gauss: fielddegreesoffreedom

TwoatomMasterequa4on

twoprobeatoms+

surroundingatoms

Twoatoms+field

effec4vetwo-atomdescrip4on

Twoatoms+field

Vprobe =�

i=1,2

piEiH � S = Te�i�

Rd�Vprobe(�)

effec4vetwo-atomdescrip4on

Fulldynamics(alldegreesoffreedomofatoms,fields)

H = Hatoms + Hfield ��

i=1,2

piEi

�65Fleischhauer, Yelin, PRA 59, 2427 (99); Lin, Yelin, Adv. Atom. Mol. Opt. Phys. 61, 295 (2012)

�66

∫ DDEi(t1)Ej(t2)

EE

trace out field degrees of freedom

�68

Canoneexpectsuperradiance?

Theimportantparameteris

n�2r

n:density,λ:wavelength,r:systemsize

op4caldepth

Lin, Yelin, Adv. Atom. Mol. Opt. Phys. 61, 295 (2012)

�68

Canoneexpectsuperradiance?

Theimportantparameteris

n�2r

n:density,λ:wavelength,r:systemsize

op4caldepth

Lin, Yelin, Adv. Atom. Mol. Opt. Phys. 61, 295 (2012)

or nλ3 ?

MasterEqua4on

�69

MasterEqua4on

�69

DDE(t)

EE

MasterEqua4on

�69

DDE(t)

EE

DDE1(t1)E2(t2)

EE

Newexperimentalsystems:example

•UltracoldRydbergatoms

(PhilGould,EdEyler,Uconn)…

…

40P

39S

38S

5S

39D

38D

5D

Rb

�70

Effec4vedecay4mesfrom40PintonS

principlequantumnumbern

τ eff/µs(in

verseEinsteinA)

vacuum

(DanielVrinceanu)

densegas

Invacuum:decayintolownisfavoredIndensegas:decayintohighnisfavored➱λlarge,nλ2rlarge!

superradiantdecay! �71

Effec4vedecay4mesfrom40PintonS

principlequantumnumbern

τ eff/µs(in

verseEinsteinA)

vacuum

(DanielVrinceanu)

densegas

Invacuum:decayintolownisfavoredIndensegas:decayintohighnisfavored➱λlarge,nλ2rlarge!

superradiantdecay! �71

long wavelengths are much favored ⇒

experiments with Rydberg, molecular,

microwave transitions likely involve

superradiance

Wang, et al.,PRA 75, 033802 (2007); Lin & Yelin Mol. Phys. 111, 1917 (2013).

ExperimentalProof!

�72Carr,Ri.er,Wade,Adams,Weatherill,PRL111,113901(2013)

lowdensity

highdensity

SuperradianceinRydbergsystems

start of measurement

experiment

time (µs)

nu

mb

er

of

Ryd

be

rg a

tom

s

theory

200

500

1000

1500

2000

2500

0 5 10 15

�73

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors

‣ Collec4ve(Lamb)levelshifs

‣ Subradiance

‣ Entanglement

‣ Collec4ve(Lamb)levelshifs

Decay dynamics

t/γ-1

excit

ed le

vel p

opul

atio

n fast

slow

cf. two atoms

�77

Subradiance?

super-radiance

sub-radiance

radiationtrapping

Subradiantstates

�78

J =N

2J =

N

2� 1 J = 0

Spontaneous superradiant decay

dipole-dipole interaction

�79

Transitions

excited state population

two-atomcoherence

Subradiance:Outlook

• Dynamicsofsubradiance=transi4ontomany-bodylocalizedstate?

➡ Create,manipulatelocaliza4on

• Engineeredsubradiancetocreatestablestateswithoutspontaneousdecay

➡ Create,stabilizemany-bodyentangledstate(Dissipa4venon-equilibriumphysics)

Collec4veLambshif“Lambshif”istheresultofinterac4onwiththevacuumfluctua4ons

Inthecaseofaltereddensityofstatesofthe“vacuum”(i.e.,thesurroundingspace),thevalueoftheshifchanges

Withahigh(superradiant)densityofradiators,thedensityofstatesinsidethemediumcanbeconsiderablyaltered

“Collec4veLambshif”Putnam, Lin, Yelin, arXiv:1612.04477

hasspontaneouspart....�ij(!) =

}2

~2

Zd⌧

DhE�i (t),E+

j (t + ⌧)iE

ei!⌧

�(ij)spont =

1

2⇡P

Zd!0 �ij(!0)

! � !0

⌦⇥E�,E+

⇤↵/

⌦⇥a, a†

⇤↵= 1

independentonnumberofphotons

Collective Shift

hasspontaneouspart....�ij(!) =

}2

~2

Zd⌧

DhE�i (t),E+

j (t + ⌧)iE

ei!⌧

�(ij)spont =

1

2⇡P

Zd!0 �ij(!0)

! � !0

⌦⇥E�,E+

⇤↵/

⌦⇥a, a†

⇤↵= 1

independentonnumberofphotons

Collec4

veLamb

Shif

Collective Shift

Collective Lamb Shift

Keaveney et al.,PRL 108, 173601 (2012), theory: Lin, Li, Yelin, in prep.

cavitywith variable

thickness

~ λ

~ λ/8

Collective Lamb Shift

Keaveney et al.,PRL 108, 173601 (2012), theory: Lin, Li, Yelin, in prep.

cavitywith variable

thickness

~ λ

~ λ/8

Collective Lamb Shift

Keaveney et al.,PRL 108, 173601 (2012), theory: Lin, Li, Yelin, in prep.

cavitywith variable

thickness

~ λ

~ λ/8

In Fig. 4 we plot the gradient of the line shift as afunction of cell thickness. For the Rb D2 resonance,!LL=N ¼ "2!"k"3, where we have used the relationshipbetween the dipole moment for the s1=2 ! p3=2 transit-

ion and the spontaneous decay rate, d ¼ffiffiffiffiffiffiffiffi2=3

phLe ¼

1jerjLg ¼ 0i (see Ref. [27]). We extract the collisional

shift by comparing the data to Eq. (8) with !col the onlyfree parameter. The amplitude and period of the oscillatorypart are fully constrained by Eq. (7). We find the collisionalshift to be !col=2! ¼ ð"0:25$ 0:01Þ & 10"7Hzcm3,similar to previous measurements on potassium vapor[24]. In this high density limit, the collisional shift is alsoindependent of hyperfine splitting. The solid line is theprediction of Eq. (7), and the agreement between themeasured shifts and the theoretical prediction is remark-able (the reduced "2 for the data is 1.7). As well asmeasuring the thickness dependence of the cooperative

Lamb shift, our data also provide a determination of theLorentz shift which can only be measured in the limit ofzero thickness. An important advance on previous studies[8] is that the results clearly show the oscillations in theshift versus the thickness which arises due to the relativephase of the reradiated dipolar field.The demonstration of the cooperative Lamb shift and

coherent dipole-dipole interactions in media with thickness'#=4 opens the door to a new domain for quantum optics,analogous to the strong dipole-dipole nonlinearity inblockaded Rydberg systems [29,30]. As the cooperativeLamb shift depends on the degree of excitation [5], exoticnonlinear effects such as mirrorless bistability [31,32] arenow accessible experimentally. In addition, given thefundamental link between the cooperative Lamb shift andsuperradiance, subquarterwave thickness vapors offer anattractive system to study superradiance in the smallvolume limit. Finally, we note that the measured coopera-tive Lamb shift is the average dipole-dipole interactionfor a homogeneous gas which contains both positive andnegative contributions. It could therefore be enhanced byeliminating directions that contribute with the undesiredsign, for example, by patterning the distribution of dipoles.These topics will form the focus of future research.We would like to thank M. P. A. Jones for stimulating

discussions. We acknowledge financial support fromEPSRC and Durham University.

*c.s.adams@durham.ac.uk[1] W. E. Lamb and R. C. Retherford, Phys. Rev. 72, 241

(1947).[2] P. Goy, J.M. Raimond, M. Gross, and S. Haroche, Phys.

Rev. Lett. 50, 1903 (1983).[3] W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi,

and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).[4] J. Eschner, C. Raab, F. Schmidt-Kaler, and R. Blatt,

Nature (London) 413, 495 (2001).[5] R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys.

Rep. 7, 101 (1973).[6] M.O. Scully and A.A. Svidzinsky, Science 328, 1239

(2010).[7] M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).[8] W.R. Garrett, R. C. Hart, J. E. Wray, I. Datskou, and

M.G. Payne, Phys. Rev. Lett. 64, 1717 (1990).[9] R. Rohlsberger, K. Schlage, B. Sahoo, S. Couet, and

R. Ruffer, Science 328, 1248 (2010).[10] S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and

M. Ducloy, Phys. Rev. A 57, R3169 (1998).[11] D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, Opt.

Commun. 200, 201 (2001).[12] G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan,

D. Sarkisyan, D. Bloch, and M. Ducloy, Europhys. Lett.63, 35 (2003).

[13] G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, J. Opt. Soc.Am. B 20, 793 (2003).

FIG. 3 (color online). Shift of resonance lines with density.Measured shift of resonance lines with density and fit to thelinear, high density region for ‘ ¼ 90 nm (red squares, dashedline) and ‘ ¼ 250 nm (blue circles, solid line).

FIG. 4 (color online). Experimental verification of the coop-erative Lamb shift. The gradient of the dipole-dipole shift !dd=Nis plotted against cell thickness ‘. A collisional shift !col=2! ¼"0:25& 10"7 Hz cm3 has been subtracted. The solid black lineis Eq. (7) with no other free parameters. The conversion betweenexperimental and universal units is outlined in the main text.

PRL 108, 173601 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

27 APRIL 2012

173601-4

shift

/ "

layer thickness

Collective Lamb Shift

�86

Optical depth = lowest

Optical depth = highest

In Fig. 4 we plot the gradient of the line shift as afunction of cell thickness. For the Rb D2 resonance,!LL=N ¼ "2!"k"3, where we have used the relationshipbetween the dipole moment for the s1=2 ! p3=2 transit-

ion and the spontaneous decay rate, d ¼ffiffiffiffiffiffiffiffi2=3

phLe ¼

1jerjLg ¼ 0i (see Ref. [27]). We extract the collisional

shift by comparing the data to Eq. (8) with !col the onlyfree parameter. The amplitude and period of the oscillatorypart are fully constrained by Eq. (7). We find the collisionalshift to be !col=2! ¼ ð"0:25$ 0:01Þ & 10"7Hzcm3,similar to previous measurements on potassium vapor[24]. In this high density limit, the collisional shift is alsoindependent of hyperfine splitting. The solid line is theprediction of Eq. (7), and the agreement between themeasured shifts and the theoretical prediction is remark-able (the reduced "2 for the data is 1.7). As well asmeasuring the thickness dependence of the cooperative

Lamb shift, our data also provide a determination of theLorentz shift which can only be measured in the limit ofzero thickness. An important advance on previous studies[8] is that the results clearly show the oscillations in theshift versus the thickness which arises due to the relativephase of the reradiated dipolar field.The demonstration of the cooperative Lamb shift and

coherent dipole-dipole interactions in media with thickness'#=4 opens the door to a new domain for quantum optics,analogous to the strong dipole-dipole nonlinearity inblockaded Rydberg systems [29,30]. As the cooperativeLamb shift depends on the degree of excitation [5], exoticnonlinear effects such as mirrorless bistability [31,32] arenow accessible experimentally. In addition, given thefundamental link between the cooperative Lamb shift andsuperradiance, subquarterwave thickness vapors offer anattractive system to study superradiance in the smallvolume limit. Finally, we note that the measured coopera-tive Lamb shift is the average dipole-dipole interactionfor a homogeneous gas which contains both positive andnegative contributions. It could therefore be enhanced byeliminating directions that contribute with the undesiredsign, for example, by patterning the distribution of dipoles.These topics will form the focus of future research.We would like to thank M. P. A. Jones for stimulating

discussions. We acknowledge financial support fromEPSRC and Durham University.

*c.s.adams@durham.ac.uk[1] W. E. Lamb and R. C. Retherford, Phys. Rev. 72, 241

(1947).[2] P. Goy, J.M. Raimond, M. Gross, and S. Haroche, Phys.

Rev. Lett. 50, 1903 (1983).[3] W. Jhe, A. Anderson, E. A. Hinds, D. Meschede, L. Moi,

and S. Haroche, Phys. Rev. Lett. 58, 666 (1987).[4] J. Eschner, C. Raab, F. Schmidt-Kaler, and R. Blatt,

Nature (London) 413, 495 (2001).[5] R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys.

Rep. 7, 101 (1973).[6] M.O. Scully and A.A. Svidzinsky, Science 328, 1239

(2010).[7] M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).[8] W.R. Garrett, R. C. Hart, J. E. Wray, I. Datskou, and

M.G. Payne, Phys. Rev. Lett. 64, 1717 (1990).[9] R. Rohlsberger, K. Schlage, B. Sahoo, S. Couet, and

R. Ruffer, Science 328, 1248 (2010).[10] S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and

M. Ducloy, Phys. Rev. A 57, R3169 (1998).[11] D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, Opt.

Commun. 200, 201 (2001).[12] G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan,

D. Sarkisyan, D. Bloch, and M. Ducloy, Europhys. Lett.63, 35 (2003).

[13] G. Dutier, S. Saltiel, D. Bloch, and M. Ducloy, J. Opt. Soc.Am. B 20, 793 (2003).

FIG. 3 (color online). Shift of resonance lines with density.Measured shift of resonance lines with density and fit to thelinear, high density region for ‘ ¼ 90 nm (red squares, dashedline) and ‘ ¼ 250 nm (blue circles, solid line).

FIG. 4 (color online). Experimental verification of the coop-erative Lamb shift. The gradient of the dipole-dipole shift !dd=Nis plotted against cell thickness ‘. A collisional shift !col=2! ¼"0:25& 10"7 Hz cm3 has been subtracted. The solid black lineis Eq. (7) with no other free parameters. The conversion betweenexperimental and universal units is outlined in the main text.

PRL 108, 173601 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

27 APRIL 2012

173601-4

shift

/ "

layer thickness

Keaveney et al.,PRL 108, 173601 (2012), theory: Lin, Li, Yelin, in prep.

�87

hasspontaneouspart....�ij(!) =

}2

~2

Zd⌧

DhE�i (t),E+

j (t + ⌧)iE

ei!⌧

�(ij)spont =

1

2⇡P

Zd!0 �ij(!0)

! � !0

...and“s4mulated”part

�ij(!) =}2

~2

Zd⌧

DDE�i (t)E+

j (t + ⌧)EE

ei!⌧

�(ij)stim =

1

2⇡P

Zd!0 �ij(!0)

! � !0

dependentonnumberofphotons

⌦⌦E�E+

↵↵ /⇠⌦⌦

a† a↵↵

= n

Collective Shift

�87

hasspontaneouspart....�ij(!) =

}2

~2

Zd⌧

DhE�i (t),E+

j (t + ⌧)iE

ei!⌧

�(ij)spont =

1

2⇡P

Zd!0 �ij(!0)

! � !0

...and“s4mulated”part

�ij(!) =}2

~2

Zd⌧

DDE�i (t)E+

j (t + ⌧)EE

ei!⌧

�(ij)stim =

1

2⇡P

Zd!0 �ij(!0)

! � !0

dependentonnumberofphotons

⌦⌦E�E+

↵↵ /⇠⌦⌦

a† a↵↵

= n

Induced

shif

Collective Shift

�88

Collective Shift: decay of inverted TLS

Putnam, Lin, Yelin, arXiv:1612.04477

Theselectures

• Coopera4veeffectsincomplexsystems

• Newapplica4on:atomicallythinmirrors

‣ Collec4ve(Lamb)levelshifs

‣ Subradiance

‣ Entanglement‣ Entanglement

�90

SuperradianceandEntanglement

Does(Dicke)superradianceneed/createentanglement?

NO

Wolfe,Yelin,PRL112,140402(’14)

Example:2-atomDicke

• PPT(Peres-Horodecki)criterion:

Eigenvaluesofpar4alposi4vetranspose≥0

�91

⇢ =X

ijkl

pijkl|iihj|⌦ |kihl|

⇢PPT =X

ijkl

pijkl|iihj|⌦ |lihk|

H Barnum, E Knill, G Ortiz, R Somma, L Viola Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence G Adesso, A Serafini, F Illuminati Energy and multipartite entanglement in multidimensional and frustrated spin models O Gühne, G Toth Multipartite entanglement in four-qubit cluster-class states YK Bai, ZD Wang Exact and asymptotic measures of multipartite pure-state entanglement CH Bennett, S Popescu, D Rohrlich, JA Smolin Geometric measure of entanglement and applications to bipartite and multipartite quantum states TC Wei, PM Goldbart Scalable multiparticle entanglement of trapped ions H Häffner, W Hänsel, CF Roos, J Benhelm, M Chwalla

�92

Howtodefine/calculatemany-par4cleentanglement?

SuperradianceandEntanglement

~ 10,000 for “definitio

n of

multipartit

e entanglement”

�93

SuperradianceandEntanglement

Does(Dicke)superradianceneed/createentanglement?(Ini4alstate:noentanglement)

Dickesuperradiant4meevolu4on

separablestates=

construc+veproof

Wolfe,Yelin,PRL112,140402(’14)

Dickesuperradiantstates

separablestates

�94

SuperradianceandEntanglement

=

Does(Dicke)superradianceneed/createentanglement?(Ini4alstate:noentanglement)

Wolfe,Yelin,Wolfe,Yelin,PRL112,140402(’14)

Dickesuperradiantstates

separablestates

�94

SuperradianceandEntanglement

oursystem:mixedstateofN-atomDickestateswithN+1knownindependent

coefficientspi

comparetomixtureofsymmetricproductstatesofN(two-level)atoms(needs

N+1coefficientsyi)

=

(N+1)-dim.equa4onsystem

Does(Dicke)superradianceneed/createentanglement?(Ini4alstate:noentanglement)

Wolfe,Yelin,Wolfe,Yelin,PRL112,140402(’14)

Formofequa4ons

• GeneralDickestates:

• Separablediagonallysymmetric:

�95

�96

SuperradianceandEntanglement

oursystem:mixedstateofN-atomDickestateswithN+1knownindependent

coefficientspi

comparetomixtureofsymmetricproductstatesofN(two-level)atoms(needs

N+1coefficientsyi)

=

(N+1)-dim.equa4onsystem

condi4

on:

allcoeffi

cients

0≤pi≤

1

Does(Dicke)superradianceneed/createentanglement?(Ini4alstate:noentanglement)

Wolfe,Yelin,PRL112,140402(’14)

�97

SuperradianceandEntanglement

oursystem:mixedstateofN-atomDickestateswithN+1knownindependent

coefficientspi

comparetomixtureofsymmetricproductstatesofN(two-level)atoms(needs

N+1coefficientsyi)

=

(N+1)-dim.equa4onsystem

condi4

on:

allcoeffi

cients

0≤pi≤

1

!

Does(Dicke)superradianceneed/createentanglement?(Ini4alstate:noentanglement)

Wolfe,Yelin,PRL112,140402(’14)

(works

!)

�98

SuperradianceandEntanglement

Drivensuperradiantsystem:

• Drivingalonedoesnotentangleatoms

• Superradiancealonedoesnotentangleatoms

• Drivingandsuperradiancetogetherentangleatoms!

FuzzyBunny?

�99

SpinSqueezing

• Correlated(“squeezed”)spinscouldimproveresolu4oninonedirec4on(“quadrature”).

�100

(Spin)Squeezing

• Howtomeasuresqueezing/measurementimprovement?

�101Kitagawa, Ueda, PRA 47, 5138 (93)

Spinsqueezing

Oldproblem:Howtoimprovemetrologybyspinsqueezingensembles

➡GroupsofBigelow,Kuzmich,Lewenstein,Mølmer,Polzik,Sanders,Sørensen,Vule4c,Wineland,…

�102

SpinSqueezing

• Correlated(“squeezed”)spinscouldimproveresolu4oninonedirec4on(“quadrature”).

�103Kitagawa, Ueda, PRA 47, 5138 (93)

(Spin)Squeezing

• Howtomeasuresqueezing/measurementimprovement?

�104(J1, J2, are uncertainties in the two directions orthogonal to the total spin J)

SuperradiantSpinSqueezing

�105

Out[31]=

N= 5 10 15 20

0 1 2 3 4 5 60.40.450.50.550.60.650.70.750.80.850.90.951.

W

x2

(driving field)Wolfe, Yelin, arXiv:1405.5288, González Tudela, Porras, PRL 110, 080502 (’13)

SuperradiantSpinSqueezing

�106(driving field)Wolfe, Yelin, arXiv:1405.5288, González Tudela, Porras, PRL 110, 080502 (’13)

BestcaseforDickeensemble

�107Wolfe, Yelin, arXiv:1405.5288, González Tudela, Porras, PRL 110, 080502 (’13)

Whataboutrealis4csystems?

• Dicke:3parameters(N,Γ,Ω)

• Realis4csystems:(OD,rel.density,Γ,Ω,γij,Δ,δij)

• Isitpossibletofindparallels?

• minimize“incoherent”aspects?

➡key:spontaneousdecay,shifinsteadofinduced!

�108

Spinsqueezinginrealis4csystems?

�109

Realistic Case (with dipole-dipole, re-absorption/re-

�110

Realistic Case (with dipole-dipole, re-absorption/re-

Out[31]=

N= 5 10 15 20

0 1 2 3 4 5 60.40.450.50.550.60.650.70.750.80.850.90.951.

W

x2Spinsqueezinginrealis4csystems?

Thank you!

�112