Atom-light interactions in ultracold anisotropic media

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At

om-Light Interactions in Ultracold Anisotropic

Media

bluk~md

Vengalattore

Submitted to the Department of Physics

in partial f~~lfillmerlt

of

the reyuirerrlerlts for the degree of

Doctor of Philosophy

at the

lCIASSACHUSETTS INSTITUTEQF

TECHhOLOGY

l&,pbz..&.t

mij,

June

2005

@

Nluku~lcl Vengalatt ore,

MMV.

All rights reserved.

The author hereby grants t o

MIT

permission to reproduce

iind

distribute publicly paper and electronic copies of

this thesis docurrlent

in whole or in part.

- .

_{. . .}

. . .

Author

. .

:

.-.:..

0 .:..

Department

of Physics

f l

June 23, 2005

Certified by.

. . .

.-

. . .

Mar3

G. Prentiss

Professor

of Physic:s, Harvartl University

n

A n

Thesis Supervisor

--

-

. .-..

. . .

Certified b;y-.

. . . .

,

. . .

::;-.-.

,

...,.

:

Davicl

E. Pritchard

Cecil

and

Ida

Green Professor

of Physics

Thesis Supeyvisor

. . .

Accepted by

.

".-

.,,

. . .

/ T h o r n a d Greytali

Professor of Physics, Associate Department

Head for Education

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Atom-Light Interactions in Ultracold Anisotropic Media

Mnk~mcl

Vengalut tore

Submit t ecl to the Depart merit of Physics

on .J111le 23. 2005, in partial fulfillrrlent of thc rccluircrnent s for t llc degree of

Doctor of Pllilosopliy

Abstract;

ii scritls of st i dies on atom-light interact ions in ultracold :misotropic xrlcdia wcrc

condllc~tccl.

110t hod^ to t ritp ult racsold n c l ~ t sit1 at oms in novel t ritps wit 11 witlcly tunable trap frc~cll~tw.irs i ~ ~ l t 1 i~riisotropies -:\-vf.re irivest igi~t rtl. 111 cxorril)i~rison t o corivrrit iorii~l rnag-

r lrltic. t ri~ps, it R-as follrltl that rnagnrt ic t r i ~ p s gerlrrilt rtl by soft frrrorrli~g~irts hi~ve

various ~dvi3nt ages such as a large dynanlic range of trap confinement. all ability

t o crew t e homogeno~~s reciprocal traps and an ability to shield ultracold a toms from

clelet erious :;urface induced effects tvhich -:vould otherwise lead to decoherence ancl

SI lc-11 rllii-.rofa hricitt ctl ferrorrlitgrlet ic "at orn chips" are prorriisirlg systems for t hc int egr;jt ion of itt om optic ~(jrnponents such its high finesse cavit ics and singlc atorrl courlttw. This (earl. ill tho rlrilr f i ~ t n r r . lratl t o prrcisr atorn sensors for niagrlrtorrirtry i111tl illclrtii~l srrisirlg. The Q-itlr tllrii~hility of the trap pari1rrlrter.s 111i~kc' s11ch iritegrr~trtl i\t orri traps ;ul i t l t ~ l syst err1 for st ~ ~ t l i r s of lo-:\-or tlirrlrlisiorial sl-st cJrris ilrltl rrlrJsosc.opic. physics in t I ie ultracold regirrle.

Ultracol( 1 anisotropic media were shown to possess rrlany novel and at tractive

properries. UUP to tlie suppression of radiation trapping in these systems. laser coul-

ing 1 k - w ~ sllon-n to 1x3 highly cfficicnt lcixding to a drarnitt ic increasc ixl t llc phase space

density o f at1 o p t i d l y cxoolt.d atomic ensemble. Subsecluent confinement of tlw rc-

s~lltirig cnselrlblc in it rrlitgrlctic trap and f~lrtller increasc of the phitse s~~itcc. tlensity 1)y rvapori~tivo cooling shoultl lri~tl t o lilrgr nnrrit>rrs of iltoriis iri a Eosc) c~orltlrrlsate.

It is also i ~ i i irit riguirig prosprct to c>orribirlr ext rerrir trap i~nisot l+opy wit 11 sub-rrc~)il

cooling scheiries to approach Bose co~ldensation through all-optical cooling.

Recoil iniiuced resonances in these anisotropic media were shown to exhibit single pass optical anlplifications on the order of 100, more than two orders of magnitude higher than observed previously. The strong dispersion associated with this resonance

IVWS I I S C ~ t o creat P an ultracold optical fibcr, thus overcorning t he diffract ion lirrlit

for at om-light int cract ions. With sllch radial confiner-rlcnt , strong dispersion was

cornl)ilirtl \I-i th i~rbitrwrily li~rgr opticill depths tlirrehy rrrltlrring this systrrli a nniclllr ~ricl(lillrll for ~ i o ~ l l i ~ i ~ f i r opt irs iri t lir sirlglr pliot 011 tlornain. This syst en1 was slio-:-:-rl to

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exhibit pro1.lounrec1 nonlinear and collective effects due to the s t n ~ n g coupling between atoms and light.

Tllesis Snptlrvisor: RIara

G.

Prentiss

Title: Professor of Pllysics. Harvarcl University

Thrsis S~q,~lrvisor: Dtwitl

E.

Pritchi~rti

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Acknowledgments

I l y years as a grndllitte student h m been. withol~t a d o ~ t h t , among thc rnost exciting. i-e\\-ilrtlirlg itntl etll~cat iorlal experirrlces I've had. I arrl now facvtl with the task of (~orlcle~~sing sis ye:~rs of frierltlsllips i~rltl co11i~l)oratioxls into ir collplr of pages.

First and foremost, I am grateful to Mars Prentiss for giving me the opportunity

t-c) work on the exciting projects described in this thesis. Her patience and inclination

t o list cn to rny ideas. however extravagant or faucifill, and 2lcr encouragcrnt3nt ixnd

(often by 111.aking llumerous mistakes) before stepping in with iilsightful suggestion::

went a ion;?, \u-1-j- in my clevelop~nent as a pllysicist. For me. these past few years

1l;xvt. been ctnc exciting journey of discovery ancl

I

will cllcrish forld ~rlelrlorics of tllcsc t irncs.

Davr P~.itc.hartl hiw beer1 a. ~vontlrrfitl co-snprrvisor. I haye rlrJvrr c.easetl t o 1 ) ~

amaze(-1 by the intuit ion and deep underst andill:, he brings to every situat ion. I've

1)enefitrd from each and every co~lversation I've had with him. whether it be or1 nmlti-

photo11 rcso tlilnces or an ixrcitne det ;xi1 of atom (.hips or tllc skills of a relicf pitchcr in l)L1~(>1)?311.

I'VP hilt1 t tlr gootl fort urle to irlteriict wit ll LYolfgilrlg I i ~ t t rrlr first as i l r l nrltlrr-

graclua t p and graduate stude~lt , learning cluant urn ~nechiznics ant1 A l I O pllysics froni him: and then as a collaborator on the Atom chip project. Wolfgang's virtues as a scaicntist h a w been well tloclunc~lted in rnitnntrs far Inorc eloql~tmt th i n

I

c.itn Inan-

age. To these.

I

will merely add that his dedicittion. foc~ls and sincerity have been a

const imt source of inspiration to rnr.

I a111 gratef~~ll to Thomas Greytak and Dan Kleppner for giving me the first taste of

ultracold atom physics during my undergraduate days. The opportullity to participate

in t llc efforts to at~hievc Bose conclensatiorl in Hydrogen in their lttbs. albeit as a mere

1111dcrgritd11il~t c , were m y first indication of t llc corlt agious e x i t cmcnt t llitt seems to

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Landhuis and Steve hIoss for t,heir patience and willingness to explain things t o me

in great detail. The wonderful experiences during my time in the Hydrogen

BEC

grollp were alrnost single-handedly resporlsiblc for rrly decision to choose ~ ~ l t r a c o l d ittorn pllysilrs its In\- field of graclllate st~ldy.

hly entry illto the Prrrltiss lilt~s was greatly aitlrtl by Gary Zal)ov. FiTht1thrr it m-i~s

it cluest ion of locating equipment, or sorting through bureaucra t ic tangles or being a

macl~iile shop 'buddy' at nlidnight. Gary often went out of his way t o help me out. His

shttrp intclligcncc. quirky wit i ~ n d 'novel' o ~ ~ t l o o k on lifc w r e 111uc.h itppreciat~d. He

was also rt3~~ponsiblr for elcvat ing our l~mchtimc bant cr to the st at us of an inst it ~ltion.

N o topic. sciclrilr(1 o ~ ~ t of bou~ltls as long its I\-r tlitin't stick t o it for r11or.r thrm five

minutes. It wasn't unusual for a serious discussion on the diffractio~i lilnits of optical

~nicroscopy to transition, in a rrlatter of minutes, to a debate 011 alternative energy

sources (soiile of 11-hich cwrc rat her unconvent io11itl. to

s

i

v

t he lritst ) , then it brief

intcrludr on u h y it shollld Elitvc bccn obviol~s t o Karl hIarx that corrlrllllrlisnl was a

tll~rlll) itlril, before prltlirig 111) in a heatel tlehatp or1 1%-hrthrr thc results of tllr

SBX

pli~yoffs hvrr r fisiltl to rrisurc. l)ig nlwrkrt rrvrrnlrs. (Is rlothing sacarrtl'?)

I arrived in this group within a week of Wilhert Rooi-jakkers. The anisotropic fer-

rorllngilctic traps t hitt werc t llc ~vorkhorsc of this thesis grew out of o11r colluboration.

I.ooking hat k. I am it~~litzecl at tllr riurrll~cr of (lifftm~nt ideas and approaches wr tricd irl tliosr fir>.t few r~lontlls. It is hiirtl to rxpliliri to tllr riel\- 1rlr~rr1l)rrs of tllr group

that Inany uf t he techniques that we now take for granted were arrived at after nlany

frnstra t in:: tnont hs of experi~nent at ion. I have been ilnpressed with his ent husias111

for ncu- idriji i~ntl persistence in the lith. Hr was also often the straight man to Gary's

wit lcitding to rnl~cll hilarity.

Aftixr Willxxrt rriov~cl iwross tllr lab t o set up H secorltl experiment, I collaboriitetl closely with another postdoc, Richard Conroy. iLIany of the results in this thesis

were a resull- of long conversations with Richard (often on the way to Tosca~lini's or

Stitrbucks). I soon grew to leitrn that Richard's easygoing nitt11r.e hid a stern critic who wilsn't going to accept Illy hand-wavv cxplanitt ions of what a-as going on. By the r)rltl o f his thl-rr yrlrwr stay irl this group, I knrw that if I conltl grt Ricllartl t o ac.c.t.pt rrly

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ixlterpretations of the data, it was bou11d t o be true.

I

will treasure meniories of the

1-wo of us working late into the night building the

BEC

chamber or microfabricating

atom callips in the clean room. I would also like to thank him for his careful rcitding

of this thesis as well RS most of u~ papers.

Ovrr tho li~st y ~ i ~ r . I have erljoye(1 I I I ~ I , I I ~ (lis(~~~ssiorls i~rl(l (wlli11)ori~tiv~ efforts with

it new gradllate student Jonathon Gillen. I am confident that I leave lrly experilnental

systerrls in qood hands and look forward to many exciting results in the near future.

I also bcncfitcd fro111 interactions with und~rgr;ttlllates Natc Grccnll~latt and .Tosir

Jlveeks ant1 visiting student Cllrist inc Aussibtxl. I've cqjoyecl nly discr~ssio~ls with t he other rnerrl1)ers of tllr gr-onp: F i ~ l ) i i ~ ~ l o Xssi, Clantliil D~nilo\~-ic-z, Efiilirrl Frirlstrirl.

Donald Lee. Scott Sanders, Pierre Striehl. Saijlun L\;u and Yanhong Xiao.

The Atcim chip collaboration with the Sodium science chalnber group was es- trtmilly inst ruct ivc and cnjoyahlc. For this.

I

wor~ld like to thank r\nitnt h C'hikkat ur.

Diwe I<ielpinski. Todd Gllsti-~vson. Gyl-Boong .To. Aitrorl Lci~nhitrtlt. Torn Pasqrlini.

Iiic.ht.1~ S ~ I ~ L i ~ ~ l t l Yong-il Shin.

Over t hi. past few mont 11s. I had many illu~ni~lat ing conversations wit 11 llisha

1,ukirl and ZiIohanlrrlad Hafezi. I woulcl like to thank the111 for this. and I arn conficlent

that this collaboration will rcsult in many int ercst ing st uclics in t lrc near f ~ l t urr. Orlc of t lie hcst feat~lres of ~vorking in the Center for Ultrac.old Atorns is the op- ~ ) o r t l ~ n i t > - to intrracet I\-itll rrlwrly rrlrrrll~rrs of t h r A110 corrlrrll~rlit-y imtl get to lt'i~rn of

different iclews. esperinie~lt s. techniclues and lines of thought . Out side the lab, this ca-

lilaraclerie e r t entled t o intramural soft ball games. soccer gitrlies. l~asket hall games and

p ~ r t i c s . Its i ~ e c n a. pleitsure to get to know hlicith Boytl. Grctcahelr Campbell. .Tit-Kec

Chin. Rob C'arvalho, Deep Dasguptit. Cort Johnson. Liit 1Iittos. Ditrl llillcr. Christittrl

Schllnck. .J~I rrlil Abo-Sharer. Arltlrr Shirot zrk, Cli~ntliu St an. .Julia St rirlt)n.grr. Igor Teprr, Kent lril Vi~rit

,

Kaiwen Xu ant1 h h r t irl Zwi~rlein.

Illy thanks to Vickie Greene and .Jan Ragusa for tolerating illy bureaucratic inepti-

t ude with const ant good h11nror and to St an Cot reau for t caching rrlc good machining

skills.

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apart rr~ent - mate Venka t esh: to Sumant h and Bhuva~ana for numerous e~~joyable dinners

and conversations about the future of my field. and for the joys of baby-sitting their

tl;tl~ghtcr, little Xecla. wllile her parents w r r off' 'thopping for a thofa'.

I

would like

to thank my parents, Brindha itrlcl Nagrtraj and 111; brother Srikar for their constant

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47

2.4.1 llagnrto-optic cai~pture in n lirwixr q l ~ a t l n ~ p o l r firltl . . . 48

2.4.2 Magneto-optic capture in w ferromagnetic trap . . . 50

3 Experirnental Setup 53 3.1 Ovc!rvit.-cv. . . 53

3.1.1 Laser syst. ern . . . 53

3.1.2 UHV syst8rrrl . . . 55

3 . 1 . Ferron1a.gnet.i~ trap . . . 56

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3.1. . 5 Optimization of a dispenser loaded hI O T . . . 57

4 Ferromagnets for integrated atom optics 63 4.1 Int rociu(.t iori . . . 64

. . . 4.2 Pl; tnas ferrornagnet ic rrricrotraps 64 4.2.1 Atom guides and Ioffe-Pritcliarcl Traps . . .

64

4.2.2 Rrciproc.il1 Traps . . . 67

4.3 Fal~rication of ferrornagnet ic at om chips . . . 7.1 4.4 Cl~ari~ctc)riztltio~l of tlie fn.rolni~grirtic atom callips . . . $6

5 Enhancement of phase space density in anisotropic traps 79 5.1 L i ~ s c ~ (looling of optivi~lly tlrrisr rllctliix . . .

80

5.1.1 Thc hlollocv fl~~orcsrcrrc~' spectrum . . . S1 5.1.2 Photorl rrill)sorptiorl in (1 tlirrirllsions . . . 83

5.1.3 The cfirtive cross scct iorr for al~sorpt ion of spor ~t aneons phot 011s 86 .5 .2 Enhancement of phase space density in an anisotropic: MOT . . . 88

5 . 1 Pliotorl rri~bsorpt ion iri a. MOT . . . 88

5.2.2 Laser cooling iri an anisotropic hIOT . . . 90

6 Suppression of radiation trapping due to trap anisotropy 97 6.1 The IIollo~v absorptio~i spectrum: Gain in a two-level ator11 . . . 98

6.2 S i ~ t l~r,r tiori of gain t l l ~ r to phot or1 rri~k)sor.pt ion . . . 100

6.2.1 Chiin in a tlilutc system . . . 101

2 Thrl inflnrric~ of pliot on rri~bsorpt ion . . . 102

. . . 6.2.3 Gain in ~ t n opt icully dcnsc

.

anisotropic trap 105 . . . 6.3 Suppression of photon reabsorption ill an anisotropic gas 107 7 Recoil induced resonances in the high gain regime 113 7.1 TheAsystern . . . 114

. . . 7.1.1 Ratliat ivr Reriorrllalizat iori of the A syst rrri 116 . . . 7.2 Re( oil-induced resonances in the perturbative regime 118 C 3 Rr( oil-irld~~cartl rpsorlarichrs in t h r high g-air1 rrgirrir . . . 121

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7.4

A

light amplified all-optical switch . . . . . . . . 126

8 Dispersive effects of t h e recoil induced resonance 129

8.1 Propagat ion of light in i~ resonilrt rrlrtlillrrl . . . . . . . . . . . 130 8.2 Strong dispersion due to the RIR . . . . . . . . . .

.

. . . . 134 8.3 Sp:] t iid effects of the R IR: lensing and waveguiding of light . . . 135

8.3.1 Few photon rlorllirlcar optics in it strongly dispcrsivc lrlcdillrrl . 136

8.3.2 Arl 11lt ri~c.oltl opt ic.i~l f i l ~ r r . . . . . . . . . . . . . . . 139

5 Conclusion and Outlook 145

A Ferromagnetic atom guide with in

situ

loading 149

B Ferromagnets for integrated atom optics 155

C A reciprocal magnetic trap for neutral atoms 161

I) Enhancement of phase space density by increasing trap anisotropy in a MOT with a large number of atoms 165

E Suppression of photon rescattering due t o spatial anisotropy in a

cold atomic gas 171

F

Recoil induced resonances in the high gain regime 175 G Radial confinement of light in an anisotropic ultracold medium 181

H

Observation of caustics in the trajectories of cold atoms in a linear

magnetic potential 185

I

A compact, robust source of cold atoms for efficient loading of a

magnetic guide 193

J Dynamical instability of a doubly quantized vortex in a Bose-Einstein

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List

of

Figures

1- 1 Esdlnples of ator11 chips ~uicrofahricatecl during tllr course of this thesis

21

2-2 ilirrotraps cbrr,~tetl by wires.

X

'Z'

t r a p carrates tl Ioffr-Pritc~liartl trap

while a 'U' trap creates a cluaclrupole trap. . . . . . . . 37

2-3 A ferrornagnet ic atom guide. The pair of ferromagnet ic foils are inaglle-

tiztd 11y solerloids 1%-rapped around the foils. If the foils are magnetized

in r ~pposit e direct ions. the field in the plant of symmcr ry is horizontal This field ciul he c.~m.elcd by an externit1 bias field to crc~tte it

cl~~iitlrl~~)olt) rnagr1r.t ic. ~lii~iiriilllli. . . . . . . . . .

11

2-4

X

(.orriparisori of the nlagrietic firltls of tlir ferrornwg~ioti( trill) ilritl a

11-ire-1:)as~d trap. The red lirie iridicates the ~llagnetic field above a

ferroiliagnetic at0111 guide. Here. the separatiorl bet~vren the foils is

0.5 rrurl and the cr~rrent thror~gh citch solenoid is IA. Thc solid blitck lint) indicittes the field al~ove it wire of width -50 j r r n for it c11rre11t of lA4. Tho di~shrcl line iriclic.ilt-0s the field for 1-111 idri-~lizc~(l wirr of zero 1vitith.

42

2-5 Tho positiorl of the iltorri (.loud as a. furlctiorl of tlir horizorit ill Ijii~s field. Since the trap is created at the field zero, the at0111 cloud can

be used to accurately determine the field of the ferronlaglletic trap as

a hnction of the hcigllt above the surface. The two curves indicate

the position of the atoms for I=O.lh (lower curve) itrlcl I=O.'A (upper

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2-6 By increasing the magnetic fields of two pairs of ferromagnetic foils in

proportion. the atorrls can be transferred from a h107' into a tightly

coi lfirling rnicrot rap without cllarlgirlg their posit ion. 'This process of squeezing the atoms citn he aiclecl by rrlaint wirlixlg laser cooling during

tllr tri~risfn.. Hrri.. = If,,,i/150rriA I\-here is tllr t~urrrnt around

t lir iriri~r pair of solenoitls. As the d i ~ t il irl (e.) iridicaatrs. t lir at orrls

are ronipressed u-hile ~riaint aining a const ant temperature even at very

high field gradients. The irlsct sho~vs a fl~~orescencc image of it 2.5 rnxn

1on.g scc~tion of tllr MOT at h = 330 G / c ~ n . . . . 46

2- 7 Thp frrrol~lag~letic foils can also be used as a cold atom .*beamsplitter"

to split or merge atom clouds. . . .

46

2-8 ( r ~ ) T l ~ r rrgiori in w-llic~h iktorris cirll be trappet1 arid caapturetl shririks at lwrgc' fi~ltl gratlients. This lratls to lo~vrr. c.aptln.o vrlocxity arltl reduced capture efiicie~icy. (b)Typical trajectories of at orns that are

captured. Above a particular velocity. atoms fly out of the region

bcforc. t hcy c.itn be trapped. ( ( 8 ) Thc vitriation of t hc ca.pt urt3 velocity

with 1-hc mitgnctic. ficltl gritdicnt. Thc cmor bars indickatc static;tic.r-tl 11rlc'vrt ?Lint ips ill t lie ril~rnrri(~r-tl sirrllllat ions. The clilsllrtl line inclic>i~t es

the I-,.,,,

-

h-q:' dependence predicted in [I]. . .

49

2-!I Thv r~litgrlttic ficltl of tllc ferrornagnctic foils decays t o srnitll vith~es far frc ,111 t llrl cll~atlrnpole zero. T ~ I I S . the t rilppirig lasers c x r i stay irl

rc~soriilnc2e with tllr iitolris owr. i~ larger voll~rrie. This lratls to rriorr rf- ficicint capture. The magnet o-opt ic force due to the ferrornagnet ic foils

(black) is co~ripared to that due to a spherical cluaclrupole field (red)

for gratlients of 10 G / m l . 30 G / c ~ r l alld 50 G/cm.Thc insets show the

rnagnrt ic fields of the spherical clc~adr~lpolc field and t l-lc krromagnet ic

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2-10 T l ~ e variation of the capture velocity with magrletic fielcl gradient for

a I'errornagnetic

MOT

(0)

is compared to that of the conventional

iLI(:)T.

It can be seer1 that the capture velocity at higher gradients is sigoificitrltly larger t llitn that of iz spllcrical cluadrupolc field. Sirlcc

tho loixtlirlg rate into the hIOT scales as r-&,. this trarl>li~trs to highly

. . .

c~%.cic)rlt caiq)t ~ u r .

. . .

- 1 Scliematic of the laser system.

- 2 Scllerrlatic of t llc

UHV

chitrnhcr with t llc ferrorrlagnet ic. trap and ittoin

chip. . . .

3 - Scl~ematic of the

UHV

chamber with the ferrolnagnetic. trap and atom

chip . . .

3 - Nurnl)er of kxtorns lot~-lcletl in the MOT vtlrsus the clurwtiori of the ('11rrer1t

. . . pul se t l-lrough the dispenser.

3-5 Delcaity

of

the LIOT at low arld high atom nl~mber. . .

6 Lifrltiine of the bright MOT ( A ) and the temporal dark SPOT

(m).

.

4-

1 Magnet ir microtraps created by planar fer'o~liagrletic itrr~ctures.

A

rn?tgnctic field rrlirlinlu~ll created by two opposing ftxrrom;tgnets does not rcslllt in large field gradients t-l11c to thc influc11c.c of cach fcrro- r1lil;i;rir.t or1 t hr otllrr..

By

c*wrlc>rling t tic. fielt

1

of t lie frrrolliagr1c.t with

. . . . prrpeiltiic*nlixr hii~s fieltl. tightly c.o~lfiilirlg traps (.an 1 ) ~ trratrtl.

4-2

A

vector plot of the rnitgnctic trap indicating t hc rnitgrlctizittion of t llc . . . ferr.orrlagnet ancl tllc orirnt at ion of the bias firld.

4-3 Col-ttour. plots of the magnetic trap with increasing bias field illustrating

the variation of the field nlinilnurn and gradient. These calculations

were perforrncd for a. currerlt of

5A

through the cb1~rrc\nt sheet and

vcrl ical bias fields of IOG, 20G. 30G, 40G and 5OG. Thr. contours are

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4-4

A

schematic of the ferromagnetic ring trap. The ferromagnetic ring

has an ilnler (outer) radius of 3 (4) 111111 and a thickness of 200 pm.

Thc current sheet that magnetizes the ferromagnetic ring is brokcrl up

into ~tlitny discrete wires. . . . 70

- 5 Results of a finite element simulation of the ring trap. ( a ) . ( b ) and (c) show false color images of the current density in the current sheet around the rcgiorl of tllc input itrld olltput leads. Tlle gap bctwecn the two loatls \\*as 2 ism. (tl), ( r ) i~rltl j f ) iritlit.ate t h r nlagn(3tic fir~ld illorlg

;I c*ircl~lilr I ) R ~ 11 corrrs~)orl(lirlg to the irlrlrr rdgr of t l i ~ f r r r ~ ~ l i i ~ g ~ l ~ t .

As in(-licated. the lnagnetic fields are sarnplecl at heigllts of 10 ,urn. 50

,urn 100 pm, and 200 ,urn above the surface of the f e r r o ~ n a g n ~ t . T h e rcsidntxl vijriitt ions in t llc rrlagrlet ic field (which arc fairly largc close to tllc fcrrornagrlet ) arc an artifact due t o the discretization of the finite rlrilirut rrltlsh. Thrsr vilrii~tiorls ilrr prrstllit rvrri in t h r itlri~l casr of a

. . .

uniformly rnagnet ized ring. 12

4-6 The. mtio of the rrlagrletic fit3lcls sarrlplcd at the points losest st t o ( B I ) . ilrltl farthest frorn(B2) the t)r.rak ill tlir c.11rrrnt shrrt at tliffrrrrlt heights

t l t ) t ) l ~ ~ tlir fc>rrorni~gnrt. T h r syrrl1)ols

.

o aritl A r q ~ r r s r n t tllr c~urrent sheets ( a ) . ( h ) and (c) respectively. This ratio is an i~itlication of the

llorliog~oeity of the trap, and is equal to 1 in the case of a homoge-

nco~lsly rriagnet izcd ring (no variation in the tritp potent i d ) . It cairn be stlril thilt tlio ferrorrli~grirt rriilgrirtizrtl by the strarltlrtl c.l~r.rrxit sliclot

. . .

ill11 )ro;lc*htls this it leal lirrlit

74

. . .

4-7 Snnlrnary of the ~nicrofijbrication process. 76

1-8 (CL) Tlir magnetic. firltl of the rrlicr.ofabricatt.tl frrrorni~giiet as it fiulc-

ti011 of height above the substrate. The data i~ldicated by the symbols

a.

(1) and

A

correspond to 3A. 5A and 10A through the current sheet

respectively. (b) Tllr field gradient

8B,/i)v

obt iti~led from fitting the

rncas~lrcd field to the rnodel. Tlle solicl, dasl-lcd and dot tccl lines corrc-

(19)

Dressecl states of an atom irracliated by an intense laser heam. The

various transit ions leading to the Mollow fluorescence triplet can he

seen. (c) Ahsorption(so1id line) and ernissiorl spectra (claslled line) for

an atom illurrlirlatecl by a lktser bear11 of intensity 12 mW/cri2 and

1 r i g - I . 5 . It c+an t)e sreri that t hr r~t)sor~)t iori cross sect ion for

ttir) t ~ l u r sitlrl~aritl is very large. (Fig(c) is tirkeri frorri

I)

['

. . . 83

h

sirrlplr rrlotlel to est irriat r t hr irifl~~c)ric.t~ of phot or1 rt1ir t)sorpt ion iri tl

. . .

c1ir:rierlsions 84

TI10 ~~o~.rriiilizetl effrcat ivr caress-sert iori as a. fi~ric*t ion of t lie t~sprcat ratio rl. 88 Scl~ rrrii~t ic. of t hr ~ x ~ ) ~ r i r r i r r i t a1 apparatus. . . 9 1

Th13 tcmpcrat ure of the ~ttoms for vitriol~s radittl optical densities. The

tlat w iri Fig(2) (a) ~ r i t l (b) arr ti1ke.11 at light shift pararlirtrrs of 0.4 arid

0

.H

rrspc.t3t ivclly. Tlic' ratlial opticeal tlrrisit itls iritlic.at rtl are irlei~s~lrrd after 1-7ms of free expansion. These values are 111easuretl for the largest

nurriber of atorrls in each data set. . . 92

The va,riat ion of the teniperature with laser cletuning. The number of

ato-tns iri the hlOT is arouricl 2.5 x 108 for each data set. The radial

OD's mcasurcd after 1 Trns of frc.tl cspansion arc

O.75(0

j

.

O.4.5(0) and -

3 A I . Tlie tlaslletl lirir stlows t h r prrt1ic.t t ~ l tc.rii1)rratlir.e of u C - rr

rr1o lasses for the. sarrir li~srr. int prisit?;. Irisrt : Ttir iriiriirri~~rri trriiprrat ~ u - r

vs. the radial optical density. . . . 93

Thr pclilk tlrrisity of t hr i ~ t orri cloud for. tliffrrerit ratlial opticaal densit ips.

The cliarlge in behavior from the density limited regime (black squares)

to the temperature lilnited regime is clearly seen. Tlle radial field grarlicnts for each data set are 10 G/crn ( W ) , 7 G/cm ( 0). 30 G/crn

(0)

aild 60 G/crn

(v).

The indicatccl optical densities folloa~ the sarrlc

(20)

5-8

The phase space density of the atoms for various radial optical de~lsi- ties.?'he Rabi Frequency per laser b e a ~ n . detuning arid field gradient for each data set itre A - (0.75

I'.

-2

I'.

10 G / c ~ n ) . - (1.2

T.

-5.5

I?.

7

Gicrrl).

A

- (1.2

I'.

-5.5

r.

10 G/cm). o - (1.2

I?.

-8

T.

TO G/crn).

.

- (

1.0

T.

-8

I'.

70 G/crrl). T h r indicated opticaal tlrrlsitirs follom- tllr sarilr

. . .

(*or l w r t ion RS in Fig. 5-5 9.5

6-1 3 ( / ) h r i ) for a ~ I I I U I ) t l r t ~ ~ n i r ~ g of -2

r

~ r i t l R ~ b i fre(p~rrl(.irs of

I?

ilrl(l 5

I?.

At large Rahi frpcll~rllc.irs. the iIppearilnc2rl of R gain frat1u.r at rrtl

. . .

clet unings can be seen. 100

6-2 The weak probe gain as a function of the optical clerisity. The gain

grows cxponcnt idly in t hc dilut c limit. As t hc optical dcrlsity grows.

the cffec~t s of photon rcabsorpt ion becornc dorni~litrlt, and t hc gain sat-

iu.i.~trs. . . 105

- 3 Nlunrricaal c~al(~nlatiox~ of tllr ilrrlplific*iltion versus ODI for tliffrrc.nt ?IS-

pect ratios. The calculatiorl is perfornied for a pump

I!K

= 2 . X and

(j = -2 T.The dot t ecl line shows the preclict ion of 110110~~-'s theory for

t 1lc:ic pararnet crs. . . . 107

6-4

Fluorc~sccncc. inlitgcs of the XIOT itt diffcrcnt trapping pi~ritmctcrs. Thc

rna:cirll~~rrl transverse opticsal tlrrlsitios of t h r clo~~cls 1aI)rl~~tl ( ;-I) t l l r o ~ ~ g l i

((1) arc. 25. 12. 5 ant1 1.5 rrsprctively. Tile peak drrlsity of t tic. LIOT is

hetlvveen 5 x 10" cm-" and 1 x 10" cm-". clepeliding or1 the gradient. 101)

- 5 Absorption s p e ~ t ~ r u n l of the probe. The pump detuning was -2

T.

The dot 1-ed line shows a fit to hlollocv's thcorv. The closcst fit to the dat ii

is oht;rined when tllc purnp Rabi frccl11c1lc.y- is avcragcd over a r m g c 2

(21)

6-6 The observed gain versus the longitudinal optical de~isity for different

triip geometries. The d a t a indicated by the synrbols 0.

v,

o and D

co I-respond to the fluorescence irrlitges (a). (b)

.

(c) and ( d) respect ivtlly in Fig.3. Tlre data itre taken for a pump ! I R x 2.5r (see text) and it tld-luiing ci = - 2 r . T h r tiottrti lirlr sllow-s the pretlication of Llol1011-'s t lloory for the rxprrirrlrnt ki1 ptlrr~rnet rrs. . . 1 1 1

A

schema tic of the recoil induced resoliallce in the case where the pump

am1 probe beams are count er-propagat ing. . . . 120

St31 icnlitt ic of the cxperinrent a1 set up. Thc lorrgit udinitl pump heit~ns hin-cl art hogorla1 p o l a r i z ~ t iorls i~rltl arr irlc.lirlrd at i h r l ax~.;lr of 10" \\-it h

ros [)e(>t to tllr at orn guitlr. The ~ w a k prolje l~er~rrl is aligncltl irlorlg t llc.

w t om guide and shares the same polarization as the count er-propagat i11g

pump I~eanl. In addition to these. a pair of transverse bearrls (not

shocvrl) in (T+ - 0- configl~rittiori ilre I I S P ~ to trap and cool i~torns in

t h c 2 D h I O T . . . . 124

.411sorptioll spec>trll~rl of the ~vrilk prol)r l~rilrn aro~lntl the rrc.oil irlcll~c.rtl

resl mance. The data shown are for lorlgit udinal optical drnsit ips of

-

10

(solid) ?mcl -50 (dashed). Inset: Absorption spectrum of the probe

(IVC r it 1%-iclcr rang(> of tlet lining sho\\-ing t hc Llollow it hsorp t ion ,t1i(1

gain f(.at~~rcs. . . 12.5

Tho gilill is lirrlit rtl by ~ x u n p (leplet ion. .4t ten~lat ing t hr prolr~r irlt rnsity resl ~ l t s in larger amplification. . . . 126

(left-) Transient decay of the a~rlplified probe upon switcllilig the probe

off. (right) Growth of the amplified probe upon switching the probe

on. Tllc sigrrloidal growth and the exponential decay :Ire charactcrizctl

(22)

7-7 The probe beam can be switched by lnodulating the frecluency of the

pump Leinu. The gain of tlie all-optical switch can be tuned by varying

the ~ n o c h ~ l a t ion dcpt ll of tlre pump benrn clet uning. The comparison of

tho switch at large and sr~iitll gain itrr shown. Thc switc.hi~ig t irrics arc

irrolalci 3 /is ilritl 1 Ars rc)sprc~tivrly. The tlrturiilig of tlir punlp bt~ani is slic:~\\-ri in dottetl lines. . . ₁₂₇ 7-8 Tllp varii~t ion of t lie slvit calling t irrl~s wit ll t lle irit rrisitirs of t h r pllrnp

. . .

arlt 1 prok)e bri~fiis. 1127

1 Dispersive effects of the recoil induced resonance. ( a ) shows pulse

propagation of a retl detllned probe. Tlle group vtllocity of thc prllsc is

itround 1000 m/s. (b) shon-s supcrluminitl group vcloc.ities for a blue

t lrt urlrtl prok,e. ( ( 1 ) shorn-s plllse splitting d l ~ r to the firiit r barit l~vitlt li

of r lir rrsor1imc.e. Tlir pulse splits into sl~bll~rriillr~l writ 1 sllprrl~~rnirl?~l

conlponent during propagation through the ultracold uiedium. . . 134

8 -

Lrrisirig t 111r to the recoil iri(l11(.~(1 r~soliarlce. (a) Xri irllage of tlir proi)r

beill11 in the abse~lce of atoms. (I:,) An image of the probe beam after

propagation through the ultracold mrdiurri. In this case, the probe is

clct~lriccl to the rctl of tllc

RIR

corresponding to guin i~licl sul~luminitl

groi ~p velocit ics. Hcncc. t hc ult racoltl rrirclillrri arnplifics the probe and t~lso iu*ts as a c-onve-rs lc.11~. ( c ) Thr irliiigr of the pro1)r whrw tltlt~uirtl

t o the blue of the

RIR.

The ~ ~ l t r a c o l d iliedium absorbs the probe and

act?! as t t coiica~e lens. . . . 140

8-3

( a ) Irr~i~grs of the rrnergerit probe bei~lri for tliffrrerit input anglrs. (1)) Corresponding images of the emerge~lt probe in the absence of atoms. It citn be seen that the fraction of light tha.t is coupled into the waveg-

uido can hc irlcreased hv changing tlic illpllt a~lglc. Also, llnlike the

1111co11plccl f'ract ion, t hc out put of the waveglliclc remains fixed in posi- tior] eve11 as the i n p ~ l t i ~ ~ i g l ~ is c~liangrd. . . 142

(23)

- 4 Evidence of an e~lhanced path length due t o optical waveguiding of the probe beam. The hottom trace (in red) shows the probe beam in the absence of the at oms. The middlt~ trace (l~~belled ( a ) ) clearly sllows a 1,imoclitl s t r ~ ~ c t u r e . This corresponds to the irnagc of the emergent ~ x o l ) r slion-irlg l)ot li a. g~dtlrtl fr.ac>t iurl and a. lerlsrci fraction. Thr (lot t c ~ 1

1irit.s (ill l)ll~r) show- a least s~llli~res fit of this olltpllt p111sr to ?I sllrll of tm-o gaussian pulses with group delays bl and

ij,,

with h2

>>

dl. The t 011 tra( .c(lahcllrd (b) ) sho~vs t hc o r ~ t put kvhrrl tllc lerlicd fritct ion is

blu(8lic~l by mcans of ;in iris. It ciin bc sccn that thc output pulse

c.or.r.~~spori(ls t o i~ singlr pnlsr 1%-it11 a tlt.li~ of O'?. T h r tr.itc.rs irrr offset

for clarity. . . . . . . . . . . . . . . . . 143

- 5 Thta ernprgence of a dual delay in the output pulse as the number of

(24)

(25)

Chapter

1 Introduction

Tllis t ilcsis corlt itirls a series of st uclics on at om-light int cract ions in ult racolcl gascs.

Thc rxpcrir~lcnts focus on the novel effccats of tl~cse intcritctions tllitt comc il11011t tluc

to the gron let ry of the ixt orllic. ~llrtlilurl. In part iczl~lar. t llr nltrncloltl i ~ t orns listtl in these st11tlir:i i-UP ('orlfirlr(1 irl large aspect ri~tio traps \\-it11 l-ligl-i ( t p t i ~ i ~ l i-~riisotropy. The

experiment a1 syst en1 describrd ill this t liesis eni~bles o11r to t urlr this anisotropy and approitch ctrl o11t icitl " I-rli~nensiorlal" syst tm cvhtw t llc int cracat ions itnd opt icid tlep t 11

in t hc radi;-tl tlimensiorr itre negligible compitrccl to t Ela t in t 1 1 ~ l o n ~ i t I ltlinitl climension.

Ttlt. theme of this rlisscrt at ion is two-fold: Thc first p ~ r t r o n c ~ n t r a t cs 011 nlilnip- 1~1i~t ion arit l co~lfin~rrlc~xlt of 111t rilcolt 1 ririltral ixt orns i~sing riovc.1 f~rrolni-\gllt.t ic. traps. These trap:, are created either by millimet rr-icalr or lnicrofabricitt ed frrromagrlet ic

structures. In corllparison t o convrntional wire-hased traps. tlle ferromagnetic traps

hnvc vitrioua itdvantitges such us it litrgc. dyn~tlrnic range in trap freclr~encaics. a tvitlcly t unal~lc itspvct ratio and it ntlgligible levcl of 'slirfacc-inducetl cBt3c.t s' d11c to neitrby roolli-t clrrll)rmt 11t.e ~ l l b s t r i l t ~ ~ . S~l(.h rlli(.rotrops car1 t)r ilitclgrat rtl \\-it11 various i ~ t o ~ n optic devicaes such as nlagrlrt ic rnirrors, iligll finrsse cavit irs, photo tlrt clct o r s i ~ l l t l si~iglr

at0111 detectors and are thus pro~nising systems for a host of studies on atom optics

and the rcaliza t ion of ultra-precise sensors wing cold at oms.

Thc secaoncl part rnakcs use of the t uni~hility of t hesc ferrornagnct ic traps to reitlize

rlovcl ultrncrkl oyticitl media with extreme anisotropy As will 'r)c shown ovrr the

(26)

optical cooling to high phase space densities. studies of nonlinrar optics at the few

l~llot 011 level and experiments on st ronglv coupled at om-light systems analogous to

~itorns in high finesse cavities.

Micromanipulation of ultracold atoms with

"

Atom

Chips"

TTrdmicl11t.s of laser cooling and trapping of ncutral atoms haw lccl to rem~trkablc

st 1ltlit.s of I ~ltrac~oltl rrlilt t rr. Bosr c*ontlrnsi~t PS i ~ r i t l tlryrrlrratr Ferriii gases. Tllrsr

~ ~ l t r a ( l o l d gases are characterized by their dilute nature, the tunability of their inter-

artio11s and the ability to isolate them fro111 the enviroilmerit. In other words. they

itrc3 rlcirr-itlcitl syst c~rls for t hc cspcrirrient a1 realizitt ion of novel strongl? int ernct ing c~r highly corrcla t rd conderwcd rnat t r r or cl11ant urrl optic rrloclrls.

Thrrc. l l i t ~ iwrrl a lot of irlt rrrst in rrlirliat 11rizirlg t hrsr cxoolirlg arid t ri~pping t ec3h-

niclues in order to integrate a variety of atom optic devices on a single substrate.

Apart frorri the benefits of rendering these ultracolcl systems conlpact and robust.

s11c.h rninitttluization opens the path to novel stl~clics of ultri~cwld mitttcr with high

firlcssc cavi t :IPS. room t ernpcrat rue sllrfitces and rnicro- or nitllo- c,mt ilc\-t\rs lcitding to ilrw rt)gilll~s of illtrac.olt1 rllrsosc.opica physic>s.

Xnot her ent icaing prospect of confining ult racold at oms above such integrated

"atom rllips' lies in the opportunity to take advantage of the hi+ sensitivity to ex-

tf'1.1liil fields cshibitcitl by these ixtoms. This sensitivitv can hc coinl~irlt~d with 'micaro- t ritpping' ant 1 ' rnicro-det cct ion' t tcllniques to realize ~lltrit-precis(> at om sensors such

magnet or~lrt ers i ~ r l ( I rot at iori serisors.

Initial drnionstrations of 'atom guiding' using lithographically patterned wires

on a substril be [:1. 4. 51 were soon followed by three dinlensio~lal trapping and the

rt:idizat ion o t' a Bose conrlensate on a chip[6. 71. However, as the itto~ns cvcre brought

closer to t he sul~stratc, it wits seen that surface induced interac.tions ant1 imperfect ions

(27)

clouds[(i, 8. 9, 101. Thus. studies of ultracold atoms confined above these chips were

usually conducted with the traps Inore than 100 p111 above the substrate. For wire-

11itsed traps. this increased separation frorrl the substrate comcs at the expense of srrlallcr trap freqllencies itrlcl srnitllcr t rzip dept 11s.

An alt e17ria.t ivr i\pproacll to rliicatrotraps r1ak)orat rtl irl this t hrsis liw irl t hr nsr of soft ferrom;rgl~rt s t o generate the trapping fields. T h r advitnt age:, of this approach lie

in stronger field gradients, larger trap freclue~lcies and a slow roll off of the fielcl away

lion1 t llc substrate. This means that tightly confining traps cijn 11e crcittcd fart her invay from tllc s~tbst rat c t hereby shielding t he 111trac.old itt olxls from surfarc induced Pffec2t s.

\lil~ly ~-t~rsiolls of wire-1)ilsrtl ant1 frrrorrlagrlrtic i~torri chips n-f1rr fi~l)ric.i\trd tluririg

I lie course of this thesis. These atoni chips \\-ere intended for trapping atorns in ~iovel

"1-clirr ~cnsional" gcometricis. for cohcrezlt split t irig ant1 mergin.; of ~ t l t ritcold at on1 c.lo11tls [l 1 . 1 21. for the study of t opologicitl excit at ions in it Bosc condensilt e [l3] a ~ i t l for t llcl c.rri~tion of arrays of rrg111arly S I ) ~ L ( ' P ( ~ rrii(hrotril~)s or a '111ilprirt ir lilt t i(.r'.

1.2 Nonlinear optics with ultracold atoms

Tllc strong interactions between atorns and ncar-resonant light has been known for

a long time. Nonlinear processes such as four-wave rr~ising and p1l;tsc c o q j u g ~ t ion l > r i o r tt r i - I o r 1 s . Viiriolls r f f c ~ t s i-~sso(.i~t e(l wit ll t llr

(28)

propagat iou of near-resonant light through vapor cells continue to fasci~lat e physicists

nearly a h~indred years after Sonlmerfeld a11d Brillouin[l4, 151 first co~lsidered the

pr ol~lcm.

At first glilrl(>r. orir rnight nssnrnr that laser c*oolirig arid tr~lppirig tec~liniqllrs tle- vclloprtl over tho liist cao~~plr of tlrcatlrs ~-0l11tl liilvr lrtl t o i~ rrvoh~tion in tlir stntlies

of ~lonlinear. optics iri dilute atomic media. After all, in comparison to a thermal

vapor. a laser cooled sample of atoms has the features of a t u ~ l a l ~ l e derisity, a negligi-

blc Dopplcr hrot~dcning. vastly reduced collisionit1 cffec t s and lollg int eraet ion t irncs.

In the couric of writing this thcsis. I chitnccd 11pon O I ~ C of thc tharly papers on laser

c,oolirlg ant1 tri~ppi1ig[l0;] i~ntl was str11c.k by a statr.rlic3rlt to\~,-vilrtls the rritl o f tlie pviipclr.

'To quote. "There are rnar1,y poten,tlnl u p s for snrnplrs of ntn.gr?,ctccnll.y or opt,cnlly

irc~pped a t o n ~ s ... T h e y alp usqful t n ~ g e t s for. ntnny s c n t t c l a n ~.rper.crn~nts rind i d ~ a l .~;rirrsplc~s jor prcc3is~orl spectrosc:opg.. . ilnothcr rrrlrqcw cl~aructrrr.strc of thc-sc. snrr~~11e.s

/ s thr- lltrye ophc>c~l t h r c ~ k r ~ ~ . s s with rleyl~qiblc Dopplrr or col1,ssor~ brundenrry. It shoc~ld

hr ~)o.s.st,hlr. lo obttrrrr (In ol~ticanl thrc>k:noss o f 10 ...

rt

ulrll nllorc~ .signific>c~ntly irrapr.o,lr~cl rr,i(r.sccrr rnr n t i of irlr.nk optic~ll pr*ofi).s.stls."

I\-llile therr have bee11 marly cle~lloilstratioils uf nonlinear optical processes in laser

(oo1i.d cnsc~nbles of txtorns. orie cvould bc liartl-prcssed to pinpoint stndics whose re-

SI 11t s ciiflvrcr 1 1ll:~rkcclly either qualit at ivcly or c111ant it at ively k o ~ n ccluic-alcrit csperi-

r urrlts or1 cv-illnri vapor cells. Of collrsr, this rxc.111drs st l~tlirs or1 atorri-light interntat ioris

i ti a Bose conclerisa t e where the coher~nce and the collective influence of the conclerl-

sate often h.tvo (lraniatic consecluenres.

Thcrc ~ 1 . c 1.1lany possiblc reasons for this conspicr~ol~s tlertr t 11 of ~lovcl nonlinear opt icsal stutli rs wit li illtracoltl at orns. Orle rrilsori tlii~t t20rrlrs to r~liiitl is t hr interplay t ~ r t ~ w r r i opticaal dept li ilriti riltliat ion t'rapping. LlTliilr t lie st rorig int rratat ioris i)etc~rrn

atoms itnd light are what makes ultracold ato~nic ensembles such a promising rnediu~ll.

orie does 1iol: have to go far in optical density before these interactions become self- dcfpitt ing. Whilc a large optical depth guarantees st rorlg norllirlear effcc t s. it also

implics txn incrcascd infi~~cncc of spont ancol~s phot ons or1 t lle a t oms. This " spl~riolls"

(29)

have made radiation trapping in ultracold atorri clouds the foc~ls of their researcIl[l'i, 181.

111 this tlic'sis. I\-r show that rilicrotraps be nsrtl to trap i~ritl cool atorris in n~)vc\l grorl~rtrirs. Iri 1)artic~nlar. ~lltrilcoltl atorrlic rrirtlia with estrrrnrly lo~ig ils1)t.cat

ri~tios and optical allisotropy can he realized. These traps have a large surface area-to-

volume ratio with a radical suppression of radiation trapping. 111 effect. the deforma- tion of the rrap shape lratls to a dcco1lpli11g of the optical density and tllc delctcrious

i f l P ( f i tI t i . Irl t fir rxprrilrirrlt s tlrscribrtl ill this t hrsis. s11c.h i~

I loforrllat ioi i lt.iltis to tlralllr~tic. effrc3t s on t fir effic1ac.y of laser c 3 0 ( )ling. t hrl rrlrlgrlit utlr

of 'inversiollless gairl' arld the behavior of tm-o-phot on resonances. It is rat her curious

that a rllc)cl~ficatio~i of the trap (ie. a change iri the bo~mclary conditions) can leacl to

sllch t1ritrna.t ic chttngcs in the rclsponsc of a tlilut c gas wit 11 an int crpart iclc spitting of 111i211~- opt ici~l ~vi~velengt 11s.

Anotlier prot~leui is tlle issue of optical depth. In the contest of norlliriear optical I,roccsses <ti the lcvel of tt few photons. it llits 11tle11 s h o n - ~ ~ optical depths on the order of 100 arc i.ctj11irctl to ol~scr-\-e significaant cHecst s[l9. 201. Such opt ic~tl depths llttve pre\-iollsly l)r*.rl the tlorni~in of Bose corltlrrisrtl ~torili(a e r ~ s r r ~ i ~ ) l t ~ s . At the very lc>ast.

t flescl o p t i ~ i ~l tlr tisitirs ilrr hilrtl t o achieve t lirongh opt icbal c.ooling rilrt hotls ant1 orirl

needs to ccmpress atoms to derlsities larger t 11an I/,\". One issue with working at such

clrrisi t irs is t lit1 t local field correcbt ions and collective effects can become dominant. Tliv c.oilit)i [lation of n lrargr optic.i~l tlrpth ( X'pL

>

100) iutl il lo~v atomic tlrnsit-

(/I,\,' 4: 1) rrcluirrs nltrilcaolt 1 rrisc~rrll)lt)s oli t ilr ortlrr of i~ fen- (:rritirrlrt rrs. At ttic)

same t irrle. to achieve large optical intensities with few phot (111 pulses. one has to ~ O ( . L L S these p ~ l s c s ~ O C V ~ to spot sizes of a few inicrons (close to the diffritction limit).

At

first g1ar1.c~. it wodd seem that the recll~irements of A long interaction length itnd

a, ~111dl spot size are r n u t ~ ~ a l l y excll~sivr clue to tliffrilctior~.

One of the results of this thesis is the clenlonstrat ion of radial confinerrlent ancl wit\-e-cg~liding of A \vc;tk opt ical pulse t hroug-11 an nl t racold nleclillrrl ovcr path lerlgt 11s

of t t f r w ccntimetcrs. This is accomplished by it cornbination of a11 itriisotropic trap

(30)

This is analogous to a graded index fiber with the added benefits of extrelnely strong and tunable interact ions and low propagat ion loss (in fact. the weak probe beam can

i3c arrlplificd th~ring propagat ion through t hr fiber).

This ability to radially confirie light in the ultracold ~ n e d i u ~ n has ~ n a d e it possible to achieve optical depths of a few huxldred even at at olnic densities such that

1. Thc t nrltt1,ili t3- of t hc dcnsi ty. t llc opt icitl clept 11 ant1 t lle il t omlight int eracat ions

coxnl)ined with tllc itbsence of Dopplcr broadening. collisionill cffccts and radiation

trirppirlg ~iii-~k~. this r~riisotropic. 111trac.oltl rnr.diurri a. luiiclnr systrr~i for nonlinear. optics

in t lie ultracold regime. The realization of this optical nlerliu~n and the dexnonstrat ion

of novel ilo~ilinear effects associated wit 21the properties of this riiediunl colist it ut e one

ct 1011.

c->f tllr rrlairll rcslllts of this disscrt. t '

1.3 Outline

of

the

thesis

This thesis is organized as follows:

Chapter 2 (:ontain.; a discussiorl of wire-based arid ferro~llagnetic microtraps. The

tlcsign itrltl implcmc~lt itt ioil of sllc2h microt raps arc tlct ailed. .An ilnport ant jssllc in

s t udics of i~ t 0111 optics r~sing rnicrotrilps is tllr ability to tritnsfor lizrgc rlllnll~crs of i ~ t orns into t hrhsf. traps wit ll high rfficierica>-. Wit ll this irl rxiirit 1. lvc. tlisc~~ss tlifferi>nt

strategies to 'nlocle-~ilatch' at 0x11s in macroscopic- traps into the i~licarotrap. N~unerical

~ilnula t ions of t lie capture efficiency of ferromagilet ila traps are prrsented.

C'hi y ~ t r r 3 caont irirls brief descxr.i~)t ions of the rsprriilirrit ill r~ppi~ratns tlii~t was built

to study soft ferrol~lagxletir neutral at 0111 traps and at 0111-light interact ion.; in these

traps. This irlclud~s descriptions of the laser system. the

UH\'

chamber ant1 the

e1t.ctronic.s t o cont ml the t irrlirlg of the rspcrirncnt .

Given the various wclvant ages of ferrolnagnet ic microt raps detailed in Chapter

2. Chapter

1

looks at methods of nlicrofabricating these ferrorrlag~letic traps on a

substrate a11.d the 110ssibilitv of integritt ing thrsc microtraps with other at 01x1 optic

tlcvic.cs. St rat tsgics airrled ixt rnirlirrlizirlg sllrhcc irld~lced cf&c t s and rnhtx~lcing the ho1liogc~11rity oE tlir irlicrotrqts are prrsrxxtrtl. The\ d(~sign ant1 f;~l~ric,atiorl of a ilovrl

(31)

reciprocal lnagnetic t r a p is discussed. This reciprocal trap is a very promising system

for an intejirated rotation sensor and studies of low dinlensional ultracold systems.

One of tllc feat urrs of the ferrornagnet ic atom traps prcsclrted in this t llesis is the ability to tune the aspect ratio of tllc atom clouds m d rcitlizr atorn clollds with vc3rjr lilrgt. optical t~rlisot ropies. Cllaptrr 5 corlt iiirls a st ntly of laser cooling iil highly flrlisot ropic. rnilgrlet o-opt ic. t rilps. It is sho~vrl that t llr efficirrlc .y of opt ic-a1 cooling jn such traps can be dramatically enhanced leading to vastly i~nprovecl phase space (lcnsi t ics in comparison to conr.(.nt ionttl rnagnet o-opt ic traps.

C'hizpter 6 titkes a microscaopic. view of optical cooling in t hrsc ttnisotropic traps.

This is prrsrritrtl in tllr corltrst of 'invrrsionlrss gitirl' and sl)rv~troscaopy of a tlrrssrd

t m-o-lrvrl syst tm. Tllr result i of this st utly prrsrrit rti nnilrrll)ig~lo~~s s i g n a t ~ ~ r r s of tllr

s ~ ~ p l ~ r e s s i o ~ i of radiation trapping ancl multiple scattering in a~lisotropic atom traps.

t 1 i t int eritc t ions involving rnl~ltilcvel svste~ns itre presented in Chapt crs

7 ~ n t l 3. rl'llt.st. rhttptcrs focus on the observation (11 a recoil intlllcccl rcsont~ncc. T'llis I)roc>rss is ilrlillogo~~s to il follr-~\-ilvr rriixirlg effrc~t in\-olvirlg i~torils arlrl light ~ r i t l

is rnttliat rd 1))- ilt onlic rrc.oil. D l ~ r to t hr large opt icxl anisotro1)y. IVP ol)srrvt) this

rpsonarlce i ~ i t hr high gain regime characterized by novel nonlirlear and (.ollective

effects. We clemonstrate a high ro~ltrast all-optical switch based on this effect.

Tht. rccsoil irl(l11ccd resont~,.nce is cilso ;~ssociittcd with strong clis1)c'r:iion leacling

t o slll)llurlir~i~l i l r l t l ~111)rrlllrnini~l group vrlocit ips of light wit hi11 t tlr nler linm. JVc) (lc3111011st rat o gr(m1) velo(.it ips of light rarlgi~lg fro111

+

1 UOO nq's to - 1UOO m/s in the

~iltrac.old rr~t~cliulu.

Due to rhc) s t r c q dispersion associated with the recoil-intluced resonance. we

also tl~rnon:;trittc radial corlfirlcrrlcrlt of light within the 111trac.oltl mcdil~m. In this

rnanx1c.r. we can ovcrcorrle the cliBritction limit and realize cxtre~rlcly large interaction

lt~ngt lls. Thus. t his coml~inilt iorl of anisot ropy arltl strong tlisprrsiori ~rlakes this an

unique system for studies of few photon no~lli~lear optics with a host of opporturiities

in quant 11111 inforrnat ion processing, ent anglerrlent of at onls and light and studies of s tro~lglt. co~lplcd at orn-light systerns.

(32)

(33)

Chapter

2 Anisotropic magnetic traps for

neutral atoms

Tills c - l ~ n p t ~ r- rli7.scm hr7.s tllr rnc~thotls used t o crrntc nnrsotrop~c mccy nctcr trnps u ~ t h l e r y

trrzp fr?qctc~rlo.rts ( ~ n d techr~rqr~cs rtspd t o load s1~c.h n~rt~rotrcrps 111rtl~ a 111,ry~ rll~rr~ber O f crtorr~s. I t ir/cxll~ol7rl.s

o thr c/cl.slgn (and r~onstr.lrc*tror~ 0.f (1, fi~r.~nrncryrrr]trc str.,rcat,rrr) to yi3r~rJrncltr) rnngnrtir

traps rcs~th hagh n s p ~ r t mtro.

o n rlr~srript~on of n

LD

s u r f ~ c c rnngr~eto-optrc trap capable of troppar~~q 1nr:qi n urn brrs Of ('Old ( L ~ U M I S ,

o (1 clrsc~ta.i..s~or~, of thr tr~clarr~q(rr)s (rsocl t o optarrtrzr. tlrr nrrrrahr r. o,f trrrpprd trtorr,.~ irr srrrir .srrrf(~,rrf t t r ~ p s .

l - h , ~ chnpte 1 rc partly bawd on thc publ~cntion

111. LCn~l~zlnttor.~.

IC:

Roorjnkkers nnA

hf.

Prrntrss. " A Ferrorna.qn~tlr ..ltorn G i ~ i d c urrth rrl srtu Londrrrg

".

Phgs.

Re

[ I .

A.

66.

0534

0:? (2001') ( I r ~ c l u d t ~ l I rl . 4 p p ~ n r l / . ~ -4,)

2.1 Introduction

The ability to trap and cool neutral atorrls to ultritcold tmlperatllres lins led to

spi.ctacr~lar stl~tlics of ultracold rrlattcr inc.lucling irlvcstigatiorls of atorrl optics. Bose colltlrnsat rs imtl tlrgrnrrat r Frrrniorlic systrrns. Irl rllilrly of t llrsr rs1)rrinlrnt s, the

(34)

~lltracold atoms are confi~led in magnet ic field 11li1li11la generated by cent i~neter scale

current carrying conductors. Analogous t o the develop~nent of ~nicroelectronics, sev-

c.r;tl groups have invest igat ccl st rat egies airrled at nliniat urizirlg i ~ ~ l d integrating t hrse churrcnt carrying c o ~ ~ d u c t o r s on R s ~ ~ b s t r t t t e . Since the size scale of the ultracold ator11 calo~~tls riuigtis horri R f ~ w rllicroris t o a fen- r~lillirriet CTS. rriirliiit llrizirlgg t lie1 (*~~rrerlt ci~r- ryirlg c.orltll~c.tors t o sirriili~r length sci~les offers ~~ossibilitirs of trixps with lixrgcl trap frecluellcies. tunable magnetic traps with extreme aspect ratios and magnet ic traps whit-h citn l ~ c clynitxrlically split into rnultiplc inininla. These rnicrotraps (.an hc inte- gra t cd with various ittorn optic components such as mirrors. hiall finesse twit ies arld ~iliglo ntoru tltltt~c.tor.s iri il i.orn1)i~c.t arltl rohlst rrlitririrr. S11c.h flrsibility al1o~1-s for

the) rtlnlizatiorl of i~ FI-iclr wtrirty of riovrl systerrls irlchulirlg r i ~ ~ ~ t r i ~ l i ~ t o ~ r i s~vitchrs aritl

transistors. ultracold lower di~nensional systems, entangled a t oniic ensembles. guided

at on1 interforornct crs for precise gritdiorncters. rnagrlctomct ers and rot at i o ~ ~ sensors. iin(l 11ltrac.o Id irlcsoscopic- co~ldrnsccl rnitt t er systems. Int cgrat ing t hesc st ruct rlrcs on

iii'i)st rat rl itlso hixs pract icai~l ~tlvalit ages of lo\\-rr powelr tlissipi~t iori arltl robnst riess.

Thc possiblli ty of using sernicondl~ct or rnicrofabric2at io11 t cchi~ology to carcate s11ch ilit ~ g r a t ~ 1 ( 1 1 ~ ~ l l t r i \ l i ~ t 0111 t r i ~ p s \\-as first ~ ) r o ~ ) o s t ~ l 19- l\Giristrixi arid Lil)l)rclc*lit

['I].

Iri

t l i ~ i r I)ill)er. t llry propose( 1 srvrral plilriar grlornc1trirs to c.rratr xllicrot raps wit 11 large

trap frrcjuellcirs. The principal nlotivat ion behind their proposal was the at t airllnent

of lleut ral n t orn maglietic traps in the Lamb-Dick regime ( \\-liere t lie vibrational spicing of the trap pot prltii~l d,,,,, esceecls the recoil energy of t hc a tom F,,, = h2k2/.2n1 n-lirr.i\ rrr is t hr rrlilss of t lie iitoxii i~rltl k = %rr/X is tlic. m7ixvrvrc.t or of t lir optitaal

t ri~risitioxl ilwtl for lilsrr caooli~ig of the atorus). Iri this regi~rir. it wonltl riot orlly 1)r

possible to tlirrctly cool the atoms to the gro~lncl state of the trap, but the resulting

ultracold at oms hvould exhibit novel collective behavior since the interparticle spacing

in this ultrac.01~1 mccliilm would bc less than the wavelength of light.

The basi(: recluirernents for such integrated microtraps are an ability to generate st-able ~nagnctir ficlcl nlini~rla with large gradients and curvat ures. In sllc.11 traps. 111- t racolcl at 0x11 s arc coxlfinetl very close to the subst ritt e support iilg t hc. rnic.rofabricitt cd

(35)

degree above absolute zero can be trapped a few lnicrons above a roorn temperature

surface wit bout significant heating. However. the ther~nal fluctuations in metallic sur-

f'accs on the. s ~ ~ b s t r i t t c can lead to decoherence and loss of at onls fro111 the rnag~letic

t rap[!Ij. In order to rninimizc such effects, it is preferable to crrat r t he trap rnore than iL 100 rrlicr'or1s i~k~ovr tlir s ~ ~ k t s t r i ~ t ~ > . AS \\-ill 1)r shon-rl iri t h ~ I I P X ~ sr('tiorl. irl ci~so

of tra1)w~'n~'ilt ctl i)y currrrit cxrrying c.orlt luct ors. this rrclliirrrri~~rit ckorlflict s with the

contlit ions necessary for tight confillernent . Also, since the capture volume of such

microtraps is ub11ally less tllitrl (100 i t ~ ~ ~ ) ' 3 . transferring a largc in~rrlbcr of prccoolccl iitollls into s11c.11 tritps lpatls t o problcnls of irlotlc rnatching ant1 loss. Again. the con- (lit ions for. highly locar~lizrtl c~orifirlrnlrrlt of at oriis in t llrsc) rliic.rot rilps oft rrl coriflict s

wit 11 st rixt rgirs i~irncltl i ~ t efficient t ransfer. of i ~ t orris irit o t llesc> tri~ps.

This (8llapti.r tlrsc.rik)rs i~ rr1r.t llotl of crtwting t igllt ly c~orifirirtl iriagrlrt ich traps nsirlg

soft fn.r.orili~ gr1c.t ic. rrlixt rrii~ls rrlr~griet izrtl by cnr.rerit c.ilrr.ying caolltlnct ors. Irl corliI)iu-

i,,orl to generating magnetic traps using ouly wires. it is shown that such a. hybrid

approach o f l r s the benefit s of tight confine~rlent and efficient loading while alleviat irlg

sllrfticc intll lccrl cffcc.t s. Whcrc applicable. the cahiiriict eristics of this ferrornugnrt ic trill) is c*orlll ) ~ r . c ) t l t o t lie pe\r.forrlli~rlcr of I ) I I I Y > ~ ~ wire basr t r i l ~ ) ~ .

2.2 Integrated magnetic traps for neutral atoms

2.2.1 Wire-based traps

I11 t 1 1 ~ prcscnc.ll of it nlngnct ic ficlcl. u riel~triil iit om cxpcricrlccs u Zcc~rlitn potential

C?,,,, = -11 B ( r ) \%-here la is thr. rnagrirtic r~lorrirnt of the ator11 arid B ( r ) is the

locai~l rrlagrlet ic firld. Iri the case 1%-1iere tho rrlagrleti(3 fieltl esprrirrlcrtl tty tlir atorn changes sufficiently slowly conlparecl to the Larnlor precessiorl frecjuency of the atomic

magnetic lnoment ie. L a , % ( r )

<<

U,,,,/h, the motion of the atom can be considered

B ( r )

itdiahnt ic. 111 ot hcr words. the oricilt itt ion of t hc mitgnctic ~norncnt with rcspcct to t l l ~ local magnetic field is invariant. In this case, the potential cxpcricnctd by tllc iltorn tltq)rrltls orily or1 t h ~ rnoth1111s of the rriagrlt>tic fieltl i~ritl

Ur,,,g

= - r r ) ~ f & 7 / [ ~ J B ( r )

I

(36)

where r n b 7 , ,qbl and ,LLB are the magnetic cluantum nurnber, the Land6 9-factor of the

atomic- hyperfine state and the Bohr magneton respectively. Atoms with r n ~ g ~ i 1

cxpericncc a. force toward regions of small nlagnetic ficlds. Such , ~ L J P U ~ ; ,field s~ekin.9

.states

can 1)c trapped in magnetic ficld minimit. Since hlax~vcll's eclnations forbid it 1r1wgrlr)tic fitlltl rrii~xiirn~ril in frrr space, lr i g l ~ firjlrl sr~oA:i.rry st(rtr1.s \\-it h rrr F ~

>

F 1 (xi~~irlot

1 ) ~ t r i ~ p p r d by static. rnagnrtic. firltls.

Thc sim plvst iinplemc~lt ittion of a lllaglletic trap rlsi~lg lit hographicall pat t er~led

wircs c+onsists of it sirlglc curreilt carrying co~ltluct or in corrlbinii t ion wit 11 i t r ~ ext erniil tlias fif.ltl. Co~isitlrr iirl infiriitrly lorig wire aligrlctl i~long the 3 axis. The rrli~giletica

field B ( r ) at a height r above a condu(:tor is given I,?

where p o / 4 i i = 10-' T-m/A, I is the current flowing in the co~lductor and

t5,

is the

Inlit vector in the azimuthal directio~l with respect to the axis of the co~lductor. This

cspression i j lalid for heigllts r litrgc cornpared to the width of the condllctor. Thc

rni\gnctic ficltl clue to this collcluct or ciin he csancelcd 11y a horizontal bias fieltl BhIiis

ilt a i)arti(allli~t. height r a O al)ove tllr wire if

s S O I i F i g - I This clrrates i k lirlr o f zrro firltl in thr. : tlirrc.tiori. In tlle

.r ~j plane. the magnetic field cont airls a zero around u.hicall the inotlulus of t lie field

in(-reasps lir~early. Such a cluadrupole field is characterized by thp inag~letic field

gr~idicnt h =-= Bhlas /rO. This configur~t ion serves its a 1-c-lirrle~lsio~litl trap or " at oxl

guide" . Ot llcr retxlizi~tions of such at oirl guides are sllown in Fig[2- 11.

Atoms confined in such cluadrupole traps are unstable due to the presence of tlie

lnag~let ic field zero. In the vicinity of this zero, the adiabatic approsimatioli breaks

do~vn and atonls have a finite probability of "flipping" their spill into thc high ficld

seeking stajtti as thcy cross this rcgion. T h ~ s c ntorrls are the11 cjected frorrl thc trap. Tllrsr prochr-;sm. trrrrletl hIcrjor.cr,rrrr s p i r , flipts cc~xl b r a tlorrlirlarit loss xrlrc.hiulisrrl for

(37)

~~ltrwc(-)l(l ittorns. Thc situatiorl c ~ l n bc rectified 1s)- applying a "holding" ficlcl Bh it1011g the) ilsis of the gnitlr. With the additiorl of this fic\ld. tllr rrlagnrtic firltl c.losr to the

trap lr~illirrlllrll k)e(.orx~os harrrlorli(. wit 11 a trap frtvll~c.rlcy

Fttr froxn this rniniml~ril ( b r

> >

Bh)

.

t hc xrlitgrletic field increases linearly.

Thrx confinc.rrlcnt in thc sy plane cil'n he corrlbincd with confinement in the I axis

t ~ y t)rrltlirlg t lie 11-ire in the shape of a

"LT"

or a " 2 " [El. This is illlwtratc~tl iri Fig['-'].

Figure 2-2: Microtraps crcatcd by wires.

A 'Z'

trap creates a Iofie-Pritcahard trap

cvl~ilc a

'LJ'

trap (-reixtes a quitdrupolc trap.

(38)

i%lld the trap frecluency. As can be seen. for a current

I

and a height T above the wire. these ( p a n t ities scale r e s p e ~ t ~ i v ~ l y as

B

-

I / r , h

-

I / r 2 and

8:

B

-

11,-%espertively. 'This scaling reveals tlle advantage of rnirliat urizirlg t he trap so that itt o ~ n s can he confined txt v c ~ y s~rlall distances from tlie wires. It sho111d be rccttlled that this scaling is only ap~)iic.i~l)le for re li~rgrr tllarl tllr ~vitltll of thr3 wire. For r. c.orrlpi~rill)lr to. or less t lli~rl tlw witit ll of the wirr. the rilagnrtic. firltl rlo lorlgrr irlc.r.ri~ses h t s i ~ t ~ u a t rs. 141sc~. the magnetic field gradient scales as h

-

I/ ( r'

+

u.7

~vhere II- is the width of the

wire. 1t car1 bc seen that the trap depth ;xiid ficltl gradients fall ~ixpidly RS the height

abovcl thc alrf'it(-c is incrrascd arid that large trap frccl~~cnc.ics c i t r l o11ly h r ~tc~c~sseel ~ ~ c ~ y closcl t ) t hrl sl1rfi~c.e of the at orn cllip. Tlnls. t h r rout r to lilrgc) trap frrclncmc.irs i ~ ~ l t l t iglit c.( )rlf<nr)rrlerit in snrh 11-ire-l)asrtl t r i ~ p s lies in t hr. fi~l~ric~at ion of very t hi11 I$-ires (typic ally a few microns in width) slid ill the confinenient of ato~ils very close

(tcns of microils) to the s11rf;xc;c of t hc atorrl chip.

This scaling of the trap parameters with the height above the co~lductor makes t hc at oms liigllly sl~scept ihlc to s11rfijc.c inclucctl r.ffrcat s. In early cspcrinlcnt s 11si11g intcgrixte(1 u-ircl-bascd i \ t ( ~ ~ n traps. concscrn was focusctl ~rlainly on the cffecst of surfacbc indl~c.rtl rffrvats or1 tirc.oherorlcr arltl spirl flip losses. Ho~l-rlver. it soon i ) r ( a i ~ ~ ~ l r rvitlcmt

[ti.

81that w fa I. rllorr tloirlirlant sl~rface i~l(lll(.r(l r f f r ~ ~ t \\-as ~ I I O to tiny i~llprx-fwt ioxfi in

t lie lit hogra phirally pat t enled or$. These i ~ n p r r f ~ c t ions, oft en less than 100 11111 ill size. (-ausrtl s~nall deviations in the magnetic field of the trap. Since the atoms arr cxtrcmely colcl. ever1 dcviatiorls or1 tl-lc order of it f t milligallss can hagmclnt ~ t ilo ator11 i. Dopcrldirly or1 t lie t rxrlpc3x-i~t 11ro of t hr colt1 at ouw. fii~grllerit at ioii lias l ; ~ ~ e r l oi )ser.votl i~1)0\7' ~vire-l)i~setl ilt or11 (.hips 1~11~11 t llr i ~ t orris itrt' 1 ~ s ~ tliarl arol11ltl IOU

p ~ n from tlie surface of the chip. This effect i~ilposes limitations on the rrlaxirilum

gradient. aspect ratio and homogeneity of the lnag~letic traps that can he achieved.

D11c to the smitll length scale of the irnprrfections on the conduc.tors, these rnagnrtic

field inhornogcncities decay rapidly away from the surface of thc atorrl chip. Thus,

orlr solllt ion to this 1)rol)lrrn is to fintl rnrt hotls t o grrlrrat r tullaljlr. tightly caorlfirling