PHYSICAL REVIEW A 82, 043425 (2010)

Dysprosium magneto-optical traps

Seo Ho Youn, Mingwu Lu, Ushnish Ray, and Benjamin L. LevDepartment of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA

(Received 9 July 2010; published 21 October 2010)

Magneto-optical traps (MOTs) of highly magnetic lanthanides open the door to explorations of novel phasesof strongly correlated matter such as lattice supersolids and quantum liquid crystals. We recently reported thefirst MOTs of the five high-abundance isotopes of the most magnetic atom, dysprosium. Described here aredetails of the experimental technique employed for repumper-free Dy MOTs containing up to half a billionatoms. Extensive characterization of the MOTs’ properties—population, temperature, loading, metastable decaydynamics, and trap dynamics—is provided.

DOI: 10.1103/PhysRevA.82.043425 PACS number(s): 37.10.De, 37.10.Gh, 37.10.Vz, 71.10.Ay

I. INTRODUCTION

Ultracold gases of fermionic dipolar atoms provide theopportunity to examine—in a pristine and tunable setting—the non-Fermi liquid, strongly correlated electronic behaviormanifest in some of the most interesting materials of late: high-Tc cuprate superconductors, strontium ruthenates, 2D electrongases, and iron-based superconductors. Strong and competinginteractions in these systems induce transitions to statesbeyond the familiar insulating, metallic, and superconducting.Specifically, phases that break rotational and translationalsymmetries emerge in a manner akin to those found inclassical liquid crystals, e.g., the nematic and smectic [1,2].Although quantum liquid crystal (QLC) theory can describethese non-Fermi liquids in a compelling and general frame-work, unwanted solid state material complexity—disorderand dynamical lattice distortions—can obscure the underlyingelectronic physics, and lack of wide system tunability canhamper efforts to fully explore QLC phase portraits.

Exploiting large dipole-dipole interactions (DDI) in ultra-cold gases will allow the exploration of QLC physics in thisinherently more tunable and characterizable system. Recenttheoretical proposals employing strongly magnetic fermionicatoms or polar fermionic molecules have begun to shed lighton the accessible QLC physics. These include predictions ofuniaxial (metanematic) [3] and biaxial nematic [4] distortionsof the Fermi surface in the presence of a polarizing field andmetanematic and smectic phases in 2D anisotropic opticallattices [5]. An exciting prospect lies in the possibility ofobserving spontaneous magnetization in dipolar systems, andRefs. [6,7] postulate the existence of observable quantumferronematic phases and spin textures in ultracold highlymagnetic fermionic atomic gases in a zero polarizing field.

While many exciting results will continue to arise from thedegenerate fermionic dipolar molecule system [8–11], to mosteasily observe true (nonmeta) QLC phases, the symmetries ofinterest should be spontaneously broken, which is not possiblewhen employing ground-state polar molecules. This is becausethe strong, r−3 character of the DDI is realized only in thepresence of a rotational symmetry breaking, polarizing electricfield that mixes opposite-parity states. Ultracold chemicalreactions can also hamper the use of fermionic polar moleculesfor studies of DDI-induced exotic phases in 3D, as recentexperiments in KRb have shown [10,11]. By contrast, highlymagnetic atoms exhibit the DDI interaction even in the absence

of a polarizing field and are largely immune to chemicaland inelastic collisions when spin-polarized in an opticaldipole trap. While both the electric and magnetic DDI canbe continuously tuned to zero, only the magnetic DDI can betuned negative [12].

One must look to the rare earth (lanthanide) series tofind atoms possessing masses and magnetic moments largeenough to support exotic bosonic and fermionic phases. Theextraordinarily large magnetic dipole of dysprosium (10 µB),which possesses the largest magnetic moment of any fermionicatom—and is tied with terbium in possessing the largestmoment among bosonic atoms1—is likely sufficient to induceQLC phases [5–7]. We describe here in detail the Dy magneto-optical traps (MOTs) [13] that may serve as a precursor todegenerate, highly magnetic Fermi—and Bose—gases.

It is not yet clear whether a degenerate gas of highly mag-netic lanthanide atoms is possible to create, but overcominga large DDI while cooling to degeneracy has precedent inthe Bose-Einstein condensation (BEC) of chromium [14]. Theattainment of Cr BEC opened the door to bosonic ultracolddipolar physics [15]. Chromium possesses the large magneticdipole moment of six Bohr magnetons (µB). This is 6 timeslarger than that of the alkali atoms’—Rb has a magneticmoment of µ = 1 µB in the doubly polarized state—andrepresents a significant 36-fold enhancement in the DDIstrength

Udd = µ0µ2

4π

1 − 3 cos2 θ

|r|3 , (1)

where r is the distance between two dipoles and θ is the anglebetween the direction of polarization and the relative positionbetween the two particles. However, as strong as Cr’s DDI maybe, recent calculations [16] suggest that novel lattice phasespredicted by the extended Bose-Hubbard (eBH) model [15],such as density waves and lattice supersolids [17], lie justbeyond the reach of Cr’s capability. Specifically, the DDIenergy must dominate the contact interaction energy, which

1Terbium has only one isotope, a boson. Unfortunately, it possessesa 400 K electronic state that could be driven by incoherent blackbodyradiation, thus limiting coherence and trap lifetimes. Additionally,thulium (4 µB ) [37] and holmium (9 µB ) have only single bosonicisotopes.

1050-2947/2010/82(4)/043425(12) 043425-1 ©2010 The American Physical Society

YOUN, LU, RAY, AND LEV PHYSICAL REVIEW A 82, 043425 (2010)

occurs when ε = µ0µ2m/12πh2as >∼ 1, where m is the mass

and as is the s-wave scattering length, and the extra factor of3 in the denominator designates ε � 1 as the regime in whichhomogeneous dipolar BECs become unstable to collapse [15].To observe novel lattice phases, ε should be >0.7–0.8 [16].For 52Cr, εCr = 0.15, and even with the demonstrated fivefoldreduction of as via a Feshbach resonance [18],2 εCr = 0.7remains at or below the threshold for new phases. In contrast,εDy = 1.34, which is 9 times larger than εCr, assuming that theas yet unmeasured scattering length for at least one of Dy’sbosonic isotopes is approximately equal to 52Cr’s as = 100 a0.With such a large εDy, exploring supersolids and density wavephases without the use of Feshbach resonances should bepossible with Dy.

As candidates for fermionic dipolar physics, existing MOTsof highly magnetic fermionic 53Cr and 167Er are not yet pop-ulous enough to contemplate cooling to degeneracy [19,20].The technique of buffer gas cooling has been used for coolinglanthanides and has proven successful in producing large500 mK samples [21]. While Dy has been adiabatically cooledto ∼50 mK at final densities of ∼109 cm−3 [22] in such anexperiment, evaporative cooling in a magnetic trap to lowertemperatures has not yet proven effective due to large inelasticcollisions. Thus, the extraordinarily populous 0.1–2 mK Dysamples discussed here open the door to a rich landscape ofphysics.

Ultracold samples of bosonic and fermionic isotopes of Dywould find application beyond the QLC and eBH physics de-scribed above. Cotrapping isotopes of Dy present an interestingsystem to explore Bose-Fermi mixtures of near equal mass,reminiscent of 3He-4He studies, but now in the presence ofsame and cross-species dipolar interactions. Studies of large-spin degenerate spinor gases [23,24], simulations of densenuclear matter [25], creation of unconventional superfluidpairing [26], and explorations of zero sound [27] and rotonmodes [28] in dipolar gases are exciting avenues of research.In addition, ultracold samples of Dy will aid precisionmeasurements of parity nonconservation and variation offundamental constants [29], single-ion implantation [19], andquantum information processing [30,31]. With regard to thelatter, the low-lying telecom (1322 nm) and InAs quantum dotamenable (1001-nm) transitions (see Fig. 1) will be useful forcreating hybrid atom-photonic or atom-quantum systems thatexploit potentially long-lived spin coherences in ensembles ofDy for quantum memory. Novel ultracold collisions [32] andcomplex Feshbach resonance-induced molecular associationphenomena are expected to appear in traps of these non-Sstate atoms, which may enable exploration of 1D stronglycorrelated gases with highly magnetic molecules [33].

II. LASER COOLING SYSTEM

A simple laser cooling and trapping method for highlymagnetic atoms has now proven successful for three magneticlanthanides: Er, Dy, and Tm [13,19,37]. Measurements ofMOT recycling dynamics show that the working principlebehind the Er and Dy MOTs is similar [13,19]. Despite the

2Rapid three-body losses preclude greater reduction of as [18].

03 4 5 6 7 8 9 10 11 12 13

Wav

enum

ber (

1000

cm

-1)

5

10

15

20

25

30

2

4f9(6Ho)5d6s2 7Ho8 4f9(6Ho)5d6s2 7Io9

4f9(6Ho)5d6s2 5Ko9

4f10(5I8)6s6p(3Po1)(8,1)o

9

4f9(6Ho)5d6s2 7Ko9

4f10(5I8)6s6p(1Po1)(8,1)o

9

4f106s2 5I8 ground state

2000

1000

667

500

400

Wavelen

gth

(nm

)

333

J value

1322 nm 1001 nm

626 nm

598 nm

421 nm (slowing and cooling transition)

741 nm

161Dy163Dy 23/221/219/217/215/213/2

13/215/217/219/221/223/2

11/2

21/219/217/215/213/2

13/215/217/219/221/2

11/2

F’ =

F =

F’ =

F =2.16 GHz1.68 GHz1.29 GHz961 MHz702 MHz

2.11 GHz1.50 GHz1.02 GHz634 MHz342 MHz

421 nm

(b) (c)

330 MHz697 MHz956 MHz

1.19 GHz1.11 GHz

1.09 GHz1.12 GHz1.08 GHz975 MHz790 MHz

421 nm

(a)

FIG. 1. (Color online) Dy energy level structure [34–36], whereJ is the total electronic angular momentum and F = J + I , thetotal electronic plus nuclear angular momentum. The prime indicatesexcited state quantum numbers. (a) The MOT and Zeeman slower usethe strongest laser cooling transition at 421 nm; there are nearly 140lower energy metastable states. Several other laser cooling transitionsexist between the ground state and the excited states. The red statesare even parity and the odd are shown in black. Dysprosium has fivehigh abundance isotopes; three bosons (164Dy, 162Dy, and 160Dy withI = 0) and two fermions (163Dy and 161Dy with I = 5/2). (b)–(c)The two fermions have oppositely signed nuclear spin, resulting in arelative inversion in the hyperfine structure.

existence of more than a hundred levels between groundand the open excited state of the cooling transition, norepumping laser is necessary because of a novel recyclingmechanism [19]: After decaying out of the MOT coolingtransition to metastable states, the highly magnetic atomsremain confined in the MOT’s magnetic quadrupole trapwhile the metasable state population recycles to the groundstate, at which point the atoms are recaptured by the MOT.The strongest transition J → J + 1 transition is used forZeeman slowing and MOT cooling. Whereas weakly magneticatoms would be lost from the trapping region during time inwhich the atoms spend in the metastable states, the strongdipole moments (7 µB for Er) allow confinement even in theMOT’s magnetic quadrupole gradient. The 1:105 branchingratio between population decay back to the ground state versusto the metastable state is sufficient for a MOT to form giventhe efficient population recycling.

We highlight four criteria necessary for the large-population, highly magnetic, repumperless MOT to workwhen using strong open transitions: (i) to be captured bythe MOT, the branching ratio must be small enough thatatoms exit the Zeeman slower in their ground state; (ii) thedecay channel through the metastable states must be rapid

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DYSPROSIUM MAGNETO-OPTICAL TRAPS PHYSICAL REVIEW A 82, 043425 (2010)

Rb D2 (780 nm)

diode laser

Rb

loopfilter

saturationabsorptionspectroscopy

opticalisolator

Ti:Sapphire laser and reference cavity2.7 W at 842 nm

to MOT, imaging, and transverse cooling

Frequency doubler600 mW at 421 nm

loopfilter

loopfilter

10 cm cavity;

PBS cube

PBS cubeλ/4

λ/4filter

filter

optical isolator

photodetector

photodetector

PZT

18.5 W at532 nm

to Zeeman slowerFrequency doubler1.5 W at 421 nmoptical isolator

loopfilter

photodetector

beat note lock

15.2 W at532 nm

Ti:Sapphire laser and reference cavity4.3 W at 842 nm

FIG. 2. (Color online) Schematic of the Dy laser cooling system.See text for details.

enough that inelastic collision processes—from background,spin-changing, or light induced collisions—do not deplete themetastable magnetic trap (MT) reservoir; (iii) decay throughthe metastable MT should be slow enough for it to serve as areservoir to capture more atoms than those cycling on the MOTtransition; (iv) for isotopes with I �= 0, the difference frequen-cies between adjacent F → F ′ = F + 1 hyperfine transitionsin the ground and excited states must be small enough that thecooling laser itself serves as a repumper (see Sec. IV B).

All of these criteria are satisfied in the five most abundantisotopes of Dy, the level structures of which are depicted inFig. 1. Before discussing the Dy MOT recycling dynamicsand population in Sec. IV, we first describe the laser systememployed for producing the light necessary to drive the Dylaser cooling transition at 421 nm.

The strongest J → J + 1 cycling transition is the421-nm line, which has a broad linewidth of 31.9(0.7) MHz[34,38]. A total of 2 W of 421-nm optical power is generated bytwo Ti:sapphire laser systems (see Fig. 2). Such high power isnecessary because the saturation intensity 58 mW/cm2 is largeand, as we discuss below, the Zeeman slower optimally uses1 W of power. The first Ti:sapphire system (TiS1) is pumpedwith 15.2 W at 532 nm, which when frequency doubledin a ring cavity with an LBO crystal produces 600 mWof continuous wave (CW) 421-nm light with a 20-kHzlinewidth [39]. The second doubled Ti:sapphire laser system(TiS2) produces up to 1.6-W CW at 421 nm (again using aring cavity frequency doubler) from a 4.3-W 842-nm beam.TiS2 is pumped by a 18.5-W 532-nm laser, and the 421-nmlight has a linewidth of ∼50 kHz at 421 nm.

TiS1 produces the 421-nm light for the MOT, transversecooling, and imaging beams, while TiS2 is used solely forthe Zeeman slower. Each laser is locked, at 842 nm, to itsown low-finesse reference cavity. These cavities exhibit a∼40-MHz/h frequency drift, so we have developed a morestable locking scheme which provides a long-term stabilityof several 100 kHz. The frequency reference is derived usingthe transfer cavity technique: the 842-nm light from TiS1 islocked to a mode of an optical cavity whose length is stabilizedby a 780-nm laser that is resonant with the cavity ∼2 × 104

Zeemanslower

transversecooling

oven

MOTchamber

Ti sub. pump

ion pumpion pump

ion pump

45o mirror

Zeeman slowerbeam

CCD

probebeam

FIG. 3. (Color online) Sketch of the Dy UHV chamber system.The blue arrows depict the slowing, cooling, and imaging laserbeams.

modes away. This 780-nm laser is itself frequency stabilizedto a hyperfine transition in Rb using saturation-absorptionspectroscopy. Thus, the stability of a medium-finesse cavitylocked to a Rb frequency reference is transferred to the 842-nmlaser of the TiS1 system. The TiS2 system is offset locked [40]at the Zeeman slower laser detuning by detecting a beat noteat 842 nm between the TiS1 and TiS2 lasers. See Appendixfor more details.

III. TRAPPING APPARATUS

Figure 3 illustrates the schematic of our Dy vacuumchamber system. A thermal atomic beam is first generated witha high-temperature oven. This atomic source is then collimatedthrough a differential pumping tube, and a larger flux isachieved by transverse cooling. The Dy atoms are deceleratedand cooled by a “spin-flip” Zeeman slower. Finally, the slowedatoms are captured and loaded into a large-gradient MOT inthe trapping chamber.

The vacuum system consists of four main sections: high-temperature oven, transverse cooling, Zeeman slower, andMOT trapping chamber. Each section—except the Zeemanslower—has an ion gauge to monitor the vacuum pressure anda dedicated ion pump. In addition, there is a stainless steeltube (inner diameter 4.6 mm, length 18 cm) that providesdifferential pumping between the oven and transverse coolingsections. The Zeeman slower (inner diameter 1.7 cm, length54 cm) also serves as a differential pumping tube between thetransverse cooling and MOT sections. A titanium sublimatorprovides additional pumping in the MOT trapping chamber.

A. High-temperature oven and transverse cooling

Because Dy has a very high melting point of 1412◦C,a dual-filament, all-tantalum high-temperature effusion cellwith a water-cooling shroud3 is used to heat mm-sized piecesof Dy. The nonisotopically purified Dy is placed in the

3Custom made from SVT Associates, Inc.

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YOUN, LU, RAY, AND LEV PHYSICAL REVIEW A 82, 043425 (2010)

tantalum crucible and heated to 1250◦C during typical MOToperation. A near-uniform temperature is achieved by twoservos controlling heaters located at the the tip and mainpart of the oven. The crucible with a 5-mm-diameter orificegenerates a Dy beam. By attaching a flexible bellow to theoven and controlling it with mechanical positioning stages,the direction of atomic beam is optimized for maximum MOTpopulation.

Because blackbody radiation from the crucible can heat theUHV chamber walls, a 2.25-inch-diameter tantalum shield isinstalled around the tip of the differential pumping tube, imme-diately before the transverse cooling section. Heat propagationthrough the vacuum system is avoided by continuously watercooling the ConFlat (CF) flange to which the tantalum diskand differential pumping tube are welded. The atomic beammay be shuttered by an in-vacuum, pneumatically controlledtantalum shield positioned a few mm from the crucible orifice.

Typical oven operation at 1250◦C provides a Dy vaporpressure inside the crucible of ∼7 × 10−2 Torr. We achievea vacuum of 1.0 × 10−9 Torr at the ion gauge of the ovensection with the use of a 75-L/s ion pump. This low pressure isachieved with help from the getter properties of the evaporatedDy on the tantalum disk [41]. Fifteen grams of Dy lasts∼400 h at 1250◦C operation. A gate valve after the oven sectionmaintains the vacuum in the rest of system while detachingthe oven for the refilling. At the transverse cooling stage,the pressure is 8.2 × 10−11 Torr when continuously evacuatedwith a 55-L/s ion pump.

A larger atomic beam flux is achieved by transverse coolingthe portion of the beam after the differential pumping tube andbefore the Zeeman slower. A detailed study of Dy transversecooling appears in Ref. [42]. The transverse cooling beamsare elliptically shaped such that they match the atomic beam;their dimensions are 4.4 by 18 mm. One beam is orientedhorizontally to the the atomic beam and is retroreflectedthrough the chamber via antireflection coated windows. Thesecond beam enters the chamber vertically, passes through aquarter-wave plate, into the chamber and is again retroreflectedthrough a quarter-wave plate before entering the chamber.Addition of the quarter-wave plates along the vertical directionenhances transfer efficiency; no such gain is observed for thehorizontal branch, presumably since the local magnetic fieldis nonzero. The cooling beams are all red detuned from the421-nm transition by 0.2–0.4 �. At a total power of ∼200 mWdivided among the horizontal and vertical beams, the MOTpopulation is enhanced by up to a factor of 4. Additionalpower slightly reduces the MOT population, ostensibly due toincreased metastable population shelving before the Zeemanslower (and possibly recoil heating). See Sec. IV B for moredetails.

B. Zeeman slower

The spin-flip (zero-crossing) Zeeman slower [43] decel-erates and cools the collimated atomic beam from 480 m/s(most probable velocity) to 30 m/s.4 Up to 1.5 W of Zeemanslower beam power is used to slow the atomic beam. A 45◦

4These are design values and have not been measured.

Nto

tal(a

rb. u

nits

)

0.3 0.6Laser power (W)

0.6

1

0.4

0.8

0.9 1.2 1.5

FIG. 4. (Color online) MOT population as a function of Zeemanslower laser power. Population saturates above 1 W of laser power.Data for 164Dy (163Dy data are similar).

aluminum mirror is installed inside the vacuum system to avoidDy coating the entrance viewport of the Zeeman slower laserbeam which is focused into the orifice of the oven crucible.The Dy film coating the mirror is reflective at 421 nm. Thediameter of the slowing laser is 2.5 cm at the vacuum windowentrance. As shown in Fig. 4, total trapped atom populationNTotal saturates at ∼1 W of input power; presumably powerbroadening aids the velocity capture range of the slower.

C. MOT trapping chamber

The MOT employs a three-retroreflected-beam configura-tion (a six-beam configuration can also be used, with similarresults). Each beam is aligned and collimated in free spacewith a waist5 of 1.1 cm, and the MOT typically has a detuningof � = −1.2 �. A total intensity of 0.17–0.2Is provides themaximum MOT population, where Is ≈ 2.7 × 58 mW/cm2.6

A stainless steel octagon chamber with two 6-inch-diameterCF viewports on top and bottom and six 2.75-in. CF viewportson the side provide the optical access necessary for the MOTbeams and imaging beam. The remaining two CF ports provideaccess for the atomic beam and counterpropagating Zeemanslower beam.

The magnetic quadrupole field used for both the MOT andmagnetic trap [13] is generated from a coil pair in near-anti-Helmholtz configuration. The coils generate 0.69 G/cm Aalong z, which points along the quadrupole axis of symmetry;each coil has a cross section of 10 rows (z) and seven columns(ρ). The coils are water cooled to support the ∼30 A usedfor the MOT. The electric current is controlled by a servoproviding a 440-µs turn-off time. Stray field cancellation coilsreduce the residual field to �1.8 mG.

We achieve a MOT chamber pressure of typically 1.2 ×10−11 Torr during MOT operation. The vacuum is createdwith the help of a 75-L/s ion pump and a titanium sublimationpump. We have noticed a lowering of the vacuum pressurefrom the evaporated Dy after the oven has run for severalhours.

5All beam waists are reported as a beam 1/e2 radius.6The additional factor of 2.7 accounts for approximately isotropic

polarization and equally distributed mJ ’s in the MOT.

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DYSPROSIUM MAGNETO-OPTICAL TRAPS PHYSICAL REVIEW A 82, 043425 (2010)

D. Imaging

After the atoms are released from the trap, absorptionimages are taken from the CCD camera installed on the sideof the trapping chamber with a probe beam pulse width of60 µs. This short pulse width ensures that that atoms areapproximately stationary and shelving into metastable statesdoes not occur during the imaging process. In order to takereliable temperature measurements of the MOT while avoidingeddy currents (lasting ∼1.5 ms) incurred during magneticquadrupole coil shutoff (at td = 0), the time-of-flight data weretaken in 500 µs steps from td = 3 to 5–7 ms.

IV. DY MOT CHARACTERISTICS

In this section we discuss a detailed, semiclassical modeland supporting data for how the repumper-less Dy MOTfunctions. Measurements of the Dy MOT population andtemperature versus MOT loading time, intensity, detuning,and magnetic quadrupole field gradient are presented. Wealso compare Dy MOT characteristics to those of the ErMOT [19,44].

A. MOT decay and motional dynamics

As mentioned in Sec. II, the Dy MOT functions without anyrepumpers due to a population recycling mechanism based onits extraordinarily large magnetic moment. Figure 5 depictsa semiclassical rate equation model describing this recyclingprocess. Population is lost from the excited state of the MOT atrate fexR1—which increases for larger excited state fractionsfex—and decays to one of the (possibly many) metastablestates (see Fig. 1). A fraction of atoms 1 − p are either in them = 0 Zeeman substate or in a strong magnetic field seekingm state and never become confined in the MT. The remainingatoms decay either through a fast decay channel at rate Rfast

and fractional population 1 − q or through a slow channelat rate Rslow. Atoms whose electronic population reaches theground state are reloaded into the MOT at rate Rreload, whichdepends on the total MOT beams’ saturation parameter, s =I /[1 + (2�/�)2], where I = I/Is and � is the detuning fromresonance. There must be some loss Rloss2 from the magnetictrap as the population cascades, but as shown in Ref. [13],spin relaxation loss is 20× slower than the time scales of themeasured Rfast and Rslow.

MOT

Rreload

Metastable states

Ground state

p.fex.R1

421

nm

Rloss2

Magnetic trap

Rloss1 = (1-p).fex.R1

Rfast Rslow

q1-q

RL

FIG. 5. (Color online) Dy MOT recycling and continuouslyloaded MT schematic.

The diagram in Fig. 5 may be represented with the followingrate equations:

NMOT = RreloadNMT − fexR1NMOT + RL,

Nfast = (1 − q)pfexR1NMOT − RfastNfast,(2)

Nslow = qpfexR1NMOT − RslowNslow,

NMT = RfastNfast + RslowNslow − RreloadNMT,

where NMOT, Nfast, Nslow, and NMT are the populations of theMOT, fast (slow) metastable state decay channel, and ground-state MT, respectively, and RL is the loading rate from theZeeman slower. Fits of these rate equations to MOT populationdecay curves allow the determination of all free parameters forboth the 164Dy boson and the 163Dy fermion:

[R163

1 ,R163fast ,R

163slow

] = [1170(20),19(2),1.5(1)]s−1,[R164

1 ,R164fast ,R

164slow

] = [1700(100),29(1),2.3(1)]s−1, (3)

[p,q] = [0.82(1),0.73(1)],

where p and q for the two isotopes are equal within error.[See the description surrounding Eq. (5) and Fig. 7 below forinformation on how R1 is determined.]

An example of the Dy MOT decay and fit are shown inFig. 6(a). To obtain these data, we collect MOT fluorescenceusing a 200-mm 2-in. aspherical lens and focus it through apinhole, using a 60-mm 2-in. aspherical lens. The light is then

1

0.1

NM

OT

(a)

Time t - tm after MOT recapture (s)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1

1.3

1.6

0 2 4 6

s 1

0 2 4 6 8 10 12 14 16 18 20

1.6

1.3

1

s << 1

(ms)

(b)

(c)

s << 1

Δ F

WH

M (m

m)

0 2 4 6 8 10 12 14 160.15

0.17

0.19

0.21

0.23

(d)

Time t - tm after MOT recapture (ms)

FIG. 6. (Color online) (a) Population ratio NMOT of recapturedMOT to steady-state MOT. The black line is fit using Eqs. (2) toNMOT with Zeeman slower and atomic beam off, and tm = 1 s delaybetween steady-state MOT and recapture. [(b) and (c)] Oscillations influorescence at the peak of the recaptured MOT population appear forMOT beam saturation parameters s � 1. (d) The Dy MOT operates inthe mechanically underdamped regime, as shown by breathing modeoscillations, and the photon scattering rate seems to be correlatedwith cloud diameter.

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YOUN, LU, RAY, AND LEV PHYSICAL REVIEW A 82, 043425 (2010)

collected on an amplified, high-bandwidth PIN photodetector.We load the MOT for 2–3 s to reach steady-state populationbefore extinguishing, at tm = 0, the MOT beams, the Zeemanslower beam, and the atomic beam (via the in-vacuum shutter).Note, the magnetic quadrupole field remains on throughoutthis experiment, providing confinement for weak-field seekingmetastable and ground-state atoms. We wait for tm = 1 sbefore recapturing the MOT by turning on the MOT beams,but we leave the Zeeman slower beam and atom beam off toensure there is no external loading of the MOT during themeasurement, i.e., RL = 0. Shorter tm times bias the resultsdue to ill-defined initial conditions: we fit the data assumingnearly all population has decayed to the ground state, allowingus to set NMOT = Nfast = Nslow = 0 at t − tm = 0, while NMT

is left free to vary and is normalized to the steady-state MOTfluorescence signal. Fluorescence traces as in Fig. 6(a) areaveraged over 16 sequential runs on a digital oscilloscope.

We noticed an oscillation of the recaptured MOT fluores-cence near peak signal when operating at small saturationparameter s � 1. The pinhole does not restrict numericalaperture so severely that the modulation is simply due toa loss of photons when the cloud is large. This oscillationdisappears when the intensity of the MOT light is increasedand/or the detuning of the beams decreased to the point thats ∼ 1 [compare Figs. 6(b) and 6(c)]. Data corrupted withoscillations could not be fit using Eqs. (2), so all the data usedto extract R1, Rfast, Rslow, p, and q were taken near s ∼ 1.

A possible explanation of these fluorescence oscillationslies in the motional dynamics of the Dy MOT. Most MOTs,e.g., of Rb, are solidly in the overdamped regime, meaningthey have a ratio α = �MOT/ωMOT > 1 of the MOT’s opticaldamping rate �MOT = β/2m to the trap oscillation frequencyωMOT = √

κ/m. In a 1D treatment, the damping coefficient β

is

β = 8hk2|�|I�(1 + I + (2�/�)2)2

, (4)

where k is the wave number of the MOT light, mass is m,and the spring constant is κ = µ′∇Bβ/hk [43]. In this latterexpression, µ′ ≡ (geme − ggmg)µB , where gi and mi are theg factors7 and Zeeman substates of the ground and excitedlevels. For a typical Rb MOT operated to maximize trappopulation, αRb >∼ 7. For the Er MOT with the parametersused in Ref. [19], αEr = 1.3 and oscillations where notreported [45]. However, the Dy MOT, when operated inthe regime that maximizes trapped atom population (seeSec. IV E), is just in the underdamped regime αDy = 0.8. Theorigin of this lower α lies in the combination of the larger(smaller) m, k, �, µ′, and ∇B (I and �/�) parameters in thehighly magnetic Dy MOT versus typical Rb MOTs.

Indeed, αDy = 0.8 corresponds to an oscillation periodof 4 ms, and a measurement of the breathing mode of theDy MOT, shown in Fig. 6(d), shows a damped oscillationwith a period of ∼6 ms after the magnetic quadrupole fieldgradient is decreased by a factor of 2 at tm = 0. We findthat the breathing mode period scales ∝ √∇B. The similarperiods support the notion that fluorescence is modulated by

7For Dy, gg = 1.24 and ge = 1.22.

−0.28−0.40−0.51

−0.03−0.15−0.27

I/Is I/Is

0 0.1 0.2 0.3 0.4 0.1 0.40.20 0.3

163Dy 164Dy3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

f exR

1(1

02s-1

)

3.2

2.8

2.4

2.0

1.6

1.2

0.8

0.4

0(a) (b)

FIG. 7. (Color online) Fits of Eq. (5) to fexR1 versus I = I/Is and� for both (a) fermionic 163Dy and (b) bosonic 164Dy. A simultaneousfit to the nine (eight) data points for 163Dy (164Dy) allow the extractionof R1 from the product fexR1 via Eq. (5).

the motion of the atoms during recapture. (Atoms confinedin the magnetic trap, from which the MOT is recaptured,possess a different spatial profile from those in the MOT.)The breathing mode should have a period half that of thetrap oscillation frequency, indicating that the actual αDy isjust slightly below unity; a 3D numerical MOT calculationincorporating magnetostatic forces on the highly magneticDy could better estimate α for these system parameters. Weconjecture that optical pumping, Zeeman shifts, and spinpolarization near the cloud edge—as well as modulation ofoptical density—could change the effective photon scatteringrate as the cloud expands and contracts. To avoid complicationscaused by these motional dynamics, we operate the MOTin the overdamped regime of s ∼ 1 for the decay ratemeasurements.

To extract MOT decay rates R1 from the product fexR1—aswell as to obtain better error estimates of the other modelparameters—we repeat the measurement in Fig. 6(a) forseveral combinations of I and �. MOTs of bosonic 164Dy andfermionic 163Dy are studied in a similar manner to investigatedifferences in decay dynamics due to hyperfine structure.Figure 7 shows the set of data simultaneously fit to thefunction

R(I,�) = R1I /[2 + 2I + 2(2�/�)2], (5)

where R = fexR1. Using this method to determine R1, wearrive at the rates in Eq. (3) for these two Dy isotopes.

Detailed simulations of the decay channels still seem be-yond the reach of tractable calculations, but such calculationsmight be able to employ the following simplification formodeling the fast decay channel. The shortest possible decaychannel (the fast channel), must involve at minimum twometastable levels due to the need to switch parity from odd(421-nm exited state) to even to odd before decaying back tothe even-parity ground state. Recent calculations reported inRef. [46] indicate that the lifetimes for the 1001-nm and 1322-nm levels are 2π · [53,23] s−1, respectively, which indicatesthat rapid decay to these levels followed by a delay given bytheir lifetime is a likely candidate for the 20–30 s−1 fast decaychannel. For the slow decay channel, it is possible that thepopulation becomes shelved in a longer-lived state that decaysto ground or an intermediate state via a nonelectric dipole (E1)allowed transition. Small-energy-difference decays could alsocontribute to the slow channel.

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DYSPROSIUM MAGNETO-OPTICAL TRAPS PHYSICAL REVIEW A 82, 043425 (2010)

160 161 162 163 1640

0.05

0.1

0.15

0.2

0.25

0.3

0.35

rela

tive

MO

T n

umbe

r natural abunance

0

5%

10%

15%

20%

25%

30%

35%

natural abundance

MOT number

Dy isotopes

FIG. 8. (Color online) Comparison of relative MOT populationto natural isotope abundance for the five highest abundance isotopesof Dy. The fermions, 163Dy and 161Dy, are highlighted in gray. TheMOT populations for the fermions equal that of the expected naturalabundance when multiplied by 6/5 for 163Dy and 6 for 161Dy toaccount for poor optical pumping of the six hyperfine states duringlaser cooling. Relative population is computed, assuming this fermionpopulation scaling is valid, as the fraction of an isotope’s MOTpopulation out of the sum total MOT population for all the isotopes.See text for details.

The large q parameter—73% of the atoms decay throughthe slow versus fast channel—serves a very useful purposein providing a continuously loaded magnetic reservoir ofmetastable atoms for the MOT. Indeed, data presented inRef. [13] show that 2.5 × (164Dy) to 3.5 × (163Dy) moreatoms are in the metastable MT plus MOT than in the visibleMOT alone, resulting in a maximum number of laser-cooledand trapped atoms nearing 5 × 108 for the Dy system. Thisis reminiscent of the continuously loaded MT in the Crsystem [47] that provides sufficiently large samples, 108 atoms,to enable Bose condensation of Cr [14].

B. MOT population versus isotope

Figure 8 plots the maximum MOT population obtained foreach stable isotope (except for low 0.1% abundance 158Dy)along with the natural abundance of the isotope. To facilitatecomparisons to natural abundance, each MOT population isnormalized by the sum of all the MOT populations of theisotopes (for the fermionic isotopes, the MOT populationis adjusted for hyperfine shelving; see below). The bosonicMOTs have relative populations very close to their proportionof the natural abundance. However, the fermionic isotopes163Dy and 161Dy have populations that are 84.0% and 17.3%their natural abundances, respectively. We try, in the following,to argue why repumper-less fermionic MOTs form and areobserved with these population ratios.

Unlike the bosons, the two fermions have nonzero nuclearspin I = 5/2, and the opposite sign of the nuclear magneticmoment between the two isotopes results in oppositely orderedhyperfine levels with respect to F versus energy [see Figs. 1(b)and 1(c)]. With a total electronic angular momentum ofJ = 8, the isotopes have six hyperfine states, F = 11/2 to21/2 and F ′ = 13/2 to 23/2, in their ground and 421-nmexcited states, respectively. Without hyperfine repumpers (arepumper is necessary for Rb and Cs MOTs), one wouldexpect that no MOT could form on the F = 21/2 → F ′ =23/2 cycling transition due to rapid decay to F < 21/2

states. Alkalis such as Rb and Cs, however, have smallerhyperfine splittings (<270 MHz) between their highest F ′excited states than does 163Dy, whose splitting is 2.11 GHz.However, such an explanation—that scattering to the lower F

hyperfine state is slower due to the larger detuning—ignoresthe 6× shorter lifetime of the Dy excited state. Togetherthis implies a depumping rate similar to Rb and Cs. Thecrucial difference, however, lies in the fact that the hyperfinesplittings in the ground and excited states of Dy are nearlymatched, whereas for Rb and Cs, they differ by more than25×. Thus for Dy, the trapping light near-resonant with theF = 21/2 → F ′ = 23/2 cycling transition also serves as anefficient repumper for the F = 19/2 → F ′ = 21/2 transition,thereby preventing complete population shelving into darkstates.

A full modeling of the intrahyperfine manifold populationtransfer as the atoms progress through the transverse cooling,Zeeman slower, and MOT stages is beyond the scope ofthis article, but we can make a simplified estimate of theF = 21/2 state decay and repumping rates in each of thestages. The atoms spend roughly 20 µs in the transversecooling beams, scatter ∼8 × 104 photons from the F ′ = 23/2state in the Zeeman slower, and spend, on average, 25 ms inthe MOT scattering photons from the 421-nm excited statebefore decaying to metastable states. Accounting for laserintensities (power broadening) and detunings, this impliesthat for 163Dy atoms, <1 photon is off-resonantly scatteredon the F ′ = 21/2 state (which can decay to F = 19/2) inthe transverse cooling stage, while nearly 100 and 50 arescattered in the Zeeman slower and MOT stages, respectively.However, the repumping rates in the Zeeman slower and MOTstages back to the F ′ = 21/2 state from F = 19/2 are onlya factor of two smaller than the cycling transition scatteringrate and are 570× and 1300× faster than the decay rates toF = 19/2, respectively: in very little time the population isrepumped back into the cycling transition. No secondary laseris necessary to repump the 163Dy system.

The situation differs in the 161Dy system due to thehyperfine structure inversion and the nearer detuning ofhyperfine levels at the larger F and F ′ end of the spectrum.In the transverse cooling, Zeeman slowing, and MOT stages,approximately 10, 3 × 103, and 2 × 103 photons are off-resonantly scattered to the F ′ = 21/2 state, respectively; the161Dy system off-resonantly scatters more than in the 163Dysystem. Nevertheless, the repumping rates are within a factor of2 of the depumping decay rates, and atoms are repumped nearlyas fast as they are depumped from the cycling transition. Again,a repumper-less MOT is able to be formed with 161Dy despiteits multitude of hyperfine levels. Reference [19] reported afermionic 167Er MOT (I = 7/2), which we suspect works in asimilar manner.

This leaves open the question why we observe as muchas 84% of the natural abundance of 163Dy, while as little as17% of 161Dy. The hyperfine population in Dy arriving fromthe high-temperature oven is likely to be distributed with abias toward the higher-multiplicity large-F states. This maycontribute to the large MOT population in 163Dy, but 161Dy’smuch lower population may be due to the competing effect ofless-efficient optical pumping and repumping to the F = 21/2state.

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Optical pumping of population into the F = 21/2 statemust occur before the Zeeman slower detunes the non-F =21/2 state atoms away from resonance. Indeed, we havealready seen that the 421-nm laser tuned to the F = 21/2 →F ′ = 23/2 transition can pump atoms out of the F = 19/2state on relatively short time scales, and we now estimateall the relative F → F ′ = F + 1 effective scattering ratesto examine the repumping efficiency from the F � 19/2states:

[F 163

21/2 : F 16319/2 : F 163

17/2 : F 16315/2 : F 163

13/2 : F 16311/2

]

= [1000 : 500 : 70 : 20 : 6 : 3].(6)[

F 16121/2 : F 161

19/2 : F 16117/2 : F 161

15/2 : F 16113/2 : F 161

11/2

]

= [1000 : 20 : 7 : 5 : 5 : 7].

These ratios are proportional to the number of photonsscattered from the F = 21/2 → F ′ = 23/2 cycling transition,denoted F

163,16121/2 and normalized to F 163

21/2 = F 16121/2 = 1000,

during the time the atoms transit the transverse cooling stageand first 5 cm of the Zeeman slower.8 F 163

11/2 = 3 for theF = 11/2 → F ′ = 13/2 transition corresponds to roughly20 scattered photons in our experiment, assuming that thepopulation is already optically pumped to the mg = F state.9

This is merely an upper bound to the number of photons anonpolarized sample would scatter since mg < F → me <

F + 1 transitions have smaller transition strengths than thecycling transition mg = F → me = F + 1.

A striking difference between the isotopes is evident. Thesingle 421-nm F = 21/2 → F ′ = 23/2 laser scatters manymore photons from F < 21/2 states in 163Dy than in 161Dy.This leads to much more efficient optical pumping to the F =21/2 state in 163Dy. We conjecture that this is why 84% of the163Dy are trapped but only 17% of the 161Dy. Coincidentally,these percentages are close—within experimental error—to5/6 and 1/6, respectively. It is tempting—but probably anoversimplification—to conclude that for 163Dy, all levels butthe lowest F state is optically pumped to F = 21/2. The caseof 161Dy is certainly more complicated: while it is likely thatF � 17/2 states are never efficiently pumped to F = 19/2(let alone F = 21/2), the initially larger F population fromthe oven should lead to larger populations than 17%. Apossible explanation lies in the inversion of the hyperfinestate energy hierarchy between the two isotopes. This causesDoppler shifts in atoms not optimally decelerated in theZeeman slower to move closer to (further from) resonancewith the F < 21/2 levels in 163Dy (161Dy). This contributes toa more efficient slowing—and therefore more efficient MOTloading—of 163Dy versus 161Dy atoms.

A thorough optical pumping simulation including all thehyperfine levels and the actual experimental parameters andgeometry could better address these questions. A repumpinglaser system is under construction to identify into whichF < 21/2 states population accumulate, and we suggest that

8This is roughly the portion of the Zeeman slower in which the fastoven beam is in resonance with the slowing laser.

9The transition strengths are nearly equal for the five stretched-stateσ+ transitions.

MOT loading dataSimulation

109

108

MO

T po

pula

tion

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Loading time (s)

FIG. 9. (Color online) Typical MOT loading data as a functionof time (blue, solid curve). The trapped atom population is detectedby a photodetector recording MOT fluorescence. The Zeeman slowerlaser and atom beam shutters open at t = 0. The green (long-dash)curve is a simulation using Eqs. (2) and (3).

only one repumper on the F = 11/2 → F ′ = 13/2 transitionfor 163Dy would be necessary to capture the full fraction ofthis isotope’s natural abundance in the MOT. Reference [42]presents other repumping schemes.

C. MOT loading

Figure 9 shows a typical MOT population loading curveafter the Zeeman slower laser and atomic beam are unblockedat t = 0. The 164Dy MOT population—proportional to theMOT florescence (atoms in the metastable MT remain dark)—rises to a steady state of 2.5 × 108 within 50 ms (blueline). A simulation of Eqs. (2) predicts, however, that within5 s the population should reach a steady state 5× larger(green dashed line). The Dy MOT population limit couldarise from light-induced two-body collisions as in the CrMOT [48]. Suppression of the Rreload term in Eqs. (2) mimicsthe experimental data for a loading rate of RL ≈ 1010 s−1.Reproduction of the loading data requires a small Rreload insimulations, while fits to decay data such as in Fig. 6(a)require Rreload to be of the order 103 s−1. A main differencebetween the MOT loading and MOT decay experiments isthe presence of the 1 W Zeeman slowing beam, which couldenhance light-induced losses of Dy and reduce Rreload. Anotherpossibility involves two-photon ionization loss while the atomsare in the metastable states (twice the cooling light energy isclose to the ionization potential) [49].

D. Comparison to Er MOT decay dynamics

As discussed earlier, the Er MOT did not exhibit un-derdamped oscillations in MOT decay florescence, whichwe believe is due to its smaller magnetic moment. Otherdifferences between the Dy and Er MOT decay dynamics arepresented in this section.

The analysis of the Er MOT decay dynamics [19] ac-counted for loss only via an RlossMT term (i.e., p ≡ 1) andwith only one decay channel through the metastable states(q ≡ 0)10. Allowing q to be nonzero (thus introducing two

10Including an RlossMT loss term is equivalent to allowing p to benonunity, but the latter can be more physically motivated.

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DYSPROSIUM MAGNETO-OPTICAL TRAPS PHYSICAL REVIEW A 82, 043425 (2010)

decay channels), provides a much better fit to the Dy MOTdecay data. The Er apparatus had a 1000× worse vacuumpressure, which might have obscured the long-time tail ofthe MOT decay and prevented a measurement of a secondmetastable state decay channel.

Perhaps coincidentally, the bosons 164Dy and 168Er have thesame, within experimental error, rate of decay to metastablestates ∼1700 s−1, and branching ratios. Interestingly, thefermion 163Dy, which possesses hyperfine structure, has asignificantly smaller decay rate 1170 s−1 as well as shortermetastable decay rates compared to 164Dy. While it is notclear why all the 164Dy decay rates are ∼1.5× larger thanthose for 163Dy, the existence of hyperfine structure in 163Dylikely plays a role.

As shown in Ref. [13], 163Dy’s smaller decay rates translateinto larger steady-state metastable MT populations, which helpto enhance its total trapped population. The large q and smallRslow that provide population enhancement in the metastableMT was also seen in MOT-loaded magnetic traps of 168Er,albeit to a lesser extent due to poor lifetimes from a highvacuum [44]. The majority of Dy atoms decay through a slowermetastable channel [2.3(1.5) s−1 versus 4.5 s−1 for 168Er].However, 27% decay through the fast channel at rates 6× (4×)larger than Rslow in 164Dy (163Dy). From simulations of Eq. (1)in Ref. [19] and Eqs. (2) here, one can see that the measuredrates imply that the Er metastable MT reservoir could holdseveral times more atoms as Dy’s; however, the severity ofEr’s magnetic trap inelastic loss rates are not yet known. Dycollisions limited the metastable trap population to 80% [13]of the maximum achievable given by the rates in Eqs. (3).

E. MOT population and temperature

As reported in Ref. [13], when the power between the threesets of MOT beams are mismatched, the Dy MOT can exhibita sub-Doppler cooled core, which depending on the detailsof the power balancing, can be anisotropic in its temperaturedistribution. However, the number of atoms in this ultracoldcore is typically less than 10% of the total MOT population.We leave the study of this minority component to Ref. [50]and instead present here the temperature and population of themajority component of the Dy MOT as a function of MOTbeam intensity I , detuning �/�, and quadrupole gradient∇Bz (see Fig. 10).

To distinguish the hotter majority from the colder minoritycomponent—when it exists—we fit a double-temperaturedistribution to the time-of-flight expansions of the MOT(Fig. 10(b) and Fig. 4 in Ref. [13]). Figure 11 shows acompilation of temperature and population data of the majoritycomponent. In both Figs. 10 and 11, the data were takenfor a ratio of MOT powers in the z versus ρ directionsof Iz/Iρ ≈ 1 and I > 0.2 (I = Iz + 2Iρ). This results in aMOT with a vertically oriented, anisotropically sub-Dopplercooled core. Data presented here are typical of the majoritycomponent in all Dy MOTs, and those containing sub-Dopplercooled cores yield larger overall MOT populations. Moreover,we choose to discuss the majority component data with theMOT beams set to Iz/Iρ � 1 and I > 0.2 since it is in thisregime that we obtain the most populous MOTs [50] and these

FIG. 10. (Color online) (a) Time-of-flight absorption image of164Dy MOT at td = 5 ms; MOT fields are extinguished at td = 0.Intensity integrations along (b) z and (c) ρ directions. The grayarrow points to region of minority component for this MOT.(b) Double-Gaussian fit (white line) to MOT expansion (the redline is a single-Gaussian which results in a poor fit). The majoritycomponent (hot outer cloud) is defined as the atoms contributing to thebroader Gaussian, while atoms in the narrower Gaussian comprise theminority component. (c) The anisotropically cooled stripe hampersmajority component temperature measurements in the z direction.The origin and temperature characteristics of the minority componentare studied in Ref. [50].

settings will be used for future laser and evaporative coolingexperiments.

The major component temperature Tmajority data in theρ direction are shown along with plots of Eq. (7), thetemperature TD from simplified Doppler cooling theory [43]:

TD = h�

4kB

1 + I + (2�/�)2

2|�|/�. (7)

The Doppler cooling limit for Dy on the 421-nm transitionis 770 µK, and for the I and �/�’s typically used in theexperiment, the Doppler cooling temperature is ∼1 mK. Theprolate MOT Tmajority data are close to that predicted byDoppler cooling theory for large s (large I , small �/�) andhigh gradients. However, Tmajority of the atoms at small s andsmall gradient is below the Doppler limit.

The low gradient and low saturation data are consistent withthe several hundred µK temperatures of the Er MOT [44].One-dimensional numerical sub-Doppler cooling simulationspresented in Ref. [44] indicate that population-wide MOTsub-Doppler cooling arises from the near-equal Lande g

factors in Er’s ground and excited states �gEr = 0.004, whichmeans that the MOT magnetic field Zeeman shifts the groundand excited mJ levels by nearly equal energies. Sphericallysymmetric intra-MOT sub-Doppler cooling has been observedin the cores of MOTs of more commonly used atoms(e.g., Rb [51]), but unlike Er, the majority of atoms are at hotterDoppler temperatures. The Dy MOT—which also possessesa near-degeneracy of g factors on the 421-nm line11—alsoexhibits population-wide MOT sub-Doppler cooling like the Er

11δgDy = 0.022 (δgDy/gDy = 1.7%), which is 5.5× larger than Er’son its MOT transition, but 7.7× less than Rb’s.

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YOUN, LU, RAY, AND LEV PHYSICAL REVIEW A 82, 043425 (2010)

(a)

I/Is0.2 0.25 0.3 0.35

00.4

0.81.2

1.6

2

-1.2 -0.40

1

2

Tmajority (mK)

-1 -0.8 -0.6

(b)

10 15 20 25 300

0.4

0.8

1.2

5 10 15 20 25 30zB (G/cm)

∆

(c) (f )

0

0.5

-1.5 -1.2 -0.9 -0.6 0

0.5

1(e)

0.20.1 0.3 0.4

1(d)N /Ntotal

∆/Γ

max

0

0.5

1

FIG. 11. (Color online) [(a)–(c)] Temperature characterization ofthe majority component of the Dy MOT versus intensity I = I/Is ,detuning �/�, and MOT magnetic field gradient ∇zB (∇ρB ≈∇zB/2). Data are the temperatures of the MOT in the ρ direction(quadrupole plane of symmetry, gravity points in the −z direction).Light blue curves are plots of Eq. (7) for the following parameters:[(a) and (d)] �/� = −1.2, ∇zB = 20 G/cm; [(b) and (e)] I = 0.17,∇zB = 20 G/cm; [(c) and (f)] I = 0.20, �/� = −1. [(d)–(f)] Totalnumber of atoms (major plus minor component) versus I , �/�,and ∇zB. The typical visible MOT maximum population is Nmax =2 × 108. Maximum density of ∼1010 cm−3 occurs for: I = 0.33 in(a) and (d); �/� = −1 in (b) and (e); and ∇zB = 20 G/cm in(c) and (f).

MOT, which is confirmed in 1D numerical simulations [13,45].Unlike Er, however, the Dy MOT population assumes adouble-temperature distribution at large s and ∇zB.

In contrast to the Er MOT, we have also ob-served anisotropic sub-Doppler cooling to much lowertemperatures—down to 10 µK—in the central cores of theDy MOTs. This phenomenon of ultracold stripes, shown inFig. 10, disappears at low MOT beam intensities—coincidentwith the appearance of sub-Doppler cooling in the majoritycomponent of the Dy MOT. The minority stripe componentsare typically 1–10% the population of the entire MOT, andas such are no more populous than 106 to 107 atoms (seeFig. 10). The Er MOT presented in Ref. [44] contained nomore than 2 × 105 atoms, and the largest Er MOT to datecontained 1.6 × 106 atoms [19]. We conjecture that the Erpopulation was limited by low Zeeman slower power, whichwas <100 mW [45]. More populous Er MOTs might alsoexhibit double temperature distributions when larger MOTbeam power is employed. The origin of this anisotropically

sub-Doppler cooled minority component located in the DyMOT core is explored in detail in Ref. [50].

V. CONCLUSION

We presented a detailed description of the creation of large-population open-shell lanthanide MOTs with the repumper-less technique. The demonstration that the repumper-lessMOT technique works for Dy in a manner similar to Er(but with important differences) lends support to endeavorsaimed at forming MOTs of other interesting highly magneticlanthanides such as holmium [31]. We also presented anin-depth characterization of the Dy MOT population, tem-perature, loading rate, isotope trapping efficiency, mechanicaldynamics, and metastable state recycling dynamics. Futurework will attempt to narrow-line laser cool Dy on the741-nm transition in a manner similar to that demonstrated forEr [52].

We note that Dy MOTs made in a similar manner toalkaline-earth-metal MOTs [53,54]—i.e., using the 421-nmlight for Zeeman slowing (and transverse cooling) but cre-ating the MOT on the closed 140 kHz-wide 598-nm transi-tion [34]—will likely be possible and would provide lowerinitial temperatures. However, for maximizing phase-spacedensity, it is not yet clear whether a lower initial temperatureoutweighs the loss of the metastable MT reservoir andassociated population gains. It remains to be seen whether suchMOTs could also trap fermionic isotopes without additionalrepumpers.

ACKNOWLEDGMENTS

We thank A. J. Berglund, J. J. McClelland, E. Fradkin,N. Leefer, and D. Budker for helpful discussions. We ac-knowledge support from the NSF (PHY08-47469), AFOSR(FA9550-09-1-0079), and the Army Research Office MURIaward W911NF0910406.

APPENDIX: TRANSFER CAVITY LOCK

We provide here further details on the transfer cavitylock, which is depicted in Fig. 2: The external cavity diodelaser at 780 nm is locked to a Fabry-Perot cavity using thePound-Drever-Hall (PDH) technique [55]. The Fabry-Perotcavity consists of plano and concave (r = 25 cm) mirrors withhigh reflectivity (99.9%) at both 780 nm and 842 nm, and themirrors are attached to a fused silica spacer with a length of10 cm. In order to scan the resonance frequencies of the cavity,a piezoelectric transducer (PZT) ring is placed between oneside of the spacer and the concave mirror. With the measuredcavity length, the corresponding free spectral range is 1.4 GHz,and the cavity has a linewidth of 1.4 MHz. The cavity isisolated from acoustic vibration and placed inside a vacuumchamber. The laser is locked to the cavity, which providesshort time scale frequency stability, and then the cavity lengthis adjusted to bring the cavity and laser in resonance with ahyperfine transition of 87Rb. Feeding back to the cavity PZT anerror signal derived by Rb saturation absorption spectroscopyensures that the cavity resonance frequencies drift by no morethan a few hundred kHz.

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DYSPROSIUM MAGNETO-OPTICAL TRAPS PHYSICAL REVIEW A 82, 043425 (2010)

The cavity now provides a stable frequency reference forTiS1’s 842 nm beam, which is picked-off from the main beamthat is directed into the ring cavity frequency doubler. Tobridge the frequency gap between the nearest 842-nm modeand the doubled 842-nm wavelength necessary for generatingthe MOT light, the 842-nm beam passes through an opticalfiber-based electro-optical modulator, which imprints strongsidebands at a frequency adjustable between 1.4–2.8 GHz. A

phase-locked loop generates this microwave frequency froma stabilized and tunable RF source. One of the sidebands isadjusted in frequency to be resonant with the optical cavity,allowing the 842-nm to be locked to the cavity using thePDH technique. Once locked, the 421-nm light from bothTiS1 and TiS2 (which is offset beat note locked to TiS1)may be scanned to the correct frequency by adjusting the RFreference.

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