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Magnetic Trapping of Ytterbium and the Alkaline-Earth Metals

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Magnetic Trapping of Ytterbium and the Alkaline-Earth Metals PHYSICAL REVIEW A, 66, 013411 ͑2002͒ Magnetic trapping of ytterbium and the alkaline-earth metals T. Loftus,* J. R. Bochinski,* and T. W. Mossberg Oregon Center for Optics and Department of Physics, University of Oregon, Eugene, Oregon 97403 ͑Received 8 June 2001; published 29 July 2002͒ Atomic ytterbium ͑Yb͒, magnesium ͑Mg͒, calcium ͑Ca͒, and strontium ͑Sr͒ possess a simple yet versatile internal level structure and a diversity of naturally abundant fermionic and bosonic isotopes, making these systems ideal for studies of cold collisions and weakly interacting quantum degenerate gases. Unlike alkali- metal atoms, however, Yb, Mg, Ca, and Sr cannot be magnetically trapped in the ground state. We analyze a solution to this problem involving magnetic trapping in a low-lying metastable excited state and predict that 1 significant magnetic trap populations can be obtained via continuous, in situ loading from Yb and Sr S0 Ϫ1 P1 magneto-optical traps. DOI: 10.1103/PhysRevA.66.013411 PACS number͑s͒: 32.80.Pj ͓ ͔ 1 Ϫ1 ͑ ͒ Magnetic trapping of ground-state neutral atoms 1 has reported S0 P1 Yb MOT 60 G/cm axial field gradient enabled unique explorations into two-body interatomic inter- ͓14,21͔. In the figure, coil windings lie in the centers of the actions ͓2͔ and collisions ͓3͔, radio-frequency and optical four black dots and equimagnitude field contours are labeled spectroscopy ͓4͔, trapped atom laser-induced ͓5͔ and evapo- in Gauss. The spatial extent of a magnetic trap employing rative cooling ͓6͔, and weakly interacting quantum degener- this field is set by the direction-dependent radius of the maxi- ate gases ͓7,8͔. Atomic ytterbium ͑Yb͒ and the alkaline-earth mum closed contour centered about the magnetic field null. atoms magnesium ͑Mg͒, calcium ͑Ca͒, and strontium ͑Sr͒ We label the magnitude of this contour BM where in Fig. ͑ ͒ ϭ ͑ ͒ 3 ϭ ͓hereafter collectively labeled singlet-triplet ͑ST͒ atoms͔ 1 a , BM 40 G. In Fig. 1 b we plot the P2 (mJ 2) mag- possess a diversity of naturally abundant fermionic and netic trap depth for each species as a function of BM . The 1 Ϫ1 bosonic isotopes ͓9͔, spectrally narrow transitions that enable trap depth is scaled by TS , the species specific S0 P1 ultralow temperature, high spatial density laser cooling ͓10– Doppler-limited MOT temperature. The inset shows the trap ͔ 1 Ϫ3 12 , and a simple internal level structure ideally suited to depth normalized by TT , the species specific S0 P1 quantitative studies of cold collisions ͓13͔. As such, ST at- oms offer unique opportunities for future studies of magneti- cally trapped samples. Lacking the requisite ground-state magnetic substructure, however, ST atoms cannot be held in ground-state magnetic traps. In this paper we analyze the solution to this problem pro- posed by Loftus et al. ͓14͔ which relies on magnetically trap- 3 ϭ ping ST atoms in the low-lying P2 (mJ 2) weak-field seeking metastable ͓15–18͔ excited-state. We begin by showing that for each ST atom a single magnetic field sup- 1 Ϫ1 ports both a S0 P1 transition magneto-optical trap ͑ ͒ 1 MOT and a pure magnetic trap capable of holding S0 Ϫ1 P1 MOT-cooled atoms. Next, we discuss three in situ 3 ϭ techniques for loading P2 (mJ 2) magnetic traps with at- 1 Ϫ1 1 Ϫ3 oms precooled in S0 P1 or S0 P1 MOTs and provide numerical estimates, based on the relevant Zeeman substate dependent decay paths ͓19͔, for the resulting magnetic trap loading rates. Finally, we discuss a zero-background tech- ͑ ͒ nique for observing the magnetically trapped atoms. For sim- FIG. 1. a Contour plot of the anti-Helmholtz magnetic field 1 Ϫ1 ͓ ͔ plicity, our discussion is confined to magnetic trapping of the used for a previously reported S0 P1 Yb MOT 14 . Coil wind- ings lie in the centers of the four black dots and equimagnitude field most abundant, even atomic mass number ST atom isotopes. ͑ ͒ 3 ϭ contours are labeled in Gauss. b P2 (mJ 2) magnetic trap depth Note, however, that the procedures outlined here are appli- ͓ϳ as a function of BM , the maximum effective trap field 40Gin cable to the remaining isotopes, even those with nonzero ͑ ͔͒ Fig. 1 a . The trap depth is scaled by TS , the species specific nuclear spin. 1S Ϫ1P Doppler-limited MOT temperature. ͑c͒ 3P (m ϭ2) ͑ ͒ ͑ 0 1 2 J Figure 1 a shows a contour plot calculated according to magnetic trap depth versus the trap size, r, with a fixed axial field ͓ ͔͒ analytic expressions given by Bergman et al. 20 of the gradient of 60 G/cm ͓the axial gradient in ͑a͔͒. Here, r is measured typical anti-Helmholtz magnetic field used for a previously relative to the magnetic field null point. Insets to ͑b͒ and ͑c͒ show 3 ϭ the P2 (mJ 2) magnetic trap depth normalized by TT , the spe- 1 Ϫ3 ͓ ͔ cies specific S0 P1 Doppler limited 22 temperatures for Yb *Present address: JILA, National Institute of Standards and Tech- and Sr. Note that a field gradient of ϳ10 G/cm ͑ϳ5 G/cm͒ is re- nology and University of Colorado, Boulder, CO 80309. quired to suspend Yb ͑Sr͒ atoms against gravity. 1050-2947/2002/66͑1͒/013411͑5͒/$20.0066 013411-1 ©2002 The American Physical Society LOFTUS, BOCHINSKI, AND MOSSBERG PHYSICAL REVIEW A 66, 013411 ͑2002͒ FIG. 2. Simplified energy-level diagrams showing ͑a͒ type I, ͑b͒ type II, and ͑c͒, type III transfer processes and a zero-background 3 technique for observing atoms magnetically trapped in the P2 ϭ ͑ ͒ (mJ 2) state. In a , transitions and states labeled with dotted- dashed lines apply only to Yb. In ͑b͒, Pump I ͑Pump II and Pump III͒ is used for incoherent ͑semicoherent͒ transfer. For all three, the detection ͑probe͒ transitions are denoted by dashed ͑dotted͒ lines. Doppler-limited ͓22͔ temperatures for Yb and Sr. Figure 1͑c͒ 3 ϭ depicts the P2 (mJ 2) magnetic trap depth as a function of the trap size, r, for a fixed axial magnetic field gradient of 60 G/cm. Here, r is measured relative to the magnetic field null ͓ ͑ ͒ ϳ point note that in Fig. 1 a , rmax 7 mm along the axial di- rection͔. For all four species the magnetic trap shown in Fig. 1͑a͒ is deep enough to capture precooled ST atoms, even those that are only cooled to TS . Figure 2 presents three techniques for loading ST atoms 3 ϭ ͓ ͑ ͔͒ into a P2 (mJ 2) magnetic trap. Type I transfer Fig. 2 a FIG. 3. Simplified energy-level diagrams for ͑a͒ Yb and ͑b͒ Sr. 1 Ϫ1 uses a S0 P1 MOT to simultaneously precool the ST at- Electric dipole and quadrupole and magnetic dipole and quadrupole oms and, through radiative branching induced MOT loss transitions are represented by solid, dashed, dotted, and dotted- ͓ ͔ 3 ϭ 23 , load the atoms into the P2 (mJ 2) state. In contrast, dashed lines, respectively. States with a superscript o have odd par- ͑ ͒ 1 Ϫ1 1 Ϫ3 type II type III transfer employs S0 P1 ( S0 P1) ity, transition wavelengths are given in vacuum ͓24,25͔, and 3 Ϫ1 MOT precooling followed by population transfer to the P2 numbers in parentheses give transition probabilities ͑in s ͓͒16–18, ϭ ͔ ͑ ͒ 1 (mJ 2) state via optical pumping. As discussed below, all 27–31 . The inset in a shows an expanded view of the Yb P1 !3 !3 three transfer schemes are applicable to Yb, Ca, and Sr D2,1 P2,1,0 decay channel. while, due to the details of the Mg internal level structure, Mg requires the use of type II or type III transfer. Note that that f and f Ј depend on spontaneous decay rates and Zeeman in all cases approximately equal populations are loaded into substate dependent weighting factors. For the former, we use the 3P (m ϭ2) and 3P (m ϭ1) weak-field seeking 2 J 2 J either measured or theoretically predicted values ͑see Fig. 3 states. As demonstrated elsewhere ͓8͔, however, the resulting and Refs. ͓13,16,17,24–32͔͒ while the latter are calculated spin-mixed sample could be purified by ejecting 3P (m 2 J according to the Wigner-Eckhart theorem ͓33͔. ϭ1) atoms from the magnetic trap with a swept-frequency rf In type I and type II transfer ͓Figs. 2͑a͒ and 2͑b͒, respec- field. The remainder of our discussion, therefore, will focus ͔ 1 Ϫ1 3 tively , the atoms are initially loaded into S0 P1 MOTs. on atoms loaded into the more tightly confined P2 (mJ ϭ2) state. In the following, we write the continuous or Type I transfer then consists of allowing the atoms to radia- 1 3 ϭ tively cascade from the P1 state to the P2 (mJ 2) state quasi-continuous type I and type II transfer rates, RM ,as ϭ ␶ ϭ Ͻ 1 !3 while they are held in the 1S Ϫ1P MOT. Note that in this RM f (NS / s) RS f where f 1 is an effective P1 P2 0 1 ϭ 3 !3 ϭ case ␶ Ͻ␶ /1000 for all four ST atoms where ␶ is the time (mJ 2) or S1 P2 (mJ 2) cascade decay fraction, NS c s c ␶ ͑ ͒ 1 Ϫ1 required to slow atoms from the MOT capture velocity to ( s) is the population lifetime of a S0 P1 MOT, and RS 1 Ϫ1 is a S0 P1 MOT loading rate.
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