Prospects of forming high-spin polar molecules from ultracold atoms

We have investigated Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations. We consider both low-anisotropy and high-anisotropy limits. In both regimes we find many resonances with a wide variety of widths. The wider resonances are suitable for tuning interatomic interactions, and some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules. These molecules might be transferred to short-range states, where they would have large magnetic moments and electric dipole moments that can be induced with very low electric fields. The results open up important prospects for a new field of ultracold high-spin polar molecules.

We have investigated Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations. We consider both low-anisotropy and high-anisotropy limits. In both regimes we find many resonances with a wide variety of widths. The wider resonances are suitable for tuning interatomic interactions, and some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules. These molecules might be transferred to short-range states, where they would have large magnetic moments and electric dipole moments that can be induced with very low electric fields. The results open up important prospects for a new field of ultracold high-spin polar molecules.
There is now much interest in creating ultracold molecules from different species and with different properties. In particular, molecules with both electric and magnetic dipole moments will open up new possibilities for designing quantum many-body systems [21,22] and for tests of fundamental symmetries [23]. In this context, there has been significant work towards producing ultracold 2 Σ molecules, both by direct laser cooling [24][25][26][27] and by association of alkali-metal and closed-shell atoms [28][29][30][31][32][33]. However, the former method still produces only relatively low densities and is highly systemspecific, while the latter method is experimentally challenging due to the sparse and very narrow Feshbach resonances in such systems.
In this paper we investigate Feshbach resonances in collisions of lanthanide atoms with large orbital angular momentum l, such as Er ( 3 H 6 ) or Dy ( 5 I 8 ), with closed-shell ( 1 S) atoms, such as Yb or Sr. All four of these elements can be cooled to ultracold temperatures [34][35][36][37][38][39][40] and have numerous abundant isotopes including both bosons and fermions. The large masses result in high densities of molecular states near threshold and produce many resonances that are suitable for molecule formation. The variety of isotopes should allow the formation of both bosonic and fermionic molecules.
The molecules formed by magnetoassociation will inherit the very large magnetic moments of Er and Dy. It * j.m.hutson@durham.ac.uk should be possible to transfer them to short-range states using Stimulated Raman Adiabatic Passage (STIRAP), as has been achieved for alkali-metal dimers [4][5][6][7][8][9]. In these short-range states they are likely to have substantial electric and magnetic dipole moments. The states will be characterized by the projection Ω of the electronic (orbital and spin) angular momentum along the internuclear axis. For molecules in states with |Ω| > 0, Ω-type doubling will allow the electric dipole moment to be oriented with much smaller fields than for molecules in Σ states [41]. The molecules will also have many spin states that can be controlled with magnetic and microwave fields and form the basis for high-dimensional quantum systems (qudits) [17].
Ultracold gases of Er and Dy are highly compatible with those of Sr and Yb. The conditions needed to cool them are similar. High densities can be produced, and for suitable isotopic combinations it is likely that mixed degenerate gases with controllable interactions can be formed. They therefore provide an ideal platform for investigating the rich phase behavior expected in such mixtures, including superfluidity and supersolidity [42], dipolar droplet properties [43] and Fermi surface deformation [44].

I. THEORETICAL METHODS AND INTERACTION POTENTIALS
The collision Hamiltonian for any pair of atoms A and X may be written where R is the interatomic distance, µ is the reduced mass, andL is the angular momentum operator for the relative motion.ĥ A andĥ X are the Hamiltonians of the separated atoms [45], including external fields if necessary, andV (R) is the interaction operator.
In the present work we consider the closed-shell atom A to be structureless, so setĥ A = 0. The states of heavy open-shell atoms such as the lanthanides Er and Dy are generally best represented using j-j coupling rather than Russell-Saunders coupling, but here we are interested principally in the lowest spin-orbit component of the ground state, with the maximum total angular momentum j allowed by the orbital configuration. Other atomic states (even excited spin-orbit states) are too high in energy to produce resonances and play little role. We therefore choose to represent the atomic states with quantum numbers l and s for the total orbital and spin angular momenta, with corresponding operatorsl andŝ, and the atomic Hamiltonian aŝ where B is the magnetic field oriented along the z axis and g s and g l are the electron spin and orbital g-factors, both defined to be positive. We take a so Dy = −516.779×hc cm −1 and a so Er = −1159.7215×hc cm −1 , which reproduce the splitting of the lowest two spin-orbit states [46]. In general there can also be hyperfine terms in the singleatom Hamiltonians, but for simplicity, we study only isotopes without nuclear spin in this paper; we choose 164 Dy, 174 Yb, 166 Er, and 88 Sr, which are the most abundant isotopes.
The interaction operatorV (R) is a function of both orbital and spin coordinates. It can in principle depend on external field, but any such dependence is neglected here. We choose to write it in the form whereV space (R) contains all terms independent of the spin degrees of freedom. Because of cylindrical symmetry,V space (R) is diagonal in λ, the projection of l onto the internuclear axis. We use the resolution of the identity 1 = l,λ |lλ lλ|. In the present work we include only a single value of l, so that the expansion reduces tô where λ takes values from −l to l and V λ (R) is independent of the sign of λ. The differences between the potential curves V λ (R) may be viewed as anisotropy in V space (R). For simplicity we neglectV spin (R), although it may be needed when making quantitative comparisons between experiment and theory at a later stage. Very little is known about the interactions in the systems we consider here. However, we can make reasonable estimates on physical grounds. The attractive parts of the potentials are likely to be dominated by dispersion forces, with little contribution from chemical bonding, because the outermost s orbitals are filled and the partially filled f shells of the lanthanides are submerged. At long range the interaction potentials are of the form V (R) = −C 6 /R 6 . In physical terms, differences between the potentials V λ (R) may come from differences in either the attractive or the repulsive part. To model these separately, we represent the interaction potentials in Lennard-Jones form, where C 12,λ is the repulsive coefficient and D e,λ is the well depth at equilibrium distance R e,λ . We obtain parameters for Er+Sr and Dy+Yb from combination rules based on the interaction potentials for the corresponding homonuclear systems. Values of the C 6 coefficients for all the homonuclear systems have been obtained experimentally [47,48] or theoretically [49][50][51][52].
We obtain values of the isotropic coefficients C (0) 6 for Er+Sr and Dy+Yb from Tang's combination rule [53], for which we use dispersion coefficients from [47,48,51,52] and the atomic polarizabilities from [54], giving 2092 and 2359 E h a 6 0 , for Dy+Yb and Er+Sr respectively. Er and Dy have tensor and vector polarizabilities that result in anisotropic C 6 coefficients. The ratio of the anisotropic coefficient C (2) 6 to the isotropic one is approximately the ratio of the tensor and scalar static polarizabilities α (2) and α (0) of the open-shell atom; values for this range from 0.016 [55] to 0.018 [51] for Er and from 0.005 [52] to 0.026 [55] for Dy. We base our main calculations on a ratio 0.017 for both systems, but have explored the effects of variations.
The interaction potential for Sr+Sr has been studied in detail spectroscopically; the well depth and equilibrium distance are known precisely to be 1081.64 cm −1 and 4.672 Å, respectively, and the potential supports 63 vibrational levels for 88 Sr [47,56]. For Yb+Yb there is considerable variation in the well depth between different levels of theory [57], but the dependence of the nearthreshold bound states on isotopic mass shows that it supports 72 vibrational levels [48,58]. We base our calculations on the depth 739.73 cm −1 obtained by Borkowski et al. [48]. Petrov et al. [59] carried out electronic structure calculations of one component of the potential for Dy+Dy and obtained a well depth of 785.7 cm −1 . To obtain interaction potentials for Er+Sr and Dy+Yb, we estimate the isotropic well depths D e as the geometric mean of those for the two homonuclear systems. For this we estimate the well depth for Er+Er as 471.1 cm −1 , obtained from the well depth for Dy+Dy [59] scaled by the square of the ratio of the C 6 coefficients. The resulting well depths for the heteronuclear systems are about 760 cm −1 for Dy+Yb and 710 cm −1 for Er+Sr.
To model the effects of long-range anisotropies, we choose a set of coefficients C 6,λ that correspond to the required value of C (2) 6 , where We obtain an isotropic repulsive coefficient from We fix C 12,λ at C 12 for all λ, so that D e,λ is different for each λ.
Short-range anisotropies are less well understood. They might be much stronger, because of the effects of higher-order dispersion, chemical bonding or repulsive forces. To model this, we choose a set of well depths D e,λ and fix C 6 at its isotropic value, so that C 12,λ is different for each λ. The isotropic potential curves described above support 52 (64) vibrational levels for Dy+Yb (Er+Sr). Because of this, a 3.1% (3.8%) scaling of the potential is sufficient to shift the scattering length through a complete cycle [60]. It thus seems likely that the scattering lengths for different values of λ are essentially random.
Varying D e with C 6 unchanged is not a simple scaling, but we nevertheless find that a scaling of D e by 4.7% (5.6%) produces a full cycle in the scattering length. Our strategy is thus to choose values of D e,λ randomly from a range from 0.93 to 1.07 (0.91 to 1.09) times the starting value. This range is chosen so that even the isotropic potential (essentially the mean V λ (R)) is random. This produces anisotropies of higher order than the dispersion anisotropy above, with k > 2 in Eq. (7). It should be emphasized that this probably represents the maximum coupling that is likely to arise from short-range anisotropy, and the coupling may turn out to be weaker.
We perform scattering calculations using the molscat package [61,62] and bound-state calculations with the bound package [61,63]. Both packages use coupledchannel methods, in which the total wavefunction is expanded in a basis set for all coordinates except the interatomic distance R. This gives a set of coupled differential equations with respect to R. The methods are similar to those of Refs. [64,65] but without terms that correspond toĥ A . We use a partially coupled basis set |(ls)jm j |LM L , where m j and M L are the projections of j and L onto the axis of the magnetic field (the z axis). Matrix elements of the interaction potential are calculated as in Ref. [66]. The only conserved quantum numbers are the projection of the total angular momentum onto the z axis, M tot = m j + M L , and the total parity (−1) l+L . We restrict our basis functions to those for j = l +s, corresponding to the lowest spin-orbit state. This restriction means that the spin-orbit coupling inĥ X has no effect except to shift the whole system by a constant energy. We include all functions with L up to L max . For the case of long-range anisotropy, the basis set converges quickly with respect to L and we choose L max = 8. For short-range anisotropy, which can be stronger, we include basis functions up to L max = 2j. This is because, in a representation where j and L are coupled to form a total angular momentum J, the s-wave channel (L = 0) at the lowest threshold corresponds to J = j; representing all states of this total J requires functions up to L = 2j. In the resulting calculations, the widest resonances are well converged. For strong anisotropy, adding higher-L basis functions shifts some of the narrower resonances and adds new narrow ones.
The coupled equations are solved using log-derivative propagators.
For scattering calculations, the logderivative matrix is propagated outwards from R min = 2.5 Å to R mid = 20 Å using the diabatic log-derivative method of Manolopoulos [67,68] with a fixed step size of 0.005 Å, then from R mid to R max = 2000 Å using the logderivative Airy propagator of Alexander and Manolopoulos with a variable step size [69,70]. The solution is matched to asymptotic boundary conditions at R max to obtain the scattering matrix S. The scattering length is calculated as a(k) = (ik) −1 (1 − S 00 )/(1 + S 00 ), where k = √ 2µE/ is the wavevector and S 00 is the diagonal S-matrix element in the incoming s-wave channel for the chosen value of m j . The kinetic energy E in the incoming channel is set to 100 nK. For bound-state calculations, one log-derivative matrix is propagated outwards from R min to R mid , and another is propagated inwards from R max to R mid . bound finds eigenenergies by searching for the energies at which these solutions can be matched at R mid as described in [71].

II. FESHBACH RESONANCES AND BOUND STATES
A magnetic Feshbach resonance occurs when a bound state is tuned across a scattering threshold with a magnetic field B. At the lowest threshold, it appears as a pole in the scattering length a(B). Molecules may be formed by sweeping the field across a resonance; this is referred as magnetoassociation. Resonances may also be used to control interactions by tuning the scattering length.
The upper panel of Figure 1 shows the s-wave scattering length that we obtain at the lowest threshold of Dy+Yb ( 5 I 8 , m j = −8) with a purely long-range anisotropy with C 12 that produces a different number of bound states but the same a iso produces very similar results.
The lower panel of Figure 1 shows the near-threshold bound states responsible for the resonances in the upper panel for the case of a iso = 54 Å. The near-horizontal line near E = −20 MHz is due to a state that is predominantly L = 0, m j = −8 in character. This has broad avoided crossings with L = 2 states and much narrower ones with L = 4 states; the slopes of these states increase and the strengths of the crossings decrease as m j increases from −8. More generally there are strong crossings between pairs of states with ∆L ≤ 2 and ∆m j ≤ 2 and weaker crossings due to higher-order interactions otherwise. For Dy+Yb the mean scattering lengthā [72] is 40.3 Å, which gives a characteristic energyĒ = 2 /(2µā 2 ) = h × 3.69 MHz. There is a bound state with L = 0 (2) in the top 36.1Ē (93.4Ē) of the well for any value of a iso [73], so in the top 133 (344) MHz here. The g-factor for the 5 I 8 state is g j = 1.25, so the relative gradient of states with m j = −8 and −6 is 2g j µ B /h = 3.50 MHz/G. The lowest-field L = 2 resonance is expected to occur at a field below 93.4Ē/2g j µ B = 98 G for any value of a iso .
We have repeated the calculations for a smaller long-range anisotropy C (2) 6 /C (0) 6 = 0.0085, which is half the value in Fig. 1. The resulting scattering lengths and bound-state energies are shown in Supplemental Material [74]. The bound-state diagram shows considerably less mixing between different states. The resonance positions change very little for the same value of a iso , but the widths scale approximately as |C (2) 6 | 2 for resonances due to L = 2 states and as |C (2) 6 | 4 for those due to L = 4 states. This indicates that a long-range anisotropy of this magnitude may be viewed as operating perturbatively. The long-range anisotropies considered here probably represent approximately the minimum degree of coupling that is likely in these systems.
We have carried out analogous calculations on Er+Sr. The results are qualitatively similar, and are shown in the Supplemental Material [74]. In this caseā = 37.7 Å, E = h × 6.18 MHz and g j = 1.17, so the lowest-field L = 2 resonance is expected to occur below 93.4Ē/2g j µ B = 176 G for any value of a iso . The resulting densities of bound states and resonances are somewhat lower than for Dy+Yb.
The upper panel of Figure 2 shows the scattering length for Dy+Yb (m j = −8) for a representative potential with short-range anisotropies chosen as described above. The lower panel shows the near-threshold bound states. Other potentials chosen in the same way give qualitatively similar patterns; examples are given in Supplemental Material. These interaction potentials are much more strongly anisotropic than those based on long-range anisotropy above, and their higher-order anisotropies cause direct couplings with larger values of ∆L and ∆m j . They all produce many Feshbach resonances with a wide variety of widths. L is now very poorly conserved, so the resonances are not limited to those for L < 6. Nevertheless, it may be seen in the lower panel of Fig. 2 that there are well-defined states that maintain their character through many avoided crossings. This demonstrates that the energy-level pattern has structure even in this high-anisotropy regime.
One advantage of these systems is the existence of many different isotopic combinations. The reduced mass may be adjusted over a range of 4.7% for Dy+Yb or 4.6% for Er+Sr. This changes the patterns of resonances and bound states in significantly different ways in the different regimes of anisotropy. For weak anisotropy a change in reduced mass µ is almost the same as scaling the isotropic potential; it changes the isotropic scattering length a iso in a smooth way. Changing the mass of the open-shell (closed-shell) atom by 2 changes µ by 0.6% (0.6%) for Dy+Yb or 0.4% (1.5%) for Er+Sr; this is sufficient to change a iso considerably, but it is also possible to change the isotope of both atoms to achieve a much smaller change in reduced mass. For strong anisotropy, however, the situation is different; in this case the positions of the widest resonances shift relatively smoothly, but even a change of 0.1% in µ causes substantial changes in the relative positions of narrower resonances. Measurements on different isotopic pairs will thus provide a powerful way to distinguish between the different regimes of anisotropy.
We have also calculated scattering lengths for collisions of open-shell atoms in excited Zeeman states, m j > −j. Examples for Dy+Yb with both long-range and shortrange anisotropies are shown in Fig. 3. Additional examples are given in Supplemental Material [74]. The scattering length is complex, a = α − iβ, because of inelastic decay to lower channels. The corresponding rate coefficient for 2-body inelastic decay in s-wave scattering is k inel 2 ≈ 2hβ/µ. The resonances show oscillations in both α and β [75,76], rather than poles as at the lowest threshold. For long-range anisotropies, the resonances are relatively weakly decayed for m j = −7, with oscillations in α and peaks in β of amplitude up to 500 Å. The amplitudes of the oscillations decrease with increasing m j , as the number of open channels increases. For short-range anisotropies the decay is substantially stronger; the resonances are progressively washed out as m j increases, and β approaches the value ofā expected in the "universal" limit of 100% loss at short range [77,78]. In this case there are visible resonances in α and β at low field even for the uppermost channel with m j = j; these arise from quasibound states trapped behind centrifugal barriers for channels with m j < j and L > 0 [79].

III. EXPERIMENTAL POSSIBILITIES
All four atomic species considered here have been cooled to quantum degeneracy for both bosonic and fermionic isotopes. From a laser-cooling perspective, the highly magnetic lanthanide atoms are remarkably similar to their closed-shell cousins, despite their complex atomic structure. Indeed, the procedure for creating Er Bose-Einstein condensates [39] was inspired by the work on Yb [34,80]. They also have similar polarizabilities in the wavelength range commonly used for optical traps (1030 to 1070 nm), so that co-trapping and simultaneous evaporative cooling of co-trapped samples should be straightforward. The atoms are thus highly compatible for experiments on mixtures.
The behavior of the mixtures will be complicated by the dense and chaotic intraspecies resonance structure of Er and Dy themselves [81][82][83]. However, the positions of these resonances are well documented and the majority have widths below 100 mG. Two possible approaches may be envisaged. Since the closed-shell atoms are unaffected by the intraspecies resonances of Dy or Er, and have no intraspecies resonances themselves, they may be used to probe the interspecies resonances, even in regions where intraspecies resonances exist. Alternatively, if the closed-shell atom is in large excess, threebody losses due to the intraspecies resonances may be sufficiently suppressed to work with the interspecies resonances. In any case there are numerous windows (up to ∼1 G wide) that are free from intraspecies resonances and suitable for working with interspecies resonances.
The resonance-free windows should also be ideal for evaporative cooling of both species to quantum degeneracy. The recent successful creation of dual-degenerate gases of Dy and Er [84] is extremely encouraging in this respect. Simultaneous evaporative cooling requires a favorable interspecies scattering length, which may be achieved either by tuning across a wide resonance with magnetic field or (in the low-anisotropy case) by a suitable choice of isotopes to achieve the required background scattering length.
Once degeneracy is achieved, it should be possible to load the mixture into a 3D optical lattice. Such a lattice provides a very sensitive environment for the detection of Feshbach resonances [85] and an ideal platform for molecule formation. A lattice with only one atom of Dy or Er per site eliminates the complication of intraspecies resonances and allows magnetoassociation at any desired magnetic field.
Magnetoassociation is usually most effective at relatively narrow resonances, with widths around 100 mG to 1 G. Many such resonances exist in both limiting regimes of anisotropy. In the low-anisotropy case they are mostly due to bound states with L = 4 or 6. The background scattering length for these resonances is moderately tunable with magnetic field, as seen in Fig. 1, but is centered around the isotropic scattering length a iso . If necessary, a iso may be selected by choosing an appropriate isotopic combination. In the high-anisotropy case there are narrow resonances suitable for magnetoassociation, with a wide variety of background scattering lengths even for a single interaction potential (or isotopic combination). In this case, careful selection of isotopes may be unnecessary.
Transferring molecules formed by magnetoassociation to short-range (low-lying) states with electric dipole moments will be a challenge. Nevertheless, it can probably be achieved by STIRAP, as has been possible for a variety of alkali-metal dimers. Detailed spectroscopy of the intermediate electronic states available for STIRAP will be required, but it outside the scope of the present paper.
The short-range states of these molecules will probably be best described by Hund's case (c) [86]. Here the atomic total angular momentum j is projected onto the internuclear axis with projection Ω, which can take values from −j to j. For each value of Ω, the total angular momentum J can take values J ≥ |Ω| in integer steps. If j is a good quantum number, states Ω and Ω with Ω − Ω = ±1 are coupled by Coriolis matrix elements proportional to [(j(j + 1) − ΩΩ )(J(J + 1) − ΩΩ )] 1/2 , which ultimately uncouple Ω from the internuclear axis at high J.
(9) The quantity in parentheses is approximately 7/3 for 3 H 6 and 5/2 for 5 I 8 . For J = |Ω| there will be 2|Ω| + 1 such states, equally spaced at low field. It should be straightforward to transfer population between these states and create coherent superpositions of them with microwave pulses, as has been achieved for alkali-metal dimers [88]. The large number of states available offer the opportunity to create fully controllable high-dimensional quantum systems, which may be used as qudits for quantum computation [17].
In zero electric field, states with positive and negative values of Ω combine to form parity eigenstates with no permanent dipole moment. However, these pairs of eigenstates are split only by coupling to Ω = 0, which exists for only one parity combination. They are thus nearly degenerate, and become more closely so with increasing |Ω|. It therefore requires only a very small electric field to mix the parity eigenstates (Ω-doublets) and form oriented states with dipole moment µ v ΩM/[J(J +1)], where µ v is the body-fixed molecular dipole moment. It should be noted that Ω and M are both signed quantities here and the space-fixed dipole depends on their relative sign.

IV. CONCLUSIONS
We have considered Feshbach resonances in collisions of an open-shell high-spin atom (Dy or Er) with a closedshell atom (Yb or Sr). We have developed model interaction potentials for Dy+Yb and Er+Sr, and calculated scattering lengths and the positions of near-threshold bound states as a function of magnetic field. For both systems we have found numerous Feshbach resonances, with a variety of widths, at moderate magnetic fields.
The couplings responsible for Feshbach resonances depend on the anisotropy of the interaction potential. We have considered two limiting regimes of anisotropy. In the first limit, we consider anisotropy due entirely to dispersion forces, which arises from the tensor polarizability of the open-shell atom. This produces quite weak anisotropies in the long-range potential for atoms like Dy and Er, in which the unpaired f electrons lie mostly inside the outermost s electrons. The resulting interaction produces direct couplings with selection rule ∆L ≤ 2, where L is the end-over-end angular momentum of the colliding pair. In this regime the strongest resonances in s-wave scattering are due to bound states with L = 2; we show that at least one such resonance must occur below 98 G for Dy+Yb and below 176 G for Er+Sr. Additional broad resonances occur at somewhat higher fields, and there are also narrower resonances due to bound states with L > 4. In the second limit, we consider much stronger anisotropy that may exist due to higher-order dispersion forces, chemical bonding or repulsive anisotropy. In this regime there is much stronger coupling between different values of L, such that L is no longer even nearly conserved. This produces many more Feshbach resonances, but still with a wide variety of widths.
The two regimes of anisotropy that we have considered span the range of likely physical behavior for these systems. The long-range model represents the minimum coupling that is likely to exist, while the short-range model represents the maximum. For both models we predict many Feshbach resonances at experimentally accessible magnetic fields, with a variety of widths.
The resonances predicted here have a wide range of possible applications. The wider resonances are very suitable for tuning interspecies interactions, both to achieve properties desirable for formation of dual degenerate gases and to investigate the novel properties of mixtures of dipolar and non-dipolar species [42][43][44]. Further tuning may be achieved by selecting from the wide variety of isotopic combinations available. The narrower resonances may be used for magnetoassociation to form highspin molecules that inherit the large magnetic moments of Er and Dy. These may in turn be transferred to short-range states where they will still have large magnetic moments. In addition, there will be near-degenerate pairs of Ω-doublets, of opposite parity, which will be easily mixed with very small electric fields to form oriented states with significant space-fixed electric dipole moments.
The general properties of the resonances predicted here will hold for a variety of systems. They apply to any combination of a heavy atom with non-zero spin and high orbital angular momentum and a heavy closed-shell atom. The densities of near-threshold states and of the resulting resonances will be lower if either atom is significantly lighter, but the general considerations still apply for atoms of mass 20 or more. They apply to transitionmetal atoms as well as lanthanides or actinides. They do not apply to open-shell atoms in S states or to very light atoms such as He and first-row elements.
In summary, we believe that this study opens up a new field of high-spin dipolar molecules. We have demonstrated the feasibility of producing such molecules from laser-cooled atoms, and outlined some of their properties and potential applications.