Observation of high partial-wave Feshbach resonances in $^{39}$K Bose-Einstein condensates

We report the new observation of several high partial-wave (HPW) magnetic Feshbach resonances (FRs) in $^{39}$K atoms of the hyperfine substate $\left|F=1,m_{F}=-1\right\rangle$. These resonances locate at the region between two broad $s$-wave FRs from 32.6 G to 162.8 G, in which Bose-Einstein condensates (BECs) can be produced with tunable positive scattering length obtained by magnetic FRs. These HPW FRs are induced by the dipolar spin-spin interaction with s-wave in the open channel and HPW in the closed channel. Therefore, these HPW FRs have distinct characteristics in temperature dependence and loss line shape from that induced by spin-exchange interaction with HPWs in both open and closed channels. Among these resonances, one $d$-wave and two $g$-wave FRs are confirmed by the multichannel quantum-defect theory (MQDT) calculation. The HPW FRs have significant applications in many-body physics dominated by HPW pairing.

💡 Research Summary

In this work the authors report the first observation of several high‑partial‑wave (HPW) magnetic Feshbach resonances (FRs) in a 39‑potassium Bose‑Einstein condensate (BEC) prepared in the hyperfine state |F = 1, mF = −1⟩. The experiment is performed in the magnetic field region between two well‑known broad s‑wave resonances at 32.6 G and 162.8 G, where the background scattering length of 39 K is positive and a stable condensate can be produced. By scanning the magnetic field from 20 G to 200 G and measuring atom loss after a controlled hold time, the authors identify five new loss features, labelled I–V.

A detailed analysis shows that three of these resonances (I, IV, V) have a symmetric Gaussian loss profile, while the other two (II, III) display an asymmetric double‑sigmoidal shape. Temperature‑dependence measurements on both a pure BEC and a thermal cloud reveal distinct behaviours: the loss depth of I, III and V decreases with increasing temperature, the loss of II remains essentially unchanged, and the loss of IV becomes deeper at higher temperature. These observations are consistent with the fact that the open channel for all five resonances is an s‑wave (l = 0, ml = 0) while the closed channel carries a higher orbital angular momentum (d‑wave for V, g‑wave for II and III).

The underlying coupling mechanism is identified as the magnetic dipole‑dipole (spin‑spin) interaction, which is weaker and highly anisotropic compared with the usual isotropic spin‑exchange interaction. The dipolar interaction obeys the selection rules |Δl| = 0, 2, 4 and Δml + Δmf = 0, allowing an s‑wave entrance channel to couple to a d‑ or g‑wave bound state in the closed channel. Consequently, the resonances do not exhibit the l + 1 multiplet splitting typical of spin‑exchange‑induced HPW resonances, and the loss line shapes are largely symmetric.

To interpret the data quantitatively, the authors employ multichannel quantum‑defect theory (MQDT). Short‑range physics is encapsulated in quantum‑defect parameters KcS,T(ε,l) with an l‑dependent correction βS,T l(l + 1). By choosing KcS(0,0)=1.7631, KcT(0,0)=−0.1999, βS=−0.0082 and βT=−0.0010, the MQDT model reproduces all previously known s‑wave resonances and predicts the positions of the newly observed HPW resonances. The generalized scattering hyper‑volume Dl(B) is calculated for l = 0, 2, 4, and the resulting resonance centers Bth and widths Δth agree well with the experimentally extracted Bexpt and loss widths Δloss.

The paper provides a comprehensive table of the observed resonances, including the experimental center, theoretical center, width, and a characteristic background length albg derived from Dlbg. The MQDT fits confirm that resonances II and III are g‑wave (l = 4) and resonance V is d‑wave (l = 2).

These high‑partial‑wave resonances open a new avenue for engineering interactions with non‑zero orbital angular momentum in ultracold gases. Because the open channel remains s‑wave, the condensate can be formed and manipulated without the centrifugal barrier that would otherwise suppress low‑temperature collisions. The ability to couple to d‑ and g‑wave molecular states via the dipolar interaction enables studies of exotic pairing mechanisms, high‑angular‑momentum superfluidity, and many‑body phenomena that are analogues of p‑wave or d‑wave superconductivity in solid‑state systems. Moreover, the precise control of HPW FRs can be used to calibrate interatomic potentials and to explore novel quantum phases such as quantum droplets, solitons, and topological excitations in 39 K condensates.

In summary, the authors have experimentally discovered five high‑partial‑wave Feshbach resonances in 39 K BECs, identified their dipolar‑spin‑spin origin, validated their positions and widths with MQDT, and highlighted the potential of these resonances for future many‑body physics research involving high‑angular‑momentum pairing.