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arXiv:2608.05512

Large anomalous shifts of potassium-39 Feshbach resonances

Ali Zaheer, Mohammed Bouras, Krzysztof Giergiel, Rudolf Grimm, Andrei Sidorov, Peter Hannaford

physics.atom-phcond-mat.quant-gasquant-phSubmitted Aug 6, 2026• Announced Aug 7, 2026• 0 citations
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Abstract

We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally with trap depth and approach zero at zero depth. We show that the large observed shifts originate from a large differential ac Stark shift between the incoming pair of potassium-39 atoms and the weakly bound Feshbach molecule, which in turn originates from an unexpectedly large dynamic polarizability of the Feshbach molecule. The polarizabilities of the Feshbach molecules extracted from the measured shifts of the 33.6 G and 39.9 G resonances are about four to seven times the sum of the polarizabilities of the two incoming potassium-39 atoms, that is, about four to seven times larger than the usual polarizability of weakly bound Feshbach molecules. The large polarizabilities of the Feshbach molecules are attributed to a near-coincidence between the frequency of the 1063.9 nm ODT laser and the frequency of a molecular transition from the last vibrational level of the lowest triplet a3Σ+u potential to a vibrational level of the excited b3Σ+g potential. Other potassium-39 Feshbach resonances we have studied exhibit a zero or very small shift, corresponding to molecular polarizabilities close to the sum of the polarizabilities of the two incoming potassium-39 atoms.

Comments
14 pages, 10 figures

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We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally with trap depth and approach zero at zero depth. We show that the large observed shifts originate from a large differential ac Stark shift between the incoming pair of potassium-39 atoms and the weakly bound Feshbach molecule, which in turn originates from an unexpectedly large dynamic polarizability of the Feshbach molecule. The polarizabilities of the Feshbach molecules extracted from the measured shifts of the 33.6 G and 39.9 G resonances are about four to seven times the sum of the polarizabilities of the two incoming potassium-39 atoms, that is, about four to seven times larger than the usual polarizability of weakly bound Feshbach molecules. The large polarizabilities of the Feshbach molecules are attributed to a near-coincidence between the frequency of the 1063.9 nm ODT laser and the frequency of a molecular transition from the last vibrational level of the lowest triplet a3Σ+u potential to a vibrational level of the excited b3Σ+g potential. Other potassium-39 Feshbach resonances we have studied exhibit a zero or very small shift, corresponding to molecular polarizabilities close to the sum of the polarizabilities of the two incoming potassium-39 atoms.
In this article we address the general approach for calculating dynamical dipole polarizabilities of small quantum systems, based on a sum-over-states formula involving in principle the entire energy spectrum of the system. We complement this method by a few-parameter model involving a limited number of effective transitions, allowing for a compact and accurate representation of both the isotropic and anisotropic components of the polarizability. We apply the method to the series of ten heteronuclear molecules composed of two of (Li,Na,K,Rb,Cs) alkali-metal atoms. We rely on both up-to-date spectroscopically-determined potential energy curves for the lowest electronic states, and on our systematic studies of these systems performed during the last decade for higher excited states and for permanent and transition dipole moments. Such a compilation is timely for the continuously growing researches on ultracold polar molecules. Indeed the knowledge of the dynamic dipole polarizabilities is crucial to model the optical response of molecules when trapped in optical lattices, and to determine optimal lattice frequencies ensuring optimal transfer to the absolute ground state of initially weakly-bound molecules. When they exist, we determine the so-called ‘magic frequencies’ where the ac-Stark shift and thus the viewed trap depth, is the same for both weakly-bound and ground-state molecules.
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic wavelengths for the 4s-np transitions for n=4,5n = 4, 5n=4,5, i.e. those wavelengths for which the two levels have the same ac Stark shifts. These facilitate state-insensitive optical cooling and trapping. The magic wavelengths for the 4s−5p4s-5p4s−5p transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interest region of 1050-1130 nm. Uncertainties of all recommended values are estimated.
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values and uncertainties are provided for the relevant electric-dipole matrix elements. Polarizabilities of the 4s4s4s, 4pj4{p}_{j}4pj​, 5s5s5s, 5pj5{p}_{j}5pj​, and 3dj3{d}_{j}3dj​ states are compared with other theoretical and experimental values when possible. We identify magic wavelengths for the $4s\ensuremath{-}np$ transitions for n=4,5n=4,5n=4,5, i.e., those wavelengths for which the two levels have the same ac Stark shifts. The magic wavelengths for the $4s\ensuremath{-}5p$ transitions are of particular interest for attaining a quantum gas of potassium at high phase-space density. We find 20 such wavelengths in the technically interesting region of 1050−−11301050--11301050−−1130 nm.
An important route toward the preparation of cold molecules is magnetically tunable Feshbach resonances. Here we investigate an inelastic Feshbach resonance between a single pair of 87Rb and 39K atoms confined in an optical tweezer, with both atoms prepared in the |F=1,mF=−1⟩ state. By developing an in-situ imaging scheme for 39K, we directly measure magnetic-field-dependent collisional loss without separating the atoms after the interaction. For weak confinement, the resonance position measured in our experiment differs from the bulk-gas experiments. In contrast, we observe a significant shift of the resonance toward higher magnetic fields as the tweezer trap depth increases. Coupled-channel calculations accounting for finite temperature effects fail to explain the magnitude of this shift, suggesting that it originates from differential optical responses of the open-channel atom pair and the weakly bound molecular state under strong confinement. Our results indicate that optical tweezer light can significantly modify Feshbach resonance properties, opening a pathway toward optical control of atom–atom interactions and weakly bound molecular states in dual-species tweezer platforms.
Recent studies demonstrated anomalous temperature shifts for some Fano-Feshbach resonances of thulium atoms. These anomalies were explained by the variation in light intensity in the optical dipole trap, which accompanied changes in temperature. In addition, a temperature-related transformation of the statistics of the inter-resonance spacing was demonstrated [Aikawa et al., Phys. Rev. Lett. 108, 210401 (2012)]. Here, we analyze the shifts of isolated sss- and ddd-type Fano-Feshbach resonances of ultracold thulium atoms with temperature for a fixed depth of an optical dipole trap. The measurements are consistent with the three-body recombination-based theory of the temperature-related resonance shift and enable the extraction of the resonance parameters, particularly the magnetic moments of closed channel states. This parameter and the known polarizability of the open channel enable us to separate the contributions of the temperature and Stark shift to the overall shift of the resonances and show the dominant role of the Stark effect in the overall shift.
This thesis studies the effects of breaking Feshbach molecules of ⁶Li confined in an Optical-Dipole Trap (ODT). We discuss the effects of breaking molecules using background collisions between Feshbach molecules and H₂ particles in our vacuum system and resonant photons. In the case of background collisions we show that despite the collisions being energetic enough to always eject one of the constituent atoms, the remaining atom will only receive a weak kick. We show that the probability of the magnitude of the kick is related to the Feshbach molecule wavefunction. We describe an experiment for measuring this probability distribution, through measuring the time dynamics of the number of atoms and molecules in our trap as a function of the trap-depth and magnetic field, and discuss some preliminary results. Our results reveal that breaking molecules using pulses of light, resonant with one of the atomic transitions, results in similar dynamics. For both experiments we derive and discuss a phenomenological rate-equation model. We also characterized the magnetic trapping potential through a measurement of the associated trap-frequencies. Using the results of these measurements and incorporating the optical trapping potential due to the ODT and effects due to gravity, we calculate the trap-depth as a function of the magnetic field, power, and small vertical displacements. We demonstrate that vertical misalignment affects the trap similarly to changes in the magnetic field.