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Formation of ultracold $^{39}$ K $^{133}$ Cs Feshbach molecules

The authors report the creation of an ultracold gas of bosonic $^{39}$ K $^{133}$ Cs Feshbach molecules via sympathetic cooling and magnetoassociation at 361.7 G, characterizing new interspecies resonances and refining interaction potentials to pave the way for producing ground-state molecules.

Original authors: Charly Beulenkamp, Krzysztof P. Zamarski, Robert C. Bird, C. Ruth Le Sueur, Jeremy M. Hutson, Manuele Landini, Hanns-Christoph Nägerl

Published 2026-08-07

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CC BY 4.0

Original authors: Charly Beulenkamp, Krzysztof P. Zamarski, Robert C. Bird, C. Ruth Le Sueur, Jeremy M. Hutson, Manuele Landini, Hanns-Christoph Nägerl

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where atoms are like tiny, shy dancers in a massive, freezing ballroom. Usually, these dancers bump into each other chaotically, but if you cool them down enough—colder than outer space—they start to move in perfect unison, behaving less like individual particles and more like a single, giant wave. This is the realm of ultracold quantum gases. In this frozen dance, scientists use invisible magnetic fields like a conductor's baton to tune how the atoms interact. Sometimes, they can even coax two different types of atoms to stick together, forming a "molecule" that is barely holding on, a fragile partnership known as a Feshbach molecule. Why do we care? Because these molecular dancers have a special superpower: an electric dipole moment, which means they can "talk" to each other over long distances. This could be the key to building super-fast quantum computers or simulating complex materials that might one day solve the mystery of high-temperature superconductivity.

Now, picture a specific pair of dancers: Potassium-39 ( $^{39}\text{K}$ ) and Cesium-133 ( $^{133}\text{Cs}$ ). For a long time, getting these two to dance together in the ultracold ballroom was a nightmare. Potassium is a bit of a loner with a tricky personality that makes it hard to cool down, while Cesium is heavy and prone to tripping over itself. Previous attempts to mix them were like trying to teach a sprinter and a marathon runner to run a relay race without a baton; it took too long and was incredibly complicated. But in this new study, a team of physicists from Innsbruck and Durham decided to try a different strategy. Instead of cooling them separately and then mixing them, they mixed them right from the start and let the Potassium act as a "cooling coach" for the Cesium.

The researchers successfully created a cloud of these two atoms so cold that they could finally make them stick together. They used a magnetic field of 361.7 Gauss to gently pull the Potassium and Cesium atoms into a weak embrace, forming about 7,600 Feshbach molecules. These molecules are like a fragile handshake between the two atoms; they are weakly bound and don't last forever. In fact, the team measured that these molecular couples survive for about 130 milliseconds before falling apart due to collisions with each other. While that sounds short, in the quantum world, it's an eternity—long enough to stabilize the system and prepare for the next big step.

The team didn't just stop at making the molecules; they became detectives, hunting for the "rules of the dance." They scanned the magnetic fields to find new "resonances"—special frequencies where the atoms are extra eager to stick together. They found several new spots where this happens, spots that previous maps of the atomic world had missed. By measuring exactly how these molecules behaved and how much energy it took to hold them together, the scientists were able to rewrite the "instruction manual" for how Potassium and Cesium interact. They found that the old manual had some errors, particularly regarding how the atoms' internal spins align. Their new, more accurate map of the interaction potentials gives them a much clearer picture of the forces at play.

While the current cooling process hits a wall where the Cesium atoms start getting lost too fast to easily form a Bose-Einstein Condensate (BEC) of the mixture right now, the paper notes that further improvements to the cooling scheme may allow for the creation of overlapping BECs in the future. The success of this experiment proves that the path is open. The team has shown that with their new cooling trick and their improved map of the atomic forces, they have laid the perfect groundwork. The next move is to use a laser technique called STIRAP to take these weak, wobbly Feshbach molecules and tighten their bond into a stable, ground-state molecule. If they succeed, they will have created a brand-new type of ultracold gas that could help unlock the secrets of quantum physics.

Technical Summary: Formation of Ultracold $^{39}\text{K}^{133}\text{Cs}$ Feshbach Molecules

Problem Statement
Ultracold heteronuclear molecules are a critical resource for quantum simulation and computing due to their permanent electric dipole moments. While Feshbach resonances have successfully enabled the creation of weakly bound molecules from various alkali pairs, the potassium-cesium (KCs) system has remained an exception. Despite theoretical predictions of resonances and observations of atom-loss peaks, previous experiments failed to achieve the actual formation of trapped KCs molecules. The primary challenge lies in the difficulty of cooling $^{39}\text{K}$ and $^{133}\text{Cs}$ simultaneously to the high phase-space densities required for magnetoassociation, particularly given the unfavorable collisional properties of $^{39}\text{K}$ (specifically its Ramsauer-Townsend minimum) and the complex loss mechanisms in mixed alkali gases.

Methodology
The authors developed a novel cooling strategy to produce an ultracold mixture of $^{39}\text{K}$ and $^{133}\text{Cs}$ , followed by a multi-stage process to create and characterize Feshbach molecules.

Sympathetic Cooling Sequence: Unlike previous sequential cooling methods, the authors mixed the species early in the process. They utilized a dual-species magneto-optical trap (MOT) followed by compression and grey molasses cooling. The mixture was transferred to a magnetic trap and then loaded into an optical dipole trap (ODT).
- Sympathetic Mechanism: Since direct evaporative cooling of $^{39}\text{K}$ is hindered by its background scattering length ( $-35 a_0$ ) causing a Ramsauer-Townsend minimum, the authors used $^{39}\text{K}$ to sympathetically cool $^{133}\text{Cs}$ . The trap depth ratio ( $U_{\text{Cs}}/U_{\text{K}} \approx 1.94$ ) suppressed direct evaporation of Cs, while the interspecies scattering length ( $60\text{--}80 a_0$ ) ensured efficient thermalization.
- Loss Management: The team characterized and mitigated specific loss channels, including three-body recombination and light-induced depolarization of Cs. They identified that trap-light scattering (specifically Raman scattering due to Cs's large vector polarizability at 1064 nm) caused one-body loss, necessitating careful optimization of trap depth.
- Spin Transfer: To reach the optimal collision channel for cooling, the authors performed a spin transfer from $(3, -3)_{\text{Cs}}$ to $(3, 3)_{\text{Cs}}$ using Raman transitions driven by a second, orthogonally polarized ODT beam, avoiding the high-loss intermediate states associated with RF coupling.
- Final Evaporation: Evaporative cooling was performed at 557 G, a magnetic field window where both species could be cooled efficiently while maintaining miscibility. This yielded a mixture with $8.7(3) \times 10^5$ K atoms and $1.9(1) \times 10^5$ Cs atoms.
Molecule Formation: Weakly bound molecules were created via magnetoassociation at a Feshbach resonance located at 361.7 G in the $(1, 1)_{\text{K}} + (3, 3)_{\text{Cs}}$ channel. The process involved:
- Transferring K atoms to the $(1, 1)$ state.
- Crossing the resonance adiabatically (3 G/s).
- Applying a magnetic field gradient to levitate the molecules while ejecting unbound atoms.
- Purifying the sample by ramping down the ODT to remove remaining Cs atoms.
Spectroscopy and Potential Fitting:
- Feshbach Spectroscopy: The authors scanned for new interspecies resonances across four different thresholds, observing several new loss peaks.
- Bound State Characterization: They measured the binding energy and magnetic moment of the state associated with the 361.7 G resonance using two-photon spectroscopy and magnetic levitation measurements.
- Potential Refitting: Using coupled-channel calculations, the authors fitted the new experimental data (resonance positions, binding energies, and singlet fractions) to refine the K-Cs interaction potentials. They replaced standard short-range extrapolations with an exponential form to ensure physical behavior, allowing for the independent determination of singlet and triplet scattering lengths.

Key Results

Molecule Production: The experiment successfully produced a trapped sample of $7.6(10) \times 10^3$ bosonic $^{39}\text{K}^{133}\text{Cs}$ Feshbach molecules.
Sample Quality: The molecular gas had a temperature of $0.69(5) \, \mu\text{K}$ and a phase-space density of $2.8(8) \times 10^{-4}$ .
Lifetime: The purified molecular sample exhibited a lifetime of approximately 130 ms, limited by two-body inelastic decay ( $\Gamma_2 = 5.6(12) \times 10^{-10} \, \text{cm}^3\text{s}^{-1}$ ). This lifetime is sufficient to stabilize the magnetic field for subsequent STIRAP transfer to the ground state.
New Resonances: The study identified several new interspecies resonances at four different thresholds, including features at 315.55 G, 463.25 G, 466.23 G, 299.56 G, 478.03 G, and 464.58 G.
Improved Potentials: The refitted interaction potentials yielded singlet and triplet scattering lengths of $a_s = -29.2(8) \, a_0$ and $a_t = 77.7(2) \, a_0$ , respectively. These values differ from previous estimates, particularly for the triplet length, due to the inclusion of resonances with a wider range of singlet fractions and precise binding energy measurements.

Significance and Claims
The paper claims to provide the first creation of a trapped ultracold sample of $^{39}\text{K}^{133}\text{Cs}$ Feshbach molecules. The authors state that this achievement establishes the necessary starting conditions for the creation of ultracold ground-state molecules via Stimulated Raman Adiabatic Passage (STIRAP).

The work resolves the long-standing difficulty in cooling the K-Cs mixture by demonstrating a robust sympathetic cooling strategy that overcomes the specific collisional limitations of $^{39}\text{K}$ . Furthermore, by combining new spectroscopic data with coupled-channel calculations, the authors provide significantly improved K-Cs interaction potentials. These potentials offer a detailed understanding of the collision physics and allow for the independent determination of singlet and triplet scattering lengths, which was not possible with previous data sets. The authors note that these potentials serve as a "good starting point" for future creation of ground-state samples and can be used to predict properties for other isotopic combinations.

Technical Summary: Formation of Ultracold 39K133Cs^{39}\text{K}^{133}\text{Cs}39K133Cs Feshbach Molecules

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Technical Summary: Formation of Ultracold $^{39}\text{K}^{133}\text{Cs}$ Feshbach Molecules