Extending optoelectrical Sisyphus cooling of chemically stable polar molecules below the submillikelvin record and into ground-state-confining traps

Optoelectrical Sisyphus cooling in a microstructured electrostatic box trap is the only demonstrated dissipative cooling method applicable to chemically stable polar molecules that cannot be laser cooled or associated from ultracold atoms; its record remains formaldehyde (H2CO) at about $420~\mu\mathrm{K}$ with $3\times10^{5}$ molecules, set in 2016. The source experiment states that no fundamental cooling limit has been reached and identifies what blocks further progress: surface charges on the electrode microstructure broaden the electric-field distribution at low trap voltages and halt the radio-frequency cooling ramp, and the cooled ensemble has never been transferred into a microwave or optical trap that confines molecules in their absolute ground state, the named prerequisite for evaporative or sympathetic cooling. The surviving open problem is to suppress the surface-charge broadening and demonstrate cooling below the record, determine the achievable temperature and phase-space-density floor with its dominant limiting mechanism, and demonstrate ground-state-confining trap transfer with quantified efficiency and lifetime. The evaporative-cooling endpoint itself has been reached on the separate associated-bialkali route.

Background

Cooling molecules to ultracold temperatures ($T<1$ mK) would extend the revolution that laser cooling brought to atoms, but most molecules cannot be laser cooled because their electronic excitation spreads over many vibrational branches, and most chemically stable species cannot be assembled from ultracold alkali atoms. Optoelectrical Sisyphus cooling, developed by the Rempe group at the Max Planck Institute of Quantum Optics, is a dissipative scheme that avoids these restrictions: it works for essentially any polar molecule with suitable rotational structure. The molecules are confined in an electrostatic trap formed by two microstructured capacitor plates that create a box-like potential for a low-field-seeking rotational state (a state whose energy rises with applied electric field, so the molecule is repelled from strong-field regions; the energy shift in an electric field is the Stark shift). Cooling proceeds Sisyphus-style: a pump laser and a microwave field move molecules between rotational states of different Stark shift so that they repeatedly climb potential-energy hills and are optically repumped at the top, draining potential energy; a radio-frequency (RF) field acts as a knife-edge filter that drives resonant transitions to untrapped states only for molecules hot enough to reach the resonant field, setting and progressively lowering the temperature. The method was first demonstrated with methyl fluoride (CH$_3$F), cooling about $10^{6}$ molecules from $390~\mathrm{mK}$ down to $29~\mathrm{mK}$ (Zeppenfeld et al., Nature 2012), and then applied to formaldehyde (H$_2$CO), reaching about $420~\mu\mathrm{K}$ with $3\times10^{5}$ molecules populating a single rotational state with over 80% purity (Prehn et al., Phys. Rev. Lett. 2016) — a kinetic-energy reduction by three orders of magnitude and a phase-space-density gain of about $10^{4}$ (the phase-space density, the number density times the cube of the thermal de Broglie wavelength, is the figure of merit for approaching quantum degeneracy). That 2016 experiment states that no fundamental cooling limit has been reached and pinpoints the obstacles to going colder. First, measurements show that at low trap voltages the electric-field distribution inside the trap is substantially broader than electrostatic simulations predict; the authors attribute this to surface charges accumulated on the polymer-coated microstructured plates, and since the final RF knife-edge frequency must approach the offset-field resonance within this distribution width, the broadening halts the cooling ramp. Second, the electrostatic trap only confines low-field-seeking (field-dressed) states, not the absolute ground state, so evaporative cooling (preferentially removing the hottest molecules and letting rethermalization cool the remainder) or sympathetic cooling (thermal contact with a colder co-trapped species) requires first transferring the ensemble into a microwave trap or optical dipole trap (confinement via the ac Stark shift induced by far-detuned laser light), which had been proposed for molecules (DeMille et al., Eur. Phys. J. D 2004) but never demonstrated for an optoelectrical-cooled sample. Third, larger starting ensembles could be obtained by loading buffer-gas-cooled (thermalized with cold helium gas) or Stark-decelerated (slowed by time-varying electric-field gradients acting on the molecular dipole moment) or centrifuge-decelerated molecular beams into the trap. Because the field distributions, the RF ramp, the trap transfer, and the sample size all govern the single figure of merit — the reachable phase-space density of chemically stable polar molecules — these items form one coherent objective rather than independent questions.

Problem Statement

Push optoelectrical Sisyphus cooling of chemically stable polar molecules beyond the demonstrated record — an ensemble of $3\times10^{5}$ H$_2$CO molecules at about $420~\mu\mathrm{K}$ in a microstructured electrostatic box trap — and establish what the method can ultimately reach. In the terms identified by the source experiment, this requires: (i) suppressing or eliminating the surface-charge-induced broadening of the trap's electric-field distribution at low trap voltages (for which ultraviolet charge removal has very recently been demonstrated as a materials procedure) sufficiently to continue the RF knife-edge cooling ramp, and demonstrating optoelectrical cooling of a chemically stable polar molecule to a temperature below the 2016 record; (ii) determining the practical temperature and phase-space-density floor of the method and identifying the dominant mechanism that enforces it (residual field inhomogeneity, pumping-rate limits, black-body effects, or collisional loss during the long cooling sequence); and (iii) transferring the cooled ensemble into a microwave trap or optical dipole trap that confines the molecules in their absolute ground state, with measured transfer efficiency and trapped lifetime — the prerequisite, named in the source, for subsequent evaporative or sympathetic cooling of these species toward deeper ultracold temperatures. Increasing the initial ensemble size by loading buffer-gas-cooled or decelerated molecular beams into the trap is a supporting objective on the same figure of merit, the achievable phase-space density. These components jointly serve one goal: establishing whether the only general cooling technique for chemically stable polar molecules can be extended from the submillikelvin regime toward the ultracold, degenerate regime.

References

1. A. Prehn, M. Ibrügger, R. Glöckner, G. Rempe, M. Zeppenfeld, "Optoelectrical Cooling of Polar Molecules to Submillikelvin Temperatures", Phys. Rev. Lett. 116, 063005 (2016). DOI: 10.1103/PhysRevLett.116.063005, https://doi.org/10.1103/PhysRevLett.116.063005; arXiv:1511.09427, https://arxiv.org/abs/1511.09427
2. M. Zeppenfeld, B. G. U. Englert, R. Glöckner, A. Prehn, M. Mielenz, C. Sommer, L. D. van Buuren, M. Motsch, G. Rempe, "Sisyphus cooling of electrically trapped polyatomic molecules", Nature 491, 570–573 (2012). DOI: 10.1038/nature11595, https://doi.org/10.1038/nature11595; arXiv:1208.0046, https://arxiv.org/abs/1208.0046
3. M. T. Ziemba, J. Phrompao, F. Jung, I. M. Rabey, G. Rempe, "Removal of high-voltage-induced surface charges by ultraviolet light", Rev. Sci. Instrum. 96, 073201 (2025). DOI: 10.1063/5.0269038, https://doi.org/10.1063/5.0269038; arXiv:2503.19662, https://arxiv.org/abs/2503.19662
4. A. Prehn, M. Ibrügger, G. Rempe, M. Zeppenfeld, "High-Resolution 'Magic'-Field Spectroscopy on Trapped Polyatomic Molecules", Phys. Rev. Lett. 127, 173602 (2021). DOI: 10.1103/PhysRevLett.127.173602, https://doi.org/10.1103/PhysRevLett.127.173602; arXiv:2110.11214, https://arxiv.org/abs/2110.11214
5. M. Löw, M. Ibrügger, G. Rempe, M. Zeppenfeld, "Coherence of Symmetry-Protected Rotational Qubits in Cold Polyatomic Molecules", Phys. Rev. Lett. 134, 113402 (2025). DOI: 10.1103/PhysRevLett.134.113402, https://doi.org/10.1103/PhysRevLett.134.113402; arXiv:2412.00775, https://arxiv.org/abs/2412.00775
6. S. C. Wright, T. E. Wall, M. R. Tarbutt, "Microwave trap for atoms and molecules", Phys. Rev. Research 1, 033035 (2019). DOI: 10.1103/PhysRevResearch.1.033035, https://doi.org/10.1103/PhysRevResearch.1.033035; arXiv:1906.05380, https://arxiv.org/abs/1906.05380
7. D. DeMille, D. R. Glenn, J. Petricka, "Microwave traps for cold polar molecules", Eur. Phys. J. D 31, 375–384 (2004). DOI: 10.1140/epjd/e2004-00163-6, https://doi.org/10.1140/epjd/e2004-00163-6
8. A. Schindewolf, R. Bause, X.-Y. Chen, M. Duda, T. Karman, I. Bloch, X.-Y. Luo, "Evaporation of microwave-shielded polar molecules to quantum degeneracy", Nature 607, 677–681 (2022). DOI: 10.1038/s41586-022-04900-0, https://doi.org/10.1038/s41586-022-04900-0; arXiv:2201.05143, https://arxiv.org/abs/2201.05143
9. Z. Shi, Z. Huang, F. Deng, W.-J. Jin, S. Yi, T. Shi, D. Wang, "Bose-Einstein condensate of ultracold sodium-rubidium molecules with tunable dipolar interactions", arXiv:2508.20518 (2025), https://arxiv.org/abs/2508.20518
10. X. Wu, T. Gantner, M. Koller, M. Zeppenfeld, S. Chervenkov, G. Rempe, "A cryofuge for cold-collision experiments with slow polar molecules", Science 358, 645–648 (2017). DOI: 10.1126/science.aan3029, https://doi.org/10.1126/science.aan3029; arXiv:1710.05988, https://arxiv.org/abs/1710.05988