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Physica Scripta

Evaporative cooling of CaF in a magnetic-assisted electrostatic quadrupole shell-trap

Yuhang Shu, Xu-Ping Shao, Xiaohua Yang

Published May 1, 2026• 0 citations
Publisher

Abstract

Abstract A magnetic-assisted electric quadrupole trap (MAEQT) is proposed for trapping CaF molecules and enabling subsequent evaporative cooling, by leveraging the hybrid-field-induced perturbation effects. Our simulation demonstrates that experimentally available [Phys. Rev. Lett. 119, 103201, 2017] 1.10 × 10 5 CaF molecules, initially at a temperature of 340 μK, can be cooled down to 4.4 μK within the MAEQT. The trapped molecular cloud exhibits a shell-like configuration, with inner and outer diameters of 270 μm and 322 μm, respectively. Furthermore, the phase-space density is enhanced from 4.38 × 10 −9 to 4.09 × 10 −6 , representing a three-order-of-magnitude increase. This shell-shaped cold CaF ensemble might be employed for sympathetic cooling of various molecules–excluding bialkali species and those with highly diagonal Franck-Condon factors–to the tens of μK regime, which paves the way for their further quantum manipulation.

DOI
10.1088/1402-4896/ae673a

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We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the $s$-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the $s$-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to $1 \ensuremath{\mu}\mathrm{K}$ within 30 s.

arXiv:1508.03987•Physical Review A•Nov 13, 2015•55 citations
Abstract A magnetic-assisted electric quadrupole trap (MAEQT) is proposed for trapping CaF molecules and enabling subsequent evaporative cooling, by leveraging the hybrid-field-induced perturbation effects. Our simulation demonstrates that experimentally available [Phys. Rev. Lett. 119, 103201, 2017] 1.10 × 10 5 CaF molecules, initially at a temperature of 340 μK, can be cooled down to 4.4 μK within the MAEQT. The trapped molecular cloud exhibits a shell-like configuration, with inner and outer diameters of 270 μm and 322 μm, respectively. Furthermore, the phase-space density is enhanced from 4.38 × 10 −9 to 4.09 × 10 −6 , representing a three-order-of-magnitude increase. This shell-shaped cold CaF ensemble might be employed for sympathetic cooling of various molecules–excluding bialkali species and those with highly diagonal Franck-Condon factors–to the tens of μK regime, which paves the way for their further quantum manipulation.
Ultracold molecules provide fundamental new insights into molecular interaction dynamics in the quantum regime and represent a new platform for chemical physics where quantum behaviors play a dominant role in molecular interaction and dynamics. An electric-field-assisted magnetic trap for trapping and further evaporative cooling of cold molecules to ultracold regime is proposed utilizing the perturbation of the hyperfine levels in a mixed field, and the depth of the trap can be tuned by adjusting the assisted electric field rapidly. Thus, the evaporative cooling of [Formula: see text]I[Formula: see text]Br molecules in the [Formula: see text] state of the rovibronic ground state is simulated. It shows that IBr molecules would be cooled from 26[Formula: see text][Formula: see text]K to 556[Formula: see text]nK within 598.9[Formula: see text]ms and eventually we would obtain a number of [Formula: see text] molecules in a volume of [Formula: see text][Formula: see text]cm3 with the number density of [Formula: see text][Formula: see text]cm[Formula: see text]. The Bose–Einstein condensation of the alkali diatomic molecules would probably be realized in the proposed trap if the present experimentally available samples are loaded.
Abstract Cold molecular physics has been the frontier of atomic, molecular and optical physics for over two decades due to the unique and unprecedented applications. We simulate the evaporative cooling of 87Rb133Cs molecules in a modified electric-assisted magnetic trap by decreasing the electric field. When 10-time loading the experimentally available cold RbCs molecules, we would achieve a number N = 811, a temperature T = 21.34 nK, a phase-space density PSD = 2.67 and a number density n = 5.01 × 1012 cm-3 of Bose–Einstein condensation RbCs molecules in 480 ms.
While cold molecule experiments are rapidly moving towards their promised benefits of precision spectroscopy, controllable chemistry, and novel condensed phases, heretofore the field has been greatly limited by a lack of methods to cool and compress chemically diverse species to temperatures below ten millikelvin. While in atomic physics these needs are fulfilled by laser cooling, magneto-optical trapping, and evaporative cooling, until now none of these techniques have been applicable to molecules. In this thesis, two major breakthroughs are reported. The first is the observation of evaporative cooling in magnetically trapped hydroxyl (OH) radicals, which potentially opens a path all the way to Bose-Einstein condensation of dipolar radicals, as well as allowing cold- and ultracold-chemistry studies of fundamental reaction mechanisms. Through the combination of an extremely high gradient magnetic quadrupole trap and the use of the OH Λ-doublet transition to enable highly selective forced evaporation, cooling by an order of magnitude in temperature was achieved and yielded a final temperature no higher than 5mK. The second breakthrough is the successful application of laser cooling and magneto-optical trapping to molecules. Motivated by a proposal in this thesis, laser cooling of molecules is now known to be technically feasible in a select but substantial pool of diatomic molecules. The demonstration of not only Doppler cooling but also two-dimensional magneto-optical trapping in yttrium (II) oxide, YO, is expected to enable rapid growth in the availability of ultracold molecules--just as the invention of the atomic magneto-optical trap stimulated atomic physics twenty-five years ago.
We observe the spontaneous evaporation of atoms confined in a bubble-like radio frequency (rf)-dressed trap (Zobay and Garraway 2001 Phys. Rev. Lett. 86 1195; 2004 Phys. Rev. A 69 023605). The atoms are confined in a quadrupole magnetic trap and are dressed by a linearly polarized rf field. The evaporation is related to the presence of holes in the trap, at the positions where the rf coupling vanishes, due to its vectorial character. The final temperature results from a competition between residual heating and evaporation efficiency, which is controlled via the height of the holes with respect to the bottom of the trap. The experimental data are modelled by a Monte Carlo simulation predicting a small increase in phase-space density limited by the heating rate. This increase was within the phase-space density determination uncertainty of the experiment.
A hybrid trap was developed to confine neutral molecules and molecular ions. We demonstrated the long-term trapping of Stark-decelerated OH radicals in the X 2Pi3/2 (v = 0, J = 3/2, MJ = 3/2, f) state in a permanent magnetic trap. The trap environment was cryogenically cooled to a temperature of 17 K in order to efficiently suppress black-body-radiation-induced pumping of the molecules out of trappable quantum states and collisions with residual background gas molecules which usually limit the trap lifetimes. The cold molecules were kept confined on timescales approaching minutes, an improvement of up to two orders of magnitude compared to room-temperature experiments, at translational temperatures on the order of 25 mK. A cryogenic ion trap was built and laser cooled Ca+ ions were confined. This ion trap can be used to confine sympathetically cooled molecular ions such as N+2or H2O+. Furthermore, a mechanism to superimpose both trap centers by moving the permanent magnets from the magnetic trap over the ion trap was developed. Both traps were characterized and their functionality was proven. The challenges of lasercooling in the strong magnetic field gradients were discussed. The present results pave the way for investigations of cold collisions and reactions with very small reaction rates between molecular ions and neutral molecules, for new avenues for the production of ultracold molecules via sympathetic cooling and for the realization of new forms of hybrid matter with co-trapped atoms or ions.
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the sss-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the sss-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to $1 \ensuremath{\mu}\mathrm{K}$ within 30 s.