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arXiv:2307.01418 · Physical Review Letters

Sympathetic Cooling and Slowing of Molecules with Rydberg Atoms

Chi Zhang, Seth T. Rittenhouse, Timur V. Tscherbul, H. R. Sadeghpour, Nicholas R. Hutzler

Published Jan 19, 2024• 10 citations
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Abstract

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low-density environment. Molecules traveling at 100 m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.

DOI
10.1103/physrevlett.132.033001

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We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low-density environment. Molecules traveling at 100 m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.
We discuss laser-dressed dipolar and van der Waals interactions between atoms and polar molecules, so that a cold atomic gas with laser admixed Rydberg levels acts as a designed reservoir for both elastic and inelastic collisional processes. The elastic scattering channel is characterized by large elastic scattering cross sections and repulsive shields to protect from close encounter collisions. In addition, we discuss a dissipative (inelastic) collision where a spontaneously emitted photon carries away (kinetic) energy of the collision partners, thus providing a significant energy loss in a single collision. This leads to the scenario of rapid thermalization and cooling of a molecule in the mK down to the μK regime by cold atoms.
This paper reports on calculations of collisional cross sections for the complexes X –C 6 H 6 ( X = 3 He, 4 He, Ne) at temperatures in the range 1 μK–10 K and shows that relatively large cross sections in the 10 3 –10 5 Å 2 range are available for collisional cooling. Both elastic and inelastic processes are considered in this temperature range. The calculations suggest that sympathetically cooling benzene to microkelvin temperatures is feasible using these co-trapped rare gas atoms in an optical trap.
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.
Cooling a range of molecules to ultracold temperatures (<1 mK) is a difficult but important challenge in molecular physics and chemistry. Collective cavity cooling of molecules is a promising method that does not rely on molecular energy level and thus can be applied to all molecules in principle. However, the initial lack of cold molecules leads to the difficulty in its experimental implementation. We show that efficient collective sympathetic cooling of molecules to sub-mK temperatures using a large ensemble of atoms within a cavity is feasible. This approach is a new type of sympathetic cooling which does not rely on direct collisions between atoms and molecules, but utilizes thermalization via their mutual interaction with a cavity field. Two important mechanisms are identified. This include: (1) giant enhancement of cavity optical field from the efficient scattering of the pump light by the atoms; (2) cavity-mediated collective interaction between the atoms and the molecules. We show an optimal cavity detuning for maximizing cooling, which is dependent on the atom and molecule numbers. We determine a threshold for the molecular pump strength and show that it is independent of molecule number when the number of atoms is much greater than the molecules. This can be reduced by orders of magnitude when compared to cavity cooling of single molecular species only. Using this new sympathetic cavity cooling technique, cooling molecules to sub-mK within a high-Q cavity could be within reach of experimental demonstration.
We propose a method to sympathetically cool polar molecules with Rydberg atoms without destroying the quantum information encoded in the polar molecules. While the interactions between the two are usually state-dependent, we show how to engineer state-insensitive interactions between the hot molecules and the cold atoms with a suitable choice of internal states and the application of external fields. The resulting interactions, which may be van der Waals or dipolar, induce a phonon swap interaction between the two species, thereby coherently cooling the polar molecules without affecting the internal state, a process which can be repeated if the atoms are cooled again or new cold atoms are brought in. Our cooling schemes open the possibility of extending quantum computation and simulation times in emerging hybrid tweezer arrays of polar molecules and neutral atoms.
We consider the prospect of using ultracold hydrogen atoms for sympathetic cooling of fluorine atoms to microkelvin temperatures. We carry out quantum-mechanical calculations on collisions between cold F and H atoms in magnetically trappable states and show that the ratio of elastic to inelastic cross sections remains high across a wide range of temperatures and magnetic fields. For F atoms initially in the spin-stretched state (2P3/2{}^{2}{P}_{3/2}2P3/2​, f=mf=+2f={m}_{f}=+2f=mf​=+2), sympathetic cooling appears likely to succeed from starting temperatures around 1 K or even higher. This occurs because inelastic collisions are suppressed by ppp-wave and ddd-wave barriers that are 600 mK and 3.2 K high, respectively. In combination with recent results on H+NH\mathrm{H}+\mathrm{NH}H+NH and H+OH\mathrm{H}+\mathrm{OH}H+OH collisions [M. L. Gonz\'alez-Mart\'{\i}nez and J. M. Hutson, Phys. Rev. Lett. 111, 203004 (2013)], this establishes ultracold H atoms as a very promising and versatile coolant for atoms and molecules that cannot be laser-cooled.