[Paper Review] A proposal for sympathetically cooling neutral molecules using cold ions

F. Robicheaux|arXiv (Cornell University)|Jan 27, 2014

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper proposes a novel method for sympathetically cooling neutral molecules with magnetic and electric dipole moments using cold ions in a magnetic field. By exploiting a repulsive 1/r⁴ interaction due to the ion's electric field and Zeeman splitting of molecular states, inelastic collisions are suppressed at low energies, enabling efficient translational cooling of molecules below 1 mK with minimal loss, as demonstrated for OH cooled by Be⁺, Mg⁺, or Ca⁺ ions.

ABSTRACT

We describe a method for cooling neutral molecules that have magnetic and electric dipole moments using collisions with cold ions. An external magnetic field is used to split the ground rovibrational energy levels of the molecule. The highest energy state within the ground rovibrational manifold increases in energy as the distance to the ion decreases leading to a repelling potential. At low energy, inelastic collisions are strongly suppressed due to the large distance of closest approach. Thus, a collision between a neutral molecule and a cold ion will lead to a decrease in the molecule's kinetic energy with no change in internal energy. We present results for the specific case of OH molecules cooled by Be$^+$, Mg$^+$, or Ca$^+$ ions.

Motivation & Objective

• To develop a method for cooling neutral molecules to ultracold temperatures below 1 mK using existing experimental setups.
• To address the challenge of cooling neutral molecules, which lack internal level structures suitable for laser cooling, by leveraging collisions with cold ions.
• To enable efficient cooling of molecules with magnetic and electric dipole moments through adiabatic collisions in a magnetic field.
• To minimize inelastic losses during cooling by exploiting long-range repulsive interactions that suppress internal state transitions.
• To demonstrate the feasibility of achieving degenerate quantum gases of cold molecules using a scalable, ion-assisted cooling mechanism.

Proposed method

• The method uses a cold positive ion (Be⁺, Mg⁺, or Ca⁺) to collide with a neutral molecule (e.g., OH) in a uniform magnetic field of 100–400 G.
• The magnetic field splits the ground rovibrational levels of the molecule, and the ion's electric field induces a repulsive 1/r⁴ potential that increases with decreasing distance.
• The system is treated classically for relative motion, while the internal quantum dynamics of the 8-state molecular system (4 spin states × 2 parity states) are solved via the time-dependent Schrödinger equation using the leapfrog algorithm.
• The interaction potential is modeled as C₄/r⁴ with C₄ derived from molecular polarizabilities, and the inelastic cross section is calculated using a Numerov algorithm for the radial Schrödinger equation.
• The energy loss rate η is computed as a function of kinetic energy, with the differential cross section weighted by (1−cosθ) to account for momentum transfer.
• The method relies on adiabatic following of the highest-energy molecular state, which prevents inelastic transitions at low collision energies.

Experimental results

Research questions

• RQ1 Can cold ions sympathetically cool neutral molecules with magnetic and electric dipole moments below 1 mK through suppressed inelastic collisions?
• RQ2 How does the magnetic field strength affect the suppression of inelastic processes in ion-molecule collisions?
• RQ3 What is the energy dependence of the inelastic collision rate for the 1/r⁴ interaction, and does it remain low at ultracold temperatures?
• RQ4 Can the inelastic loss rate due to molecule-molecule collisions be outpaced by the cooling rate from ion collisions?
• RQ5 Is the classical approximation valid for calculating collision rates at microkelvin and nanokelvin energies?

Key findings

• For a 300 G magnetic field, the inelastic cross section is suppressed by a factor of 10⁵ compared to the elastic cross section when the OH kinetic energy is below 20 mK.
• The energy loss rate η remains nearly constant from 10 mK to 10 nK, scaling as η ∝ v ∫(1−cosθ)(dσ/dcosθ) dcosθ, indicating robust cooling efficiency at ultracold temperatures.
• The quantum energy loss rate for an isotropic 1/r⁴ potential changes by less than 1% between 10 mK and 10 nK, supporting the classical approximation down to μK and nK scales.
• The inelastic collision rate between two OH molecules decreases rapidly with temperature, allowing sympathetic cooling to proceed effectively even as density increases.
• With ion densities as low as 1/10,000 of the OH density, temperatures below 1 mK are achievable, and the ion space charge is a minor perturbation.
• The method is generalizable to other molecules with magnetic and electric dipole moments due to the universal nature of the suppression mechanism in perturbed quantum systems.