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arXiv:physics/0008017 · Physical Review A

Inelastic collisions of ultracold polar molecules

John L. Bohn

Published Apr 17, 2001• 80 citations
arXivHTMLPDF

Abstract

The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular $\ensuremath{\Lambda}$ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as ${10}^{\ensuremath{-}20} {\mathrm{cm}}^{3}/\mathrm{sec}$ and as high as ${10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{sec}.$ Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.

DOI
10.1103/physreva.63.052714

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The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as 10\ensuremath−20cm3/sec{10}^{\ensuremath{-}20} {\mathrm{cm}}^{3}/\mathrm{sec}10\ensuremath−20cm3/sec and as high as 10\ensuremath−10cm3/sec.{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{sec}.10\ensuremath−10cm3/sec. Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.
Collisions of polar $^{1}\ensuremath{\Sigma}$ state molecules at ultralow energies are considered, within a model that accounts for long-range dipole-dipole interactions, plus rotation of the molecules. We predict a substantial suppression of dipole-driven inelastic collisions at high values of the applied electric field, namely, field values of several times ${B}_{0}∕\ensuremath{\mu}$. Here B0{B}_{0}B0​ is the rotational constant, and $\ensuremath{\mu}$ is the electric dipole moment of molecules. The sudden large drop in the inelastic cross section is attributed to the onset of degeneracy between molecular rotational levels, which dramatically alters the scattering Hamiltonian. This capability could, in principle, be used to stabilize ultracold gases against collisional losses.
Two elementary models of molecular structure are used to investigate inelastic collisions in cold trapped dipolar gases. A two-state model of a polar molecule (such as one with a Λ-doublet) permits analytic description of the inelastic collision process at energies considerably higher than the gap energy, predicting rate constants and cross sections given by elementary formulae. Alternatively, a three-state model of a rotor molecule in an electric field is investigated, with resultant rate constants and cross sections scaling simply with molecular mass, rotational constant, dipole moment and polarizing field strength. Semiclassical inelastic collision cross sections and rate constants are demonstrated to depend strongly on the model used, especially as regards their dependence on the polarizing field. Inelastic cross sections among doublet dipoles decrease with increasing field strength, while they increase in proportion to the square of the field strength for collisions between rotor dipoles.
Ultracold collisions of polar OH molecules are considered in the presence of an electrostatic field. The field exerts a strong influence on both elastic and state-changing inelastic collision rate constants, leading to clear experimental signatures that should help disentangle the theory of cold molecule collisions. Based on the collision rates, we discuss the prospects for evaporative cooling of electrostatically trapped OH. We also find that the scattering properties at ultralow temperatures prove to be remarkably independent of the details of the short-range interaction, owing to avoided crossings in the long-range adiabatic potential curves. The behavior of the scattering rate constants is qualitatively understood in terms of a novel set of long-range states of the [OH]2[\mathrm{OH}{]}_{2}[OH]2​ dimer.
The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and longrange dipolar interactions.Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7 D. We observe a stepwise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions.Varying the temperature of our sample, we find good agreement with theoretical loss rates assuming complex formation as the main loss process.Our results shed new light on the understanding of complex molecular collisions in the presence of strong dipolar interactions and also demonstrate the versatility of modifying molecular interactions with electric fields.
Inelastic collisions between dipolar molecules, assumed to be trapped in a static electric field at cold (> 10−3K) temperatures, are investigated and compared with elastic collisions. For molecules with a Λ-doublet energy-level structure, a dipole moment arises because of the existence of two nearly degenerate states of opposite parity, and the collision of two such dipoles can be solved entirely analytically in the energy range of interest. Cross sections and rate constants are found to satisfy simple, universal formulas. In contrast, for molecules in a Σ electronic ground state, the static electric field induces a dipole moment in one of three rotational sublevels. Collisions between two rotor dipoles are calculated numerically; the results scale simply with molecule mass, rotational constant, dipole moment, and field strength. It might be expected that any particles interacting only under the influence of the dipole-dipole interaction would show similar behavior; however, the most important and general result of this research is that at cold temperatures inelastic rate constants and cross sections for dipoles depend strongly upon the internal structure of the molecules. The most prominent difference between the Λ-doublet and rotor molecules is variation of the inelastic cross section with applied field strength. For Λ-doublet dipoles, cross sections decrease with increasing field strength. For rotor dipoles, cross sections increase proportionally with the square of field strength. Furthermore, the rate constants of the two types of molecules depend very differently on the angular orientations of the dipoles in the electric field.
Trapped samples of ultracold molecules are often short-lived because close collisions between them result in trap loss. We investigate the use of shielding with static electric fields to create repulsive barriers between polar molecules to prevent such loss. Shielding is very effective even for RbCs, with a relatively low dipole moment, and even more effective for molecules such as NaK, NaRb, and NaCs, with progressively larger dipoles. Varying the electric field allows substantial control over the scattering length, which will be crucial for the stability or collapse of molecular Bose-Einstein condensates. This arises because the dipole-dipole interaction creates a long-range attraction that is tunable with electric field. For RbCs, the scattering length is positive across the range where shielding is effective because the repulsion responsible for shielding dominates. For NaK, the scattering length can be tuned across zero to negative values. For NaRb and NaCs, the attraction is strong enough to support tetra-atomic bound states, and the scattering length passes through resonant poles where these states cross threshold. For KAg and CsAg, there are multiple bound states and multiple poles. For each molecule, we calculate the variation of the scattering length with field and comment on the possibilities for exploring new physics. Published by the American Physical Society 2024