Quasi-universal dipolar scattering in cold and ultracold gases

We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from universality are expected to occur in the intermediate energy range.We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from universality are expected to occur in the intermediate energy range.

arXiv:0901.1281New Journal of PhysicsMay 14, 2009111 citations

Inelastic semiclassical collisions in cold dipolar gases

M. J. Cavagnero, Catherine Newell

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.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.

New Journal of PhysicsMay 14, 200910 citations

Energy dependence of scattering ground-state polar molecules

Christopher Ticknor

We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on $\mathrm{RbCs}$ and $\mathrm{RbK}$ . An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total $M$ to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on $\mathrm{RbCs}$ and $\mathrm{RbK}$. An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total $M$ to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.

arXiv:0707.3003Physical Review ANov 7, 200722 citations

Universal resonant ultracold molecular scattering

Vladimir Roudnev, M. J. Cavagnero

The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.

arXiv:0806.1982Physical Review AJan 9, 200931 citations

s -wave-scattering resonances induced by dipolar interactions of polar molecules

Zhe-Yu Shi, Ran Qi, Hui Zhai

We show that the $s$ -wave-scattering resonances induced by dipolar interactions in polar molecular gases have a universal large and positive effective range, which is very different from Feshbach resonances previously realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequences in many-body physics. At a high-temperature regime, a positive effective range gives rise to a stronger repulsive interaction energy for positive scattering length, and a weaker attractive interaction energy for negative scattering length. At low temperatures, we study a polaron problem formed by a single-impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are opposite to narrow Feshbach resonances, where the effective range is negative.We show that the $s$-wave-scattering resonances induced by dipolar interactions in polar molecular gases have a universal large and positive effective range, which is very different from Feshbach resonances previously realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequences in many-body physics. At a high-temperature regime, a positive effective range gives rise to a stronger repulsive interaction energy for positive scattering length, and a weaker attractive interaction energy for negative scattering length. At low temperatures, we study a polaron problem formed by a single-impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are opposite to narrow Feshbach resonances, where the effective range is negative.

arXiv:1108.3510Physical Review AFeb 27, 201216 citations

INELASTIC COLLISIONS IN COLD DIPOLAR GASES

Catherine Newell

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.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.

Bulletin of the American Physical SocietyJan 1, 20100 citations

We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on

\mathrm{RbCs}

and

\mathrm{RbK}

. An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total

M

to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.

We show that the

s

-wave-scattering resonances induced by dipolar interactions in polar molecular gases have a universal large and positive effective range, which is very different from Feshbach resonances previously realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequences in many-body physics. At a high-temperature regime, a positive effective range gives rise to a stronger repulsive interaction energy for positive scattering length, and a weaker attractive interaction energy for negative scattering length. At low temperatures, we study a polaron problem formed by a single-impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are opposite to narrow Feshbach resonances, where the effective range is negative.