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arXiv:1508.02289 · Physical Review A

Dynamics of ultracold dipolar particles in a confined geometry and tilted fields

Goulven Quéméner, Maxence Lepers, Olivier Dulieu

Published Oct 14, 2015• 9 citations

Abstract

We develop a collisional formalism adapted for the dynamics of ultracold dipolar particles in a confined geometry and in fields tilted relative to the confinement axis. Using tesseral harmonics instead of the usual spherical harmonics to expand the scattering wave function, we recover a good quantum number $\ensuremath{\xi}=\ifmmode\pm\else\textpm\fi{}1$ which is conserved during the collision. We derive the general expression of the dipole-dipole interaction in this convenient basis set as a function of the polar and azimuthal angles of the fields. We apply the formalism to the collision of fermionic and bosonic polar KRb molecules in a tilted electric field and in a one-dimensional optical lattice. The presence of a tilted field drastically changes the magnitude of the reactive and inelastic rates as well as the inelastic threshold properties at vanishing collision energies. Setting an appropriate strength of the confinement for the fermionic system, we show that the ultracold particles can even further reduce their kinetic energy by inelastic excitation to higher states of the confinement trap.

DOI: 10.1103/physreva.92.042706

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We develop a collisional formalism adapted for the dynamics of ultracold dipolar particles in a confined geometry and in fields tilted relative to the confinement axis. Using tesseral harmonics instead of the usual spherical harmonics to expand the scattering wave function, we recover a good quantum number

\ensuremath{\xi}=\ifmmode\pm\else\textpm\fi{}1

which is conserved during the collision. We derive the general expression of the dipole-dipole interaction in this convenient basis set as a function of the polar and azimuthal angles of the fields. We apply the formalism to the collision of fermionic and bosonic polar KRb molecules in a tilted electric field and in a one-dimensional optical lattice. The presence of a tilted field drastically changes the magnitude of the reactive and inelastic rates as well as the inelastic threshold properties at vanishing collision energies. Setting an appropriate strength of the confinement for the fermionic system, we show that the ultracold particles can even further reduce their kinetic energy by inelastic excitation to higher states of the confinement trap.

We present a time-independent quantum formalism to describe the dynamics of molecules with permanent electric dipole moments in a two-dimensional confined geometry such as a one-dimensional optical lattice, in the presence of an electric field. Bose versus Fermi statistics and selection rules play a crucial role in the dynamics. As examples, we compare the dynamics of confined fermionic and bosonic polar KRb molecules under different confinements and electric fields. We show how chemical reactions can be suppressed, either by a ``statistical suppression'' which applies for fermions at small electric fields and confinements, or by a ``potential energy suppression,'' which applies for both fermions and bosons at high electric fields and confinements. We also explore collisions that transfer molecules from one state of the confining potential to another. Although these collisions can be significant, we show that they do not play a role in the loss of the total number of molecules in the gas.

We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to

\sqrt{ε/\hbar ω_0}

, where

ε

is the kinetic energy and

ω_0

is the oscillation frequency of the trapped particles in the confinement potential.

Fundamental aspects of ultracold collisions between identical bosonic or fermionic dipoles are studied under quasi-two-dimensional (Q2D) confinement. In the strongly dipolar regime, bosonic and fermion species are found to share important collisional properties as a result of the confining geometry, which suppresses the inelastic rates irrespective of the quantum statistics obeyed. A potential negative is that the confinement causes dipole-dipole resonances to be extremely narrow, which could make it difficult to explore Q2D dipolar gases with tunable interactions. Such properties are shown to be universal, and a simple WKB model reproduces most of our numerical results. In order to shed light on the many-body behavior of dipolar gases in Q2D we have analyzed the scattering amplitude and developed an energy-analytic form of the pseudopotentials for dipoles.

We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one-dimensional confinement and an applied electric field is envisioned.

We consider ultracold collisions of polar molecules confined in a one-dimensional optical lattice. Using a quantum scattering formalism and a frame transformation method, we calculate elastic and chemical quenching rate constants for fermionic molecules. Taking

^{40}\mathrm{K}

^{87}\mathrm{Rb}

molecules as a prototype, we find that the rate of quenching collisions is enhanced at zero electric field as the confinement is increased but that this rate is suppressed when the electric field is turned on. For molecules with 500 nK of collision energy, for realistic molecular densities, and for achievable experimental electric fields and trap confinements, we predict lifetimes for KRb molecules to be

1

s. We find a ratio of elastic to quenching collision rates of about

100

, which may be sufficient to achieve efficient evaporative cooling of polar KRb molecules.

We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-two-dimensional geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ϵ/\ensuremath{\hbar}{\ensuremath{\omega}}_{0}}$, where

ϵ

is the kinetic energy and ${\ensuremath{\omega}}_{0}$ is the oscillation frequency of the trapped particles in the confinement potential.