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arXiv:1003.4026 · Physical Review A

Electric field suppression of ultracold confined chemical reactions

Goulven Quéméner, John L. Bohn

Published Jun 9, 2010• 66 citations
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Abstract

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.

DOI
10.1103/physreva.81.060701

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Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2011•0 citations
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 111 s. We find a ratio of elastic to quenching collision rates of about 100100100, which may be sufficient to achieve efficient evaporative cooling of polar KRb molecules.
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 consider ultracold collisions of ground-state heteronuclear alkali-metal dimers that are susceptible to four-center chemical reactions $2AB\ensuremath{\rightarrow}{A}_{2}+{B}_{2}$ even at submicrokelvin temperatures. These reactions depend strongly on species, temperature, electric field, and confinement in an optical lattice. We calculate ab initio van der Waals coefficients for these interactions and use a quantum formalism to study the scattering properties of such molecules under an external electric field and optical lattice. We also apply a quantum threshold model to explore the dependence of reaction rates on the various parameters. We find that, among the heteronuclear alkali-metal fermionic species, LiNa is the least reactive, whereas LiCs is the most reactive. For the bosonic species, LiK is the most reactive in zero field, but all species considered, LiNa, LiK, LiRb, LiCs, and KRb, share a universal reaction rate once a sufficiently high electric field is applied. For indistinguishable bosons, the inelastic/reactive rate increases as d2{d}^{2}d2 in the quantum regime, where ddd is the dipole moment induced by the electric field. This is a weaker power-law dependence than for indistinguishable fermions, for which the rate behaves as d6{d}^{6}d6.
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a C6{C}_{6}C6​ coefficient) for each asymptotic value of partial-wave quantum numbers $|L,{M}_{L}\ensuremath{\rangle}$. From this, the electric-field dependence of the collision rates follows automatically. We present examples for reactive species, such as KRb, and nonreactive species, such as RbCs.
The creation of a gas of ultracold polar molecules with a high phase space density brings new possibilities beyond experiments with ultracold atomic gases. In particular, long-range, anisotropic, and tunable dipole-dipole interactions open the way for novel quantum gases, with applications including strongly correlated many-body systems, and ultracold chemistry. This thesis will present the final steps to complete control over both internal and external degrees of freedom of the molecule which allows us to control, and even completely suppress, the chemical reactions between molecules. First, the control over internal states has been achieved through coherent state transfer to the ro-vibronic ground state and coherent manipulations of the hyperfine and rotational states with microwave radiation. Second, external degrees of freedom are controlled by loading the gas into an optical lattice. With the molecules loaded into a one-dimensional lattice, the orientation of the molecular collisions is controlled by manipulating both internal (hyperfine states) and external (motional states in the direction of tight confinement) degrees of freedom. Most striking is that by preparing the molecules all in the lowest band of the lattice in the same internal state, the molecular collisions can only occur in a side-by-side" orientation, where the chemical reaction rate is suppressed by the repulsive dipole-dipole interactions. The chemical reaction can be suppressed completely by further constraining the motion in the trap in a strong 3D lattice. Here we see lifetimes longer than 20 s, limited by o-resonant light scattering. Finally, the ac polarizability of the molecules is explored and controlled. The different rotational states of the molecule have different polarizabilities and will experience a different trapping force in both the optical dipole trap or lattice. We show that there is a magic angle" between the quantization axis and the polarization of the trapping laser at which the polarizabilities of two different rotational states can be matched, eliminating dephasing and allowing for coherent manipulations between rotational states.
Recent experimental developments in the loading of ultracold KRb molecules into quasi-two-dimensional traps, combined with the ability to tune the ratio between elastic and loss (inelastic, reactive) collisions through application of an external electric field, are opening the door to achieving efficient evaporative cooling of reactive polar molecules. In this paper, we use Monte Carlo simulations and semianalytic models to study theoretically the experimental parameter regimes in which evaporative cooling is feasible under current trapping conditions. We investigate the effect of the anisotropic character of dipole-dipole collisions and reduced dimensionality on evaporative cooling. We also present an analysis of the experimentally relevant antievaporation effects that are induced by chemical reactions that take place when more than one axial vibrational state is populated.
Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.