Stability of triplet rubidium ground-state molecules B. J. Verhaar and S. J. J. M. F. Kokkelmans Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands (Dated: December 19, 2014) Experiments involving ultracold molecules require sufficiently long lifetimes, which can be very short for excited rovibrational states in the molecular potentials. For alkali atoms such as rubidium, molecular, rovibrational ground-states can both be found in the electronic singlet and triplet config- urations. The molecular singlet ground state is absolutely stable, however, the triplet ground state can decay to a deeper bound singlet molecule due to a radiative decay mechanism that involves the interatomic spin-orbit interaction. We investigate this mechanism, and find the lifetime of rubidium molecules in the triplet rovibrational ground-state to be about 13 minutes. This is sufficiently long for experimental purposes. Stable ultracold molecules are of high experimental and theoretical interest [1]. In particular molecules with a permanent electric dipole moment offer the opportu- nity to explore many-body states [2] that are impossible to reach with the isotropic nature of the short-range ul- tracold atomic interactions. One of the routes to create ultracold diatomic molecules is to associate them from ul- tracold atoms. Initially atoms are associated into weakly- bound Feshbach molecules by sweeping a magnetic field across resonance. Subsequently stimulated Raman adia- batic passage (STIRAP) is performed on these molecules to convert them to the molecular ground state of a par- ticular ground state potential [3]. This technique has proven to be very efficient, and in 2008 the first sample of diatomic KRb molecules in the rovibrational ground state was produced [4]. More recently, this also succeeded for RbCs [5, 6], which in contrary to KRb is chemically stable under two-body collision processes [7]. Also non- dipolar Rb 2 [8] and Cs 2 [9] ground-state molecules have been created in this way. The stability of these molecules is crucial for exper- iments, and therefore it is only natural to create the molecules in the absolute ground state. This is the rovi- brational ground state of the electron spin singlet po- tential A 1 Σ u . The singlet potential is energetically very profound, and to reach its ground state via STIRAP, typ- ically an additional laser system is required. However, the spin triplet ground state is much less profound, and can be reached more easily with the laser set-up which is usually present for laser cooling and trapping purposes. While singlet ground-state molecules are absolutely stable with respect to radiative decay, triplet ground- state molecules are not. However, the question is whether the radiative lifetime will be a practical limiting factor to current experiments. Recent experimental and the- oretical work shows that a gas of singlet ground-state molecules has a very short reactive lifetime resulting from 3-body collisions [5, 10]. On the other hand, ground- state triplet Rb 2 molecules produced in an optical lattice [8] are not sensitive to other types of decay apart from the radiative process, and may potentially have a much longer lifetime than the reactive lifetime of the equivalent FIG. 1. Classical picture of the decay mechanism via an inter- atomic spin-orbit interaction. (a) We consider the two atom system to consist of two electrons and two Rb + ions. the ions are indicated by A + and B + , the electrons by 1 and 2. We consider a frame, which is fixed to ion B + , where the z-axis is chosen to be in the direction of the external magnetic field ~ B. The charge +e of B + generates an electric field ~ E at the po- sition of electron 1 (velocity ~v, spin ~s1) near ion A + . (b) Now we consider the same mechanism in the rest frame of electron 1. The interatomic spin-orbit field ~ Bso = -(~v/c 2 ) × ~ E is the result of the velocity -~v of B + . The spin ~s1 precesses in the field ~ B + ~ Bso, inducing a spin flip as a result of the interaction -~ μs · ~ Bso. singlet ground state. In this paper, we investigate the lifetime of the triplet molecular ground state. These molecules are not abso- lutely stable, as the combined electron spin may form a lower energetic singlet configuration. An energy- conserving spin-flip, which would be a result of the mag- netic dipole-dipole interaction [11], has a low probability due to the compact nature of the triplet ground-state molecule. However, there is a more probable spin-flip mechanism arXiv:1412.5799v1 [cond-mat.quant-gas] 18 Dec 2014