Photoinduced Two-Body Loss of Ultracold Molecules

The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of $\mathrm{NaK}+\mathrm{NaK}$ collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.

Figure 1

A one-dimensional cut of the $\mathrm{NaK}+\mathrm{NaK}$ PESs for the ground state and several excited states. The geometry is $r_1=r_2=6.9$ $a_0$, ${\theta }_1=3\pi /4$, ${\theta }_2=\pi /4$, $\varphi =\pi$. Ab initio points were calculated over the entire range of $R$ with intervals of $0.5a_0$. The dashed line indicates the ground state energy curve plus the photon energy $\hslash \omega$ of a 1064 nm laser. With this geometry, the complex has a $C_{2h}$ symmetry. The colors in the graph correspond to the irreducible representations of the states, blue for $A_g$, green for $A_u$, red for $B_u$, and cyan for $B_g$.

Figure 2

A one-dimensional cut of two $\mathrm{NaK}+\mathrm{NaK}$ squared-TDM surfaces. The geometry is $r_1=r_2=6.9a_0$, ${\theta }_1=3\pi /4$, ${\theta }_2=\pi /4$, and $\varphi =\pi$. The TDMs plotted are those between the ground state and the first two excited states with $B_u$ symmetry, corresponding to the red lines in Fig. 1. The black line corresponds to the sum of those two squared TDMs.

Figure 3

The calculated laser excitation rate to the first three excited states as a function of the laser photon energy $\hslash \omega$. The vertical black dotted lines indicate the energies of the $10\mu \mathrm{m}$, 1550 nm, and 1064 nm lasers. To calculate ${\mathrm{\Gamma }}_{\text{laser}}$, a trap depth of $10\mu \mathrm{K}$ was used. For the above wavelengths, this corresponds to laser intensities of 12.6, 10.2, and $7.3\mathrm{kW}{\mathrm{cm}}^{-2}$, respectively. The grey shaded region indicates the error margin, which is estimated as described in the Supplemental Material [32].

Figure 4

The laser-excitation lifetime, ${\tau }_{\text{laser}}$ (in the blue, left-hand axis, for a 1064 nm laser) and the half-life of NaK molecules in a crossed optical dipole trap, ${\tau }_{\mathrm{NaK}}$ (in the red, right-hand axis), as a function of the laser intensity. The solid, dashed, and dashed-dotted red lines show results obtained using the full ab initio TDM surfaces for 1064 nm, 1550 nm, and $10\mu \mathrm{m}$, respectively. The red shaded areas indicate the estimated error [32]. The vertical black dotted line indicates a typical experimental laser intensity of $10\mathrm{kW}{\mathrm{cm}}^{-2}$. We used an initial molecule density of $0.4\times {10}^{11}{\mathrm{cm}}^{-3}$, temperature of 500 nK, and $p$-wave diatom-diatom collision rate of $3\times {10}^{-11}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. The NaK lifetime, ${\tau }_{\mathrm{NaK}}$, accounts for both laser excitation and sticking-amplified three-body loss.