Catalysis of Stark-tuned interactions between ultracold Rydberg atoms

We have experimentally investigated a catalysis effect in the resonant energy transfer between ultracold ${}^{85}\mathrm{Rb}$ Rydberg atoms. We studied the time dependence of the process, $34p+34p\to 34s+35s$, and observed an enhancement of $34s$ state population when $34d$ state atoms are added. We have also performed numerical model simulations, which are in qualitative agreement with experiment and indicate that the enhancement arises from a redistribution of $p$-state atoms due to the presence of the $d$-state atoms.

Figure 1

(a) Förster resonance for the process $34p_{3/2,|m_j|=1/2}+34p_{3/2,|m_j|=1/2}\to 34s_{1/2}+35s_{1/2}$. The polarization of the excitation laser is in the $z$ direction. (b) The polarization of the excitation laser is in the $x$ direction. Inset: Stark structures of the pair states for $34p+34p\to 34s+35s$ resonant energy-transfer interaction.

Figure 2

Interaction time dependence of the $34s$ state population for the resonance of $34p_{3/2,|m_j|=3/2}+34p_{3/2,|m_j|=3/2}\to 34s_{1/2}+35s_{1/2}$ with ($•$) and without ($\square$) excitation of the $34d$ state atoms.

Figure 3

Ratio of the $34s$ state population vs interaction time with and without $34d$ included in the interaction for the resonant energy-transfer process: (a) $34p_{3/2,|m_j|=1/2}+34p_{3/2,|m_j|=1/2}\to 34s_{1/2}+35s_{1/2}$, (b) $34p_{3/2,|m_j|=3/2}+34p_{3/2,|m_j|=1/2}\to 34s_{1/2}+35s_{1/2}$, and (c) $34p_{3/2,|m_j|=3/2}+34p_{3/2,|m_j|=3/2}\to 34s_{1/2}+35s_{1/2}$. Inclusion of the $34d$ atoms alters the time evolution of the energy-transfer process, especially at early times.

Figure 4

Simulated $34s$ signal for cases including three $34p$ atoms, a number of $34d$ atoms ranging from 0 to 22, and electric-field gradients from 0 to $0.2\mathrm{kHz}/\mu \mathrm{m}$. The signal is expressed as a ratio to the case with no $34d$ atoms and averaged over $20\mu \mathrm{s}$ with lighter shades of gray indicating larger enhancement, as shown in the legend. The atoms are evenly spaced along a line with length varied between 50 and $100\mu \mathrm{m}$. The position of each atom is randomly perturbed by a few microns and we average over 20 instances for each unique set of parameters. The dipole moments used are similar to the experimental values. The simulation indicate a wide range of parameters for which enhancement might be visible.

Figure 5

The $34s$ fraction at an electric-field gradient of $100\mathrm{Hz}/\mu \mathrm{m}$ for two coaxial 80-$\mu \mathrm{m}$-long cylinders. Four $34p$ atoms are randomly distributed over a volume with radius $9\mu \mathrm{m}$ and six $34d$ atoms are randomly distributed over a volume of radius $5.5\mu \mathrm{m}$. The time step is $0.05\mu \mathrm{s}$ and we average over 8000 instances. The $p\to s$ dipole moments are set to $120e{a}_0$ and the $p\to d$ dipole moment is set to $50e{a}_0$. (a) The fraction for the case with no $34d$ atoms is shown as a dashed blue line and the signal with $34d$ atoms is shown as a solid red line. (b) The ratio of the two signals, showing enhancement that is most significant at earlier times. (c) A closer view of the early time behavior, showing where the enhancement is most pronounced.