Observation of a Resonant Four-Body Interaction in Cold Cesium Rydberg Atoms

Cold Rydberg atoms subject to long-range dipole-dipole interactions represent a particularly interesting system for exploring few-body interactions and probing the transition from 2-body physics to the many-body regime. In this work we report the direct observation of a resonant 4-body Rydberg interaction. We exploit the occurrence of an accidental quasicoincidence of a 2-body and a 4-body resonant Stark-tuned Förster process in cesium to observe a resonant energy transfer requiring the simultaneous interaction of at least four neighboring atoms. These results are relevant for the implementation of quantum gates with Rydberg atoms and for further studies of many-body physics.

Figure 1

Calculated four-atom energy for the two relevant 2-body resonances (${\mathrm{a}}_1$) and (${\mathrm{a}}_2$) and the $p\to d$ 4-body resonance (b) as a function of the electric field.

Figure 2

Thirty-shot-averaged normalized time-of-flight signals for laser excitation to the Stark-mixed $d$, $s$, $p^{\prime }$ and $p$ states. The four traces have been vertically offset for clarity, with the respective zero levels shown as horizontal dashed lines. The electric field is set to $79\mathrm{V}/\mathrm{cm}$, far from any FRET resonance. The gates for the $d$, $s$, and $p$ signals are shown as gray shaded regions.

Figure 3

Number of detected Rydberg atoms as a function of applied electric field. (a) percentage of detected $s$ atoms when exciting the $p$ state. (b) percentage of $d$ detected when exciting the $s$ state. (c) percentage of $d$ detected when exciting the $p$ state. The error bars account for the corrections to the cross talk coefficients, which are larger for $s$ than for $d$, and for the observed field inhomogeneity that affects more the $p$ excitation, leading to larger error bars than in the $s$ excitation case. The results of our calculation for four equidistant atoms are overlaid as dashed blue lines, with the $p\to s$ calculation amplified by a factor of 2 and the $s\to d$ divided by a factor of 3 to coincide with experimental results. The three resonant field values are illustrated by the vertical dotted lines.

Figure 4

Figure (a) shows the number of detected $d$ atoms as a function of the applied electric field for exciting the $p$ (red +) and $s$ (blue ×) states, with an $s$ density comparable or greater in the $s$ excitation than in the $p$ excitation. The on-resonant 4-body process creates more than a factor of 4 more $d$ atoms than the off-resonant $s\to d$ 2-body process at $79.99\mathrm{V}/\mathrm{cm}$. Figure (b) shows the number of detected $d$ atoms when exciting the $p\to s$ resonance for the $|m_J|=1/2$ ($79.94\mathrm{V}/\mathrm{cm}$) and $|m_J|=3/2$ ($88.14\mathrm{V}/\mathrm{cm}$). We observe no significant $d$ state population in the $|m_J|=3/2$ case.

Figure 5

Number of detected Rydberg atoms as the intensity of the Rydberg excitation laser is varied. (a) Number of $d$ atoms as a function of $s$ detected atoms. (b) Number of detected $s$ atoms as a function of the total number of detected Rydberg atoms. (c) Number of $d$ atoms created vs the total number of detected Rydberg atoms. Best fits below $1.6\times {10}^5\mathrm{atoms}$ (demarcated with a vertical dotted line) are shown as the dashed blue lines.