Microwaves Probe Dipole Blockade and van der Waals Forces in a Cold Rydberg Gas

We show that microwave spectroscopy of a dense Rydberg gas trapped on a superconducting atom chip in the dipole blockade regime reveals directly the dipole-dipole many-body interaction energy spectrum. We use this method to investigate the expansion of the Rydberg cloud under the effect of repulsive van der Waals forces and the breakdown of the frozen gas approximation. This study opens a promising route for quantum simulation of many-body systems and quantum information transport in chains of strongly interacting Rydberg atoms.

Figure 1

(a) Scheme of the central part of the setup with ionization ($I$) and ion deflection ($D$) electrodes. (b) Scheme of the superconducting atom chip. The $U$-shaped $LJ$ wire is used for a MOT trap. The $Z$-shaped $GL$ wire is used for the Ioffe-Pritchard magnetic trap. The $KM$ wire feeds radio frequency for evaporative cooling. The axes $x$,$y$, and $z$ are defined in the two panels. The origin $O$ is at the center of the $Z$ wire $LG$.

Figure 2

Microwave spectra of the $60S–57S$ two-photon transition for (a) $\mathrm{\Delta }=0$, (b) $\mathrm{\Delta }=1\mathrm{MHz}$, (c) $\mathrm{\Delta }=2\mathrm{MHz}$. The dots are experimental with statistical standard deviation error bars and the solid line results from a simple model. The origin of the frequency axis (thin vertical line) corresponds to the resonance position in a low-density cloud.

Figure 3

Rydberg atoms’ interaction energy spectrum, for an excitation laser detuning $\mathrm{\Delta }=1\mathrm{MHz}$, as a function of the delay $\tau$ between atomic preparation and microwave probe (0.5, 10, 15, 20, 30, 50, $100\mu \mathrm{s}$ from bottom to top). The points are experimental (error bars not shown for clarity) and the lines result from the model (see text). The different spectra are shifted vertically by a fixed offset (0.15) for the sake of clarity.

Figure 4

Variation of the average interaction energy as a function of time for (a) $\mathrm{\Delta }=1\mathrm{MHz}$ and (b) $\mathrm{\Delta }=2\mathrm{MHz}$. The points (connected by a solid line for visual convenience) are experimental. The thick dot-dashed line results from our model. The dashed line corresponds to a single Rydberg atom pair expansion model.