Collective Many-Body Interaction in Rydberg Dressed Atoms

We present a method to control the shape and character of the interaction potential between cold atomic gases by weakly dressing the atomic ground state with a Rydberg level. For increasing particle densities, a crossover takes place from a two-particle interaction into a collective many-body interaction, where the dipole-dipole or van der Waals blockade phenomenon between the Rydberg levels plays a dominant role. We study the influence of these collective interaction potentials on a Bose-Einstein condensate and present the optimal parameters for its experimental detection.

Figure 1

(a) Setup for the ground state dressing with the Rydberg level $|r⟩$ via the intermediate $|p⟩$ state with the corresponding Rabi frequencies and detunings. (b) Diagram showing the crossover from the two-body interaction potential into the regime with a collective many-body interaction. The crossover line is determined by $\Delta \sim -{\Omega }^{4/5}$ (red dashed line), which preempts the condition of weak dressing $\Omega \lesssim |\Delta |$.

Figure 2

(a) Energy functional ${\partial }_n{E}_{\mathrm{eff}}[n]$ for $|\Omega /\Delta |=0.072$. The dashed line describes the behavior at low densities $E_{\mathrm{eff}}[n]=g_{\mathrm{eff}}{n}^2/2$, and its deviation indicates the early breakdown of the two-particle interactions, while the dotted line accounts for the saturation at high densities, although this saturation is very slow. The inset shows the behavior in the blockade radius across the critical density $n_c$ (dotted line is guide to the eye). (b) Behavior of the density profile for a Bose-Einstein condensate with $g_s=0$ and the collective many-body interaction $E_{\mathrm{eff}}^{\prime }[n]$ for increasing particle numbers in a harmonic trap with $\omega =20\mathrm{Hz}$. A characteristic feature is the strong increase of the central density $n(0)$ in contrast to the conventional Thomas-Fermi scaling $n(0)\sim N^{2/5}$.

Figure 3

Density profile $n(r)$ for a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ atoms in a harmonic trap $\omega =100\mathrm{Hz}$ with background scattering length $a_s=5.7\mathrm{nm}$ for increasing influence of the Rydberg dressed interaction. The inset shows the path within the parameter space for increasing interaction strengths.