$$ \frac{\hat{H}}{\hbar}=\frac{\Omega}{2}\sum_j\hat{\sigma}^x_j-\Delta \sum_j\hat{n}j + \sum{j<k}U_{jk} \hat{n}_j \hat{n}_k $$

Theory:

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Fast Quantum Gates for Neutral Atoms, Phys. Rev. Lett. 85, 2208 (2000).

M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles, Phys. Rev. Lett. 87, 037901 (2001).

Experiments:

K. Singer, M. Reetz-Lamour, T. Amthor, L. G. Marcassa, and M. Weidemüller, Suppression of Excitation and Spectral Broadening Induced by Interactions in a Cold Gas of Rydberg Atoms, Phys. Rev. Lett. 93, 163001 (2004). (Cold atom gas)

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Observation of Collective Excitation of Two Individual Atoms in the Rydberg Blockade Regime, Nature Phys 5, 115 (2009). (Single atom tweezer) E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, Observation of Rydberg Blockade between Two Atoms, Nature Phys 5, 110 (2009). (Single atom tweezer)