Interactions between Rydberg-dressed atoms

We examine interactions between atoms continuously and coherently driven between the ground state and a Rydberg state, producing “Rydberg-dressed atoms.” Because of the large dipolar coupling between two Rydberg atoms, a small admixture of Rydberg character into a ground state can produce an atom with a dipole moment of a few debye, the appropriate size to observe interesting dipolar physics effects in cold atom systems. We have calculated the interaction energies for atoms that interact via the dipole-dipole interaction and find that because of blockade effects, the $R$ dependent two-atom interaction terms are limited in size and can be $R$ independent up until the dipolar energy is equal to the detuning. This produces $R$ dependent interactions different from the expected $1/R^3$ dipolar form that have no direct analogy in condensed-matter physics and could lead to interesting quantum phases in trapped Rydberg systems.

Figure 1

The energy levels of the two-atom state for $\Omega /2\pi =10$ MHz, $\delta /2\pi =100$ MHz and (a) $c_3/2\pi =-1000$ MHz $\mu$m${}^3$ and (b) $c_3/2\pi =1000$ MHz $\mu$m${}^3$.

Figure 2

A detail of the interaction energies for the cases shown in Fig. 1. (b) The convergence with an interaction $~1/r^3$ at longer distances.

Figure 3

The energy of the dressed state, for two different interactions: the dipole-dipole that varies as $1/R^3$ (solid) and the Van der Waals that varies as $1/R^6$ (dashed) for $\delta /2\pi =100$ MHz, $c_3/2\pi =1000$ MHz $\mu$m${}^3$, and $c_6/2\pi =500$ MHz $\mu$m${}^6$.

Figure 4

The energy levels of the three-atom system in the two-dimensional configuration for $\Omega /2\pi =10$ MHz, $\delta /2\pi =100$ MHz, and $c_3/2\pi =-1000$ MHz $\mu$m${}^3$.

Figure 5

The energy levels of the three-atom system in the one-dimensional configuration for $\Omega /2\pi =10$ MHz, $\delta /2\pi =100$ MHz, and $c_3/2\pi =-1000$ MHz $\mu$m${}^3$.

Figure 6

The time-dependent evolution of the three eigenstates for atoms separated by $1$ $\mu$m for (a) no atom-atom interactions, (b) nonzero interations but no detuning, and (c) both detuning and interactions. The colors show the evolution of the states $|\mathit{gg}\rangle$ (dashed), $1/\sqrt{2}(|\mathit{gr}\rangle +|\mathit{rg}\rangle )$ (solid), and $|\mathit{rr}\rangle$ (dotted).

Figure 7

The population of the doubly excited state after a pulse of duration $t=16/\Omega$ at different detunings.