Probing the interaction between Rydberg-dressed atoms through interference

We study the dynamics of an atomic Bose-Einstein condensate in an optical lattice in which the electronic ground state of each atom is weakly coupled to a highly excited Rydberg state by a far off-resonant laser. This dressing induces a switchable effective soft-core interaction between ground-state atoms which, in the lattice, gives rise to on-site as well as long-range interaction terms. Upon switching on the dressing laser the coherence properties of the atomic superfluid undergo a nontrivial collapse and revival dynamics which can be observed in the interference pattern that is created after a release of the atoms from the optical lattice. This interference signal strongly depends on the strength and the duration of the dressing laser pulse and can be used to probe and characterize the effective interaction between Rydberg-dressed atoms.

Figure 1

(a) Schematics of the two-photon coupling between the ground state and Rydberg state. The laser which couples the state $|g\rangle$ to the intermediate $|P\rangle$ state is far detuned from resonance such that the ground state $|g\rangle$ and the Rydberg $|nS\rangle$ state form an effective two-level system. Here $\Omega$ is the effective Rabi frequency and $\Delta$ the (two-photon) detuning of the excitation laser frequencies with respect to the atomic transition. (b) Effective interaction potential between dressed atoms and its length scales in relation to the optical lattice. At short distances ($R\ll R_{\mathrm{c}}$) the interaction potential is constant and at large distances ($R\gg R_c$) it is of van der Waals type. (c,d,e) Envisioned experimental sequence and timings. First (c), a BEC is prepared in an optical lattice. Second (d), an off-resonant laser coupling the ground state to the Rydberg state is applied for a certain time. After the excitation laser pulse, the optical lattice is switched off immediately and the dressed ground-state atoms expand freely. Finally (e), interference patterns are recorded by taking absorption images of the expanded atomic cloud.

Figure 2

(a) Dynamical evolution of $F_2\left(t\right)$ for various values of $d/R_c$. (b, c) Dotted curves show calculations merely taking into account the on-site and nearest-neighbor interactions. Solid lines show calculations including all interactions up to next-next-nearest neighbors.

Figure 3

Quasimomentum distribution of $N=82$ atoms released from a one-dimensional optical lattice with $L=41$ sites. (a) On-site interaction only [i.e., $\gamma \left(m\right)=0$ (corresponding to $d/R_c\gg 1$)]. (b) On-site and nearest-neighbor interactions for $d/R_c=1.5$ ($\gamma \left(1\right)\approx 0.08g$). (c,d) Cuts through $S\left(k_x\right)$ at different values of the quasimomentum. The panels show cuts along (c) $k_x=0$ and (d) $k_x=\pi$. The solid and dashed curves correspond to the parameters of panels (a) and (b).

Figure 4

Natural logarithm of the quasimomentum distribution $S\left(\mathbf{k}\right)$ of atoms released from a two-dimensional $15\times 15$ lattice and an average particle number in each sites of ${\left|\alpha \right|}^2=2$. The figures show snapshots taken different times: (a,d) $gt=0$, (b,e) $gt=\pi /2$, and (c,f) $gt=2\pi$. Panels (a)–(c) show data that have been obtained by taking only on-site interactions into account. The data shown in panels (d)–(f) include also nearest-neighbor interactions.