Antiblockade in Rydberg Excitation of an Ultracold Lattice Gas

It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to efficiently solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the observed excitation blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is most pronounced for atoms arranged on a lattice. Since the effect is robust against a large number of lattice defects it should be experimentally realizable with an optical lattice created by ${\mathrm{CO}}_2$ lasers.

Figure 1

Sketch of the two-step excitation scheme.

Figure 2

The population $P_e$ of the Rydberg state $|e⟩$ in the three-level system of Fig. 1 according to the equation (2) (solid) and the optical Bloch equation (dashed) for different pulse lengths $\tau$. The parameters are $\Omega =4$, $\omega =0.2$, $\Gamma =6\mathrm{MHz}$ for the left set (a)–(d) and $\Omega =22.1$, $\omega =0.8$, $\Gamma =6\mathrm{MHz}$ for the right set (e)–(h).

Figure 3

The fraction of Rydberg atoms $f_e$ as a function of increasing excitation $n$ and for laser pulse lengths of 0.5 (dashed line), 1 (dotted line), 2 (solid line), and $5\mu \mathrm{s}$ (dotted-dashed line). The density of the ultracold gas is $\rho =8\times {10}^9{\mathrm{cm}}^{-3}$, and the laser parameters are $\Omega =22.1$, $\omega =0.8$, $\Gamma =6\mathrm{MHz}$.

Figure 4

The fraction of excited Rydberg atoms $f_e$ as a function of increasing excitation $n$ for atoms regularly arranged in a three-dimensional simple cubic lattice with lattice constant $5\mu \mathrm{m}$ ($\rho =8\times {10}^9{\mathrm{cm}}^{-3}$) and parameters as in Fig. 3; (a) perfect filling of lattice sites, (b) 20% lattice defects (i.e., empty lattice sites). The inset in (a) shows the peak of $f_e$ corresponding to atom spacing $a_2$ (see text) as function of the inverse lattice constant $a^{-1}$ at $n=82$ and $\tau =2\mu \mathrm{s}$.

Figure 5

Boundary in $\omega \mathrm{\text{−}}\Omega$ space between the blockade (upper area) and the antiblockade (lower area) regime for different pulse lengths and fixed $\Gamma =6\mathrm{MHz}$. The dashed lines are the linear approximations for $\Omega \gg \omega$, see text. The parameters of Fig. 2 are indicated by black dots.