Anomalous excitation facilitation in inhomogeneously broadened Rydberg gases

When atomic gases are laser driven to Rydberg states in an off-resonant way, a single Rydberg atom may enhance the excitation rate of surrounding atoms. This leads to a facilitated excitation referred to as Rydberg antiblockade. In the usual facilitation scenario, the detuning of the laser from resonance compensates the interaction shift. Here, we discuss a different excitation mechanism, which we call anomalous facilitation. This occurs on the “wrong side” of the resonance and originates from inhomogeneous broadening. The anomalous facilitation may be seen in experiments of attractively interacting atoms on the blue detuned side, where facilitation is not expected to appear.

Figure 1

(a) Schematic overview of the two-step excitation mechanism in the incoherent antiblockade regime. Here, an inhomogeneous broadening is indicated by the red shaded region. At the facilitation radius $r_{\mathrm{fac}}$, the detuning compensates the interaction shift, i.e., $\mathrm{\Delta }=V\left(r_{\mathrm{fac}}\right)$. The blockade radius $a_{\mathrm{B}}={(C_{\alpha }/{\gamma }_0)}^{(1/\alpha )}$ is always larger than the facilitation radius $r_{\mathrm{fac}}$. (b) Incoherent excitation rate normalized to the spontaneous decay rate ${\mathrm{\Gamma }}_{\mathrm{s}}$ of the Rydberg state in the presence of one Rydberg excitation with distance $r$ for different detunings $\mathrm{\Delta }$. We set the Rabi frequency $\mathrm{\Omega }=1$ as the natural energy scale and $a=1$ as the characteristic length scale. In these units, the parameters are ${\mathrm{\Gamma }}_{\mathrm{s}}=0.05$, ${\gamma }_0=2$, and $C_6=10\omega$ with linewidth $\omega ={\gamma }_0\sqrt{4{\mathrm{\Omega }}^2/{\mathrm{\Gamma }}_{\mathrm{s}}{\gamma }_0+1}$.

Figure 2

Incoherent excitation rate ${\mathrm{\Gamma }}_{\uparrow }/{\mathrm{\Gamma }}_{\mathrm{s}}(\mathrm{\Delta },r)$ in the presence of one Rydberg atom at distance $r$ with detuning $\mathrm{\Delta }$ for attractive interaction $C_6=-10\omega$ with parameters as in Fig. 1 and $D_6=0.3C_6$. (a) Anomalous facilitation on the blue detuned side and (b) usual facilitation on the red detuned side with attractive interaction. The insets show the excitation profile ${\mathrm{\Gamma }}_{\uparrow }\left(r\right)$ for (a) blue ($\mathrm{\Delta }/\omega =-4$) and (b) red ($\mathrm{\Delta }/\omega =4$) detuning. The white solid line follows $|C_6{/\mathrm{\Delta }|}^{(1/6)}$.

Figure 3

For the same parameters as in Fig. 2 and a cubic lattice with lattice spacing $a$, we determine the total facilitation rate ${\mathrm{\Gamma }}_{\mathrm{fac}}$ for all atoms within a blockade radius $a_{\mathrm{B}}/a\simeq 2$. We determine the region (gray shaded) where both conditions for facilitation (i) ${\mathrm{\Gamma }}_{\mathrm{fac}}>{\mathrm{\Gamma }}_0$ and (ii) ${\mathrm{\Gamma }}_{\mathrm{fac}}>{\mathrm{\Gamma }}_{\mathrm{s}}$ are fulfilled. The blue dashed lines show the facilitation rate for different distances $r_j$ to the excited Rydberg atom. Due to the lattice structure, we encounter a discrete set of resonances. The blue solid line is the total facilitation rate.