Artificial Abelian gauge potentials induced by dipole-dipole interactions between Rydberg atoms

We analyze the influence of dipole-dipole interactions between Rydberg atoms on the generation of Abelian artificial gauge potentials and fields. When two Rydberg atoms are driven by a uniform laser field, we show that the combined atom-atom and atom-field interactions give rise to nonuniform, artificial gauge potentials. We identify the mechanism responsible for the emergence of these gauge potentials. Analytical expressions for the latter indicate that the strongest artificial magnetic fields are reached in the regime intermediate between the dipole blockade regime and the regime in which the atoms are sufficiently far apart such that atom-light interaction dominates over atom-atom interactions. We discuss the differences and similarities of artificial gauge fields originating from resonant dipole-dipole and van der Waals interactions. We also give an estimation of experimentally attainable artificial magnetic fields resulting from this mechanism and we discuss their detection through the deflection of the atomic motion.

Figure 1

Vector plot of ${\mathbf{B}}_a^{+}$ for $\delta /\left|\Omega \right|=0$ and ${\mathbf{k}}_L=(0,0,k_L)$. Color indicates the magnetic field strength, from black (strong magnetic field) to white (zero magnetic field). The blue dot shows the position of the fixed atom with which atom $a$ interacts.

Figure 2

Only nonvanishing component of the dimensionless artificial vector potentials ${\mathbf{A}}_{\alpha }^i/\hslash k_L$ (green dotted curve, $i=1$; blue dashed curve, $i=-$; orange solid curve, $i=+$) as a function of the interatomic distance $r_{ab}/r_c$ for $\delta /\left|\Omega \right|=0$, (top panel) resonant dipole-dipole interactions, and (bottom panel) van der Waals interactions.

Figure 3

The $\phi$-component of the dimensionless magnetic fields ${\mathbf{B}}_a^i/B_0$ (green dotted curve, $i=1$; blue dashed curve, $i=-$; orange solid curve, $i=+$) as a function of the interatomic distance $r_{ab}/r_c$ for $\delta /\left|\Omega \right|=0$, (top panel) resonant dipole-dipole interactions and (bottom panel) van der Waals interactions.

Figure 4

The $\phi$ component of the dimensionless magnetic field ${\mathbf{B}}_a^1/B_0$ as a function of the interatomic distance $r_{ab}/r_c$ for different values of the detuning and RDD interactions. (From bottom to top) $\delta /\left|\Omega \right|=-3,-2,-1,0,1$. (Inset) Largest value of the artificial magnetic field given by the minimum value of its $\phi$ component as a function of the dimensionless detuning $\delta /\left|\Omega \right|$.

Figure 5

The $\phi$ component of the dimensionless magnetic field ${\mathbf{B}}_a^{+}/B_0$ as a function of the interatomic distance $r_{ab}/r_c$ for different values of the detuning and RDD interactions. (From top to bottom) $\delta /\left|\Omega \right|=-3,-2,-1,0,1$. (Inset) Largest value of the artificial magnetic field given by the maximum value of its $\phi$ component as a function of the dimensionless detuning $\delta /\left|\Omega \right|$.

Figure 6

The $\phi$ component of the dimensionless magnetic field ${\mathbf{B}}_a^{-}/B_0$ as a function of the interatomic distance $r_{ab}/r_c$ for different values of the detuning and RDD interactions. (From top to bottom) $\delta /\left|\Omega \right|=-3,-2,-1,0,1$. (Inset) Largest value of the artificial magnetic field given by the minimum value of its $\phi$ component as a function of the dimensionless detuning $\delta /\left|\Omega \right|$.