Optical binding with cold atoms

Optical binding is a form of light-mediated forces between elements of matter which emerge in response to the collective scattering of light. Such a phenomenon has been studied mainly in the context of the equilibrium stability of dielectric sphere arrays which move amid dissipative media. In this article, we demonstrate that optically bounded states of a pair of cold atoms can exist, in the absence of nonradiative damping. We study the scaling laws for the unstable-stable phase transition at negative detuning and the unstable-metastable one for positive detuning. In addition, we show that angular momentum can lead to dynamical stabilization with infinite-range scaling.

Figure 1

Two atoms evolve in the $z=0$ plane, trapped in 2D by counterpropagating plane waves, with the wave vector orthogonal to that plane. The light exchange between the atoms induces the 2D two-body optically coupled dynamics.

Figure 2

Two-atom equilibrium distance pattern for (a) different $\ell$ and (b) different detunings.

Figure 3

(a) Stability diagram around the equilibrium point $r\approx \lambda$ for the 1D dynamics with $\ell =0$. Free-particle states are found for low laser strength (black region), bound states on the red-detuned side (light blue area), and metastable states on the blue-detuned side (color gradient). (b) Typical dynamics of free-particle, bound, and metastable states around the equilibrium point. Simulations realized with particles with an initial temperature $T=1\mu \text{K}$, as throughout this article.

Figure 4

Logarithm of the escape time $\tau$ vs the detuning for different values of $\mathrm{\Omega }/\mathrm{\Gamma }$. $r\approx \lambda$ for the 1D dynamics with $\ell =0$.

Figure 5

Rotating states for the pair of atoms for (a) and (b) fixed interparticle distance, (c) and (d) vibrational mode, and (e) and (f) metastable state. As the orbits of both atoms coincide in (a), only a single orbit is displayed. Simulations realized with $\ell =0.09, \mathrm{\Omega }/\mathrm{\Gamma }=0.25$, and $T=1\mu \text{K}$, where the ${}^{87}\mathrm{Rb}$ atom mass was adopted.

Figure 6

Stability diagram around the equilibrium point $r\approx \lambda$ for $\ell =0.09$. Free-particle states are found for low pump intensity (black region), bound states on the red-detuned side (light blue), and metastable states in the blue-detuned side, where the color gradient denotes the state lifetime. Simulations realized with particles with an initial temperature $T=1\mu \mathrm{K}$, where the conversion between temperature and velocity was realized using the Rb atom mass.

Figure 7

Stability diagram for the equilibrium point around $r\approx 2\lambda$.