Shaping interactions between polar molecules with far-off-resonant light

We show that dressing polar molecules with a far-off-resonant optical field leads to new types of intermolecular potentials, which undergo a crossover from the inverse power to oscillating behavior depending on the intermolecular distance, and whose parameters can be tuned by varying the laser intensity and wavelength. We present analytic expressions for the potential energy surfaces, thereby providing direct access to the parameters of an optical field required to design intermolecular interactions experimentally.

Figure 1

Lowest rotational energy levels of a molecule in a far-off-resonant laser field, depending on the field-strength parameter $\Delta \eta$. Different colors correspond to $M=0$ (black), 1 (red), and 2 (blue). Energy is in units of $B$; the two lowest tunneling doublets are labeled as $\mathrm{J̃},M$. For $\Delta \eta \gtrsim 15$ the splitting of the lowest tunneling doublet can be accurately estimated as $\Delta E=\left|E\right|\exp (3.6636-2\sqrt{\Delta \eta })$, with $E=2\sqrt{\Delta \eta }-\Delta \eta -1$ [12].

Figure 2

Short-range behavior of optically induced KRb-KRb potentials in the $\mathit{XZ}$ plane ($\varphi =0$), for different values of $\Delta \eta$. Left and right columns correspond, respectively, to the ground $|\tilde{0}0,\tilde{0}0\rangle$ state, and excited $|\tilde{1}0,\tilde{1}0\rangle$ state potentials, as given by Eq. (16). The dependence of the short-range potentials on $\varphi$ is negligible. Potential energy is in units of $B$, with $V_{\mathrm{eff}}(r\to \infty )$ chosen as zero. The laser beam propagates along the $Y$ axis, $\mathbf{k}\parallel \stackrel{\wedge }{\mathbf{Y}}$, with the polarization $\stackrel{\wedge }{\mathbf{e}}\parallel \stackrel{\wedge }{\mathbf{Z}}$. See text.

Figure 3

Long-range behavior of the ground $|\tilde{0}0,\tilde{0}0\rangle$ state potentials in the $\mathit{XZ}(\varphi =0)$ and $\mathit{YZ}(\varphi =\pi /2)$ planes, for $\Delta \eta =100$. Long-range behavior is similar for the excited $|\tilde{1}0,\tilde{1}0\rangle$ state, the magnitude of the oscillations scales with $\Delta \eta$, as given by Eq. (18). Potential energy is in units of $B$, with $V_{\mathrm{eff}}(r\to \infty )$ chosen as zero. The laser beam propagates along the $Y$ axis, $\mathbf{k}\parallel \stackrel{\wedge }{\mathbf{Y}}$, with the polarization $\stackrel{\wedge }{\mathbf{e}}\parallel \stackrel{\wedge }{\mathbf{Z}}$. See text.