Magic wavelength

The magic wavelength (also known as a related quantity, magic frequency) is the wavelength of an optical lattice where the polarizabilities of two atomic clock states have the same value, such that the AC Stark shift caused by the laser intensity fluctuation has no effect on the transition frequency between the two clock states.

[1][2] The laser field in an optical lattice induces an electric dipole moment in the atoms to exert forces on them and hence confine them.

However, the difference in polarizabilities of the atomic states leads to an AC Stark shift in the transition frequency between the two states, a shift that is dependent on the laser optical intensity at the particular atom location in the lattice.

Despite having different function forms, the polarizabilities of two atomic states do have a dependency on the wavelength of the laser field.

In some cases, it is then possible to find a particular wavelength at which the two atomic states happen to have exactly the same polarizability.