We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped $^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped $^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

arXiv:0912.1528Physical Review AMar 29, 201065 citations

Magic wavelengths for the np−ns transitions in alkali-metal atoms

Bindiya Arora, Marianna S. Safronova, Charles W. Clark

Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest $ns$ , $n{p}_{1∕2}$ , $n{p}_{3∕2}$ states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find ``magic'' wavelengths in alkali-metal atoms for which the $ns$ and $n{p}_{1∕2}$ and $n{p}_{3∕2}$ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest $ns$, $n{p}_{1∕2}$, $n{p}_{3∕2}$ states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find ``magic'' wavelengths in alkali-metal atoms for which the $ns$ and $n{p}_{1∕2}$ and $n{p}_{3∕2}$ atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.

arXiv:0709.0130Physical Review ANov 15, 200794 citations

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped

^{87}\mathrm{Rb}

atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

ns

n{p}_{1∕2}

n{p}_{3∕2}

states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states of alkali-metal atoms. We find ``magic'' wavelengths in alkali-metal atoms for which the

ns

and

n{p}_{1∕2}

and

n{p}_{3∕2}

atomic levels have the same ac Stark shifts, which facilitates state-insensitive optical cooling and trapping.