Physical Review A

Zeeman frequency shifts in an optical dipole trap used to search for an electric-dipole moment

Michael V. Romalis, E. Norval Fortson

Published Jun 1, 1999• 69 citations

Abstract

We calculate the Zeeman frequency shifts due to interactions with the light in a far-off-resonance optical dipole trap. These shifts are important for potential use of such a trap to search for an atomic permanent electric-dipole moment (EDM). We present numerical results for Cs and Hg, as examples of paramagnetic and diamagnetic atoms. The vector and tensor light shifts are calculated for a large range of trap optical frequencies, for both red-detuned and blue-detuned traps. We also consider frequency shifts resulting from magnetic dipole and electric quadrupole transitions mixed in by a static electric field. These shifts are particularly important for EDM experiments since they are linear in the electric field. The Zeeman frequency shifts represent a substantial problem for EDM experiments in a dipole trap and must be controlled with care to achieve theoretical sensitivity.

DOI: 10.1103/physreva.59.4547

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Physical Review A

Zeeman frequency shifts in an optical dipole trap used to search for an electric-dipole moment

Michael V. Romalis, E. Norval Fortson

Published Jun 1, 1999• 69 citations

Publisher

Abstract

DOI: 10.1103/physreva.59.4547

Related papers

Design of an atomic physics experiment to search for the electron electric dipole moment

Melanie Kittle

This thesis describes efforts towards the design and construction of an apparatus to measure the electric dipole moment (edm) of the electron. The current experimental bound on the electron edm, d[subscript e], is |d[subscript e]| ≤ 1.6×10⁻²⁷ e·cm [1]. Our system is designed to be sensitive to an electron dipole moment as small as 10⁻²⁹ e·cm. The experiment will use laser-cooled Cs atoms loaded and captured in optical molasses from a separate 2D MOT cold atom source. The atoms diffusing in the optical molasses will be trapped by two side-by-side standing wave, far-off resonance optical dipole force traps. High voltage electrodes will apply opposite polarity electric fields to the two traps. The signature of an edm would be a first-order electric field shift of the atomic Zeeman levels upon reversal of the electric fields. We have paid special attention to the magnetic noise generated by Johnson noise currents of conductors in the design of this apparatusThis thesis describes efforts towards the design and construction of an apparatus to measure the electric dipole moment (edm) of the electron. The current experimental bound on the electron edm, d[subscript e], is |d[subscript e]| ≤ 1.6×10⁻²⁷ e·cm [1]. Our system is designed to be sensitive to an electron dipole moment as small as 10⁻²⁹ e·cm. The experiment will use laser-cooled Cs atoms loaded and captured in optical molasses from a separate 2D MOT cold atom source. The atoms diffusing in the optical molasses will be trapped by two side-by-side standing wave, far-off resonance optical dipole force traps. High voltage electrodes will apply opposite polarity electric fields to the two traps. The signature of an edm would be a first-order electric field shift of the atomic Zeeman levels upon reversal of the electric fields. We have paid special attention to the magnetic noise generated by Johnson noise currents of conductors in the design of this apparatus

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\mathbf{E}

field are also given and there are results for the averaging of the

\mathbf{B}

field in the absence of an

\mathbf{E}

field.

The permanent electric dipole moment (EDM) of the

^{171}\mathrm{Yb}

(I=1/2)

atom is measured with atoms held in an optical dipole trap. By enabling a cycling transition that is simultaneously spin-selective and spin-preserving, a quantum nondemolition measurement with a spin-detection efficiency of 50% is realized. A systematic effect due to parity mixing induced by a static

E

field is observed, and is suppressed by averaging between measurements with optical dipole traps in opposite directions. The coherent spin precession time is found to be much longer than 300 s. The EDM is determined to be $d(^{171}\mathrm{Yb})=\phantom{\rule{0ex}{0ex}}(\ensuremath{-}6.8\ifmmode\pm\else\textpm\fi{}{5.1}_{\text{stat}}\ifmmode\pm\else\textpm\fi{}{1.2}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\text{ }\text{ }e\text{ }\mathrm{cm}$, leading to an upper limit of $|d(^{171}\mathrm{Yb})|<1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{ }e\text{ }\mathrm{cm}$ (95% C.L.). These measurement techniques can be adapted to search for the EDM of

^{225}\mathrm{Ra}

m=0

magnetic sublevel, the shot-noise-limited uncertainty of these measurements is

1/\sqrt{2F(F+1)}

smaller than that of a Larmor precession measurement. When the populations in the even (or odd) magnetic sublevels are combined, we show that these measurements are independent of the tensor Stark shift and the second order Zeeman shift. We discuss the complicating effect of a transverse magnetic field and show that when the ratio of the tensor Stark shift to the transverse magnetic field is sufficiently large, an EDM measurement with atoms initialized in the superposition of the stretched states can reach the optimal sensitivity.