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Physical Review A

Elimination of the Stark shift from the vibrational transition frequency of optically trapped 174 Yb 6 Li molecules

Masatoshi Kajita, Geetha Gopakumar, Minori Abe, Masahiko Hada

Published Aug 10, 2011• 47 citations
Publisher

Abstract

Transition frequencies of cold molecules must be accurately evaluated to test the variance in the proton-to-electron mass ratio. Measuring the $X{\phantom{\rule{0.16em}{0ex}}}^{2}\ensuremath{\Sigma}(v,N)=(0,0)\ensuremath{\rightarrow}(1,0)$ transition frequency of optically trapped ${}^{174}$Yb${}^{6}$Li molecules is a promising method for achieving this goal. The Stark shifts induced by trap and probe (for the Raman transition) lasers are eliminated by choosing appropriate frequencies (magic frequencies) during the construction of the optical lattice. In the far-off resonance region, the Stark shift is found to be less than 10${}^{\ensuremath{-}16}$ even when the laser frequencies are detuned from the magic frequencies by $\ensuremath{\sim}$1 MHz.

DOI
10.1103/physreva.84.022507

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Transition frequencies of cold molecules must be accurately evaluated to test the variance in the proton-to-electron mass ratio. Measuring the X2\ensuremathΣ(v,N)=(0,0)\ensuremath→(1,0)X{\phantom{\rule{0.16em}{0ex}}}^{2}\ensuremath{\Sigma}(v,N)=(0,0)\ensuremath{\rightarrow}(1,0)X2\ensuremathΣ(v,N)=(0,0)\ensuremath→(1,0) transition frequency of optically trapped 174{}^{174}174Yb6{}^{6}6Li molecules is a promising method for achieving this goal. The Stark shifts induced by trap and probe (for the Raman transition) lasers are eliminated by choosing appropriate frequencies (magic frequencies) during the construction of the optical lattice. In the far-off resonance region, the Stark shift is found to be less than 10\ensuremath−16{}^{\ensuremath{-}16}\ensuremath−16 even when the laser frequencies are detuned from the magic frequencies by \ensuremath∼\ensuremath{\sim}\ensuremath∼1 MHz.
The attainable accuracy of the $X\phantom{\rule{0.16em}{0ex}}{}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}(v,N)=(0,0)\ensuremath{\rightarrow}({v}_{u},0)$ transition frequencies of optically trapped 174{}^{174}174Yb6{}^{6}6Li molecules are analyzed (vu=1,2,3,4)({v}_{u}=1,2,3,4)(vu​=1,2,3,4) to test the variation in the proton-to-electron mass ratio. We eliminate the Stark shifts induced by the trap and Raman lasers by choosing appropriate frequencies (magic frequencies). For vu=1{v}_{u}=1vu​=1 and 2, we obtain more than one experimentally useful magic frequency, thereby leading to more choice in the trap laser. For vu=3{v}_{u}=3vu​=3 and 4, the choice in the trap laser is limited. The systematic frequency uncertainty is given by the trap laser frequency detuning from the magic frequency and the fluctuation of the power ratio of the two Raman lasers and can be lower than 10${}^{\ensuremath{-}16}$ for all these transition frequencies. To obtain lower statistical uncertainty, measurement with vu=4{v}_{u}=4vu​=4 is more advantageous than that with ${v}_{u}=1\ensuremath{-}3$.
Precision measurements of the X 2 Σ( v , N ) = (0, 0) → ( v u , 0) ( v u = 1, 2, 3, 4) transition frequencies from optically trapped 88 Sr 6 Li and 40 Ca 6 Li molecules are proposed, with the intention to test the variation in the proton-to-electron mass ratio m p / m e . The Stark shifts induced by the trap and Raman lasers are eliminated by choosing appropriate frequencies (magic frequencies). These transitions are measurable with an uncertainty lower than 10 −16 and can be used to test the variation in m p / m e , as already shown with 174 Yb 6 Li molecular transitions.
The laser cooling and trapping of molecules have recently been achieved. In this paper, the possibility of precisely measuring the vibrational transition frequencies of optically trapped 40Ca19F molecules is discussed. The quadratic Stark shift induced by the trap laser is eliminated using the trap laser frequencies where the Stark energy shifts at upper and lower states are equal (magic frequencies). At one value of the magic frequency, molecules are trapped at the positions where the power density is minimum, therefore, the measurement is not sensitive to the detuning of the trap laser frequency from the magic frequency. Measurement with an uncertainty of 10−17 appears to be possible using the (v,N,J,F,M)=(0,0,1/2,1,±1)→(1,0,1/2,1,±1)(v,N,J,F,M) = (0,0,1/2,1, \pm 1) \to (1,0,1/2,1, \pm 1)(v,N,J,F,M)=(0,0,1/2,1,±1)→(1,0,1/2,1,±1) transition frequency.
The 2S1/2 (F = 0) - 2F7/2 (F = 3, m F = 0) transition at 467 nm in a single, trapped, laser cooled ion of 171Yb+ has the potential to be an extremely accurate optical frequency reference. Systematic shifts have been evaluated and are currently dominated by the ac-Stark shift. However, this is not expected to be the case as probe laser linewidth is reduced. A heterodyne measurement of the probe laser shows it to have a width of 20 Hz on a 1 minute timescale. The atomic spectrum on the other hand, has been found to have a broadened width of 200 Hz. Using heterodyne detection of light reflected from the trap electrodes, Doppler shifting due to vibration of the trap is identified as the additional source of broadening.
Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the Sr2{\mathrm{Sr}}_{2}Sr2​ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. Sr2{\mathrm{Sr}}_{2}Sr2​ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.