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Physical Review A

Sensitive measurement of phase shifts due to the ac Stark effect in a Ca optical Ramsey interferometer

Atsuo Morinaga, Toshiharu Tako, Nobuhiko Ito

Published Aug 1, 1993• 31 citations
Publisher

Abstract

We constructed an optical Ramsey atomic interferometer, which has a resolution of 8 fm for the difference between arms of the interferometer, and used it to examine the phase shift due to the ac Stark effect of the excited state of the intercombination line ${(}^{1}$${\mathit{S}}_{0}$${\mathrm{\ensuremath{-}}}^{3}$${\mathit{P}}_{1}$) of Ca. It was clearly observed that the phase shift is in proportion to the field power and in inverse proportion to the detuning frequency of the laser. The proportionality coefficient obtained was in good agreement with the theoretical one.

DOI
10.1103/physreva.48.1364

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Physical Review A•Aug 25, 2011•4 citations
We constructed an optical Ramsey atomic interferometer, which has a resolution of 8 fm for the difference between arms of the interferometer, and used it to examine the phase shift due to the ac Stark effect of the excited state of the intercombination line {(}^{1}$${\mathit{S}}_{0}$${\mathrm{\ensuremath{-}}}^{3}$${\mathit{P}}_{1}) of Ca. It was clearly observed that the phase shift is in proportion to the field power and in inverse proportion to the detuning frequency of the laser. The proportionality coefficient obtained was in good agreement with the theoretical one.
An atomic polarizing white-color interferometer composed of the wave packets in the m=+1m=+1m=+1 and $m=\ensuremath{-}1$ states of the excited 3P1{}^{3}{P}_{1}3P1​ state of Ca, has been developed using a thermal atomic beam excited by a pair of two resonant lights at two separate zones under a homogeneous magnetic field. The interferometer generated the Ramsey fringes as a detuning of the rf frequency between two resonant lights from the Zeeman-frequency shift, while it generates white-color interference fringes as a detuning of laser frequency. The interferometer was used for the direct and short-time measurement of the Aharonov-Casher phase by removing the main part of dc Stark phase shift and without the influence of the frequency fluctuation of a laser. The measured dependence of the Aharonov-Casher phase on the electric field agreed with the predicted one within a relative uncertainty of 2.9%. The tensor polarizability in the 3P1{}^{3}{P}_{1}3P1​ state was determined to be ${\ensuremath{\alpha}}_{2}=2.623\ifmmode\pm\else\textpm\fi{}0.015 \mathrm{k}\mathrm{H}\mathrm{z}/(\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}{)}^{2}$ from the frequency shift between the m=+1m=+1m=+1 and $m=\ensuremath{-}1$ states.
In an optical Ramsey atomic interferometer using Ramsey separated oscillating fields method, AC Stark effect shows that an interference feature is superimposed on the AC Stark level shift dispersion line-shape. This phenomenon has never been observed before. In this report, an analytic expression of the AC Stark shift in optical Ramsey atomic interferometer has been derived, and the numerical result of this interesting feature has been analyzed. Finally, the condition to measure the Interference of AC Stark Effect has been discussed.
We have measured the ac Stark shift of the 4s21S0−−4s4p3P14{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}4s21S0​−−4s4p3P1​ line in 40Ca^{40}\mathrm{Ca}40Ca for perturbing laser wavelengths between 780nm780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}780nm and 1064nm1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}1064nm with a time domain Ramsey-Bord\'e atom interferometer. We found a zero crossing of the shift for the mS=0−−mP=0{m}_{S}=0--{m}_{P}=0mS​=0−−mP​=0 transition and $\ensuremath{\sigma}$ polarized perturbation at 800.8(22)nm800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}800.8(22)nm. The data was analyzed by a model deriving the energy shift from known transition wavelengths and strengths. To fit our data, we adjusted the Einstein AAA coefficients of the 4s3d3D−−4s4p3P4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P4s3d3D−−4s4p3P and 4s5s3S−−4s4p3P4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P4s5s3S−−4s4p3P fine structure multiplets. With these we can predict vanishing ac Stark shifts for the 1S0m=0−−3P1m=1^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=11S0​m=0−−3P1​m=1 transition and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light at 983(12)nm983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}983(12)nm and at 735.5(20)nm735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}735.5(20)nm for the transition to the 3P0^{3}P_{0}3P0​ level.
We observed the phase shift of the atomic wave function induced from the dc Stark effect using an atom interferometer comprised of four copropagating traveling laser beams. We calculated the interference signal for the interferometer in the case of a thermal atomic beam. By comparing the observed interference fringes with the calculated ones, the difference between the polarizabilities of the 3P1^{3}P_{1}3P1​ state and the 1S0^{1}S_{0}1S0​ state of calcium was obtained to be $\ensuremath{\alpha}(^{3}P_{1})\ensuremath{-}\ensuremath{\alpha}(^{1}S_{0})=(13.4\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm3{\mathrm{cm}}^{3}cm3. This value was consistent with that deduced from the Stark frequency shift.
A time-domain atom interferometer with a cold calcium atomic ensemble has been developed with a phase resolution ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}=140/\sqrt{\ensuremath{\tau}}$ mrad/s1/2{}^{1/2}1/2 at the integration time $\ensuremath{\tau}$. Using this atom interferometer, the dispersion-shaped ac Stark phase shift with a sharp reversal on resonance was demonstrated under the perturbation light near the resonance frequency of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{4pt}{0ex}}{m}_{J}=0{\ensuremath{-}}^{3}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{P}_{1},\phantom{\rule{4pt}{0ex}}{m}_{J}=\ensuremath{-}1$ transition. The phase shift was well described by a convolution of functions of the ac Stark potential and a Rabi excitation, and it was found that the lifetime of the 3P1{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}3P1​ state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.
A symmetrical atom interferometer with a thermal calcium atom beam has been developed using a narrow linewidth diode laser stabilized to the resonance of a high-finesse cavity. The linewidth of the diode laser was estimated to be less than 1 Hz relative to the cavity resonance in noise measurement over the range of 100 Hz to 1 MHz, and the phase instability of the interference fringes obtained from the Allan deviation was improved to 2 mrad at an integration time of 300 s. Using this atom interferometer, the ac Stark phase shift between the 1{}^{1}1S0{S}_{0}S0​ and 3{}^{3}3P1{P}_{1}P1​ states of a Ca atom was measured as a function of a laser power near the resonance of the ${}^{1}{S}_{0}{\ensuremath{-}}^{1}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ transition at a wavelength of 423 nm. The decay rate of the 1{}^{1}1P1{P}_{1}P1​ state was determined to be $\ensuremath{\gamma}=1.91(33)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ s${}^{\ensuremath{-}1}$.