Physical Review A

Dispersion-shaped ac Stark phase shift of Ca intercombination transitions with a time-domain atom interferometer

Tomoya Akatsuka, Kazuya Tanihara, Kenji Komito, Kentaro Ooi, Atsuo Morinaga

Published Aug 28, 2012• 1 citation

Abstract

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/s${}^{1/2}$ 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 ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.

DOI: 10.1103/physreva.86.023418

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

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Wavelength-dependent ac Stark shift of the S01‐P13 transition at 657nm in Ca

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Physical Review AFeb 29, 201625 citations

Physical Review A

Dispersion-shaped ac Stark phase shift of Ca intercombination transitions with a time-domain atom interferometer

Tomoya Akatsuka, Kazuya Tanihara, Kenji Komito, Kentaro Ooi, Atsuo Morinaga

Published Aug 28, 2012• 1 citation

Publisher

Abstract

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/s

{}^{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

{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}

state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.

DOI: 10.1103/physreva.86.023418

Related papers

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

Atsuo Morinaga, Toshiharu Tako, Nobuhiko Ito

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.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.

Physical Review AAug 1, 199331 citations

Thermal calcium atom interferometer with a phase resolution of a few milliradians based on a narrow-linewidth diode laser

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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 ${}^{1}$ ${S}_{0}$ and ${}^{3}$ ${P}_{1}$ 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 ${}^{1}$ ${P}_{1}$ state was determined to be $\ensuremath{\gamma}=1.91(33)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ s${}^{\ensuremath{-}1}$.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}$${S}_{0}$ and ${}^{3}$${P}_{1}$ 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}$${P}_{1}$ state was determined to be $\ensuremath{\gamma}=1.91(33)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ s${}^{\ensuremath{-}1}$.

Physical Review AAug 25, 20114 citations

Wavelength-dependent ac Stark shift of the S01‐P13 transition at 657nm in Ca

C. Degenhardt, Hardo Stoehr, Uwe Sterr +2 more

We have measured the ac Stark shift of the $4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}$ line in $^{40}\mathrm{Ca}$ for perturbing laser wavelengths between $780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with a time domain Ramsey-Bord\'e atom interferometer. We found a zero crossing of the shift for the ${m}_{S}=0--{m}_{P}=0$ transition and $\ensuremath{\sigma}$ polarized perturbation at $800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ . 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 $A$ coefficients of the $4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ and $4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ fine structure multiplets. With these we can predict vanishing ac Stark shifts for the $^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1$ transition and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light at $983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and at $735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for the transition to the $^{3}P_{0}$ level.We have measured the ac Stark shift of the $4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}$ line in $^{40}\mathrm{Ca}$ for perturbing laser wavelengths between $780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with a time domain Ramsey-Bord\'e atom interferometer. We found a zero crossing of the shift for the ${m}_{S}=0--{m}_{P}=0$ transition and $\ensuremath{\sigma}$ polarized perturbation at $800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. 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 $A$ coefficients of the $4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ and $4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ fine structure multiplets. With these we can predict vanishing ac Stark shifts for the $^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1$ transition and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light at $983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and at $735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for the transition to the $^{3}P_{0}$ level.

arXiv:physics/0406018Physical Review AAug 27, 200446 citations

Direct measurement of the Aharonov-Casher phase and tensor Stark polarizability using a calcium atomic polarization interferometer

Shinya Yanagimachi, M. Kajiro, 守町屋 +1 more

An atomic polarizing white-color interferometer composed of the wave packets in the $m=+1$ and $m=\ensuremath{-}1$ states of the excited ${}^{3}{P}_{1}$ 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 ${}^{3}{P}_{1}$ 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 $m=+1$ and $m=\ensuremath{-}1$ states.An atomic polarizing white-color interferometer composed of the wave packets in the $m=+1$ and $m=\ensuremath{-}1$ states of the excited ${}^{3}{P}_{1}$ 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 ${}^{3}{P}_{1}$ 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 $m=+1$ and $m=\ensuremath{-}1$ states.

Physical Review AMar 14, 200228 citations

Interferometry with Ca atoms

F. Riehle, P. Kersten, Th. Kisters +3 more

Separated field excitation of a calcium atomic beam using four traveling laser fields represents two distinct atom interferometers utilizing the internal degrees of freedom of the atoms. Phase shifts between the atomic partial waves have been realized by phase shifts of the laser wave fields, by the ac-Stark shift, and by rotation of the interferometer (Sagnac effect). One particular interferometer can be selected by interaction of the atomic waves with extra laser fields. We furthermore report on the preparation of a laser cooled and deflected calcium atomic beam that can be utilized to largely increase the sensitivity of the interferometer.Separated field excitation of a calcium atomic beam using four traveling laser fields represents two distinct atom interferometers utilizing the internal degrees of freedom of the atoms. Phase shifts between the atomic partial waves have been realized by phase shifts of the laser wave fields, by the ac-Stark shift, and by rotation of the interferometer (Sagnac effect). One particular interferometer can be selected by interaction of the atomic waves with extra laser fields. We furthermore report on the preparation of a laser cooled and deflected calcium atomic beam that can be utilized to largely increase the sensitivity of the interferometer.

European Quantum Electronics Conference (EQEC)Aug 24, 20050 citations

Precision test of the ac Stark shift in a rubidium atomic vapor

Filippo Levi, James C. Camparo, B. Francois +3 more

The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.

Physical Review AFeb 29, 201625 citations

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/s

{}^{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

{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}

state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.

{(}^{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.

{}^{1}

{S}_{0}

and

{}^{3}

{P}_{1}

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}

{P}_{1}

state was determined to be $\ensuremath{\gamma}=1.91(33)\ifmmode\times\else\texttimes\fi{}{10}^{8}$ s${}^{\ensuremath{-}1}$.

We have measured the ac Stark shift of the

4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}

line in

^{40}\mathrm{Ca}

for perturbing laser wavelengths between

780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and

1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

with a time domain Ramsey-Bord\'e atom interferometer. We found a zero crossing of the shift for the

{m}_{S}=0--{m}_{P}=0

transition and $\ensuremath{\sigma}$ polarized perturbation at

800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{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

A

coefficients of the

4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

and

4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

fine structure multiplets. With these we can predict vanishing ac Stark shifts for the

^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1

transition and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light at

983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and at

735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

for the transition to the

^{3}P_{0}

level.

An atomic polarizing white-color interferometer composed of the wave packets in the

m=+1

and $m=\ensuremath{-}1$ states of the excited

{}^{3}{P}_{1}

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

{}^{3}{P}_{1}

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=+1

and $m=\ensuremath{-}1$ states.

^{87}\text{Rb}

0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the

{D}_{1}

absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.