Physical Review A

Multistate interferometric measurement of the nonlinear ac Stark shift

Junnosuke Takai, Kosuke Shibata, Naota Sekiguchi, Takuya Hirano

Published May 11, 2023• 2 citations

Abstract

The authors develop an experimental method for measuring the quadratic ac Stark shifts between Zeeman sublevels in an ${}^{87}$Rb Bose--Einstein condensate using a multistate atomic interferometer. The measured quadratic shifts are shown in good agreement with the theoretical calculations. The method could be useful for improving atomic sensors, such as magnetometers and atomic clocks.

DOI: 10.1103/physreva.107.053308

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Physical Review A

Multistate interferometric measurement of the nonlinear ac Stark shift

Junnosuke Takai, Kosuke Shibata, Naota Sekiguchi, Takuya Hirano

Published May 11, 2023• 2 citations

Publisher

Abstract

The authors develop an experimental method for measuring the quadratic ac Stark shifts between Zeeman sublevels in an

{}^{87}

Rb Bose--Einstein condensate using a multistate atomic interferometer. The measured quadratic shifts are shown in good agreement with the theoretical calculations. The method could be useful for improving atomic sensors, such as magnetometers and atomic clocks.

DOI: 10.1103/physreva.107.053308

Related papers

Multi-state interferometric measurement of nonlinear AC Stark shift

Junnosuke Takai, Kosuke Shibata, Naota Sekiguchi +1 more

We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels in an $^{87}$ Rb Bose--Einstein condensate using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin $F = 2$ state due to the light being near-resonant to the D $_1$ line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirms the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near-resonant dual-color light pulses with opposite quadratic shifts.We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels in an $^{87}$Rb Bose--Einstein condensate using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin $F = 2$ state due to the light being near-resonant to the D$_1$ line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirms the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near-resonant dual-color light pulses with opposite quadratic shifts.

arXiv:2206.05465Jun 11, 20220 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.

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Measurement of the ac Stark shift with a guided matter-wave interferometer

Benjamin Deissler, K. J. Hughes, John H. Burke +1 more

The dynamic polarizability of $^{87}\mathrm{Rb}$ atoms was measured using a guided-wave Bose-Einstein condensate interferometer. Taking advantage of the large arm separations obtainable in our device, a well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. The technique requires relatively low laser intensity and works for arbitrary optical frequencies. For off-resonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states.The dynamic polarizability of $^{87}\mathrm{Rb}$ atoms was measured using a guided-wave Bose-Einstein condensate interferometer. Taking advantage of the large arm separations obtainable in our device, a well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. The technique requires relatively low laser intensity and works for arbitrary optical frequencies. For off-resonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states.

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Mark Sadgrove, Yujiro Eto, Sawako Sekine +2 more

We perform atom interferometry using the Zeeman sublevels of a spin-2 Bose-Einstein condensate of $^{87}$ Rb. The observed fringes are strongly peaked, and fringe repetition rates higher than the fundamental Ramsey frequency are found in agreement with a simple theory based on spin rotations. With a suitable choice of initial states, the interferometer could function as a useful tool for magnetometry and studies of spinor dynamics in general.We perform atom interferometry using the Zeeman sublevels of a spin-2 Bose-Einstein condensate of $^{87}$Rb. The observed fringes are strongly peaked, and fringe repetition rates higher than the fundamental Ramsey frequency are found in agreement with a simple theory based on spin rotations. With a suitable choice of initial states, the interferometer could function as a useful tool for magnetometry and studies of spinor dynamics in general.

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Subhadeep Gupta, Kai Dieckmann, Zoran Hadzibabic +1 more

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called "contrast interferometry." Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of h/m and the fine structure constant alpha.

arXiv:cond-mat/0202452Physical Review LettersSep 10, 2002165 citations

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

The authors develop an experimental method for measuring the quadratic ac Stark shifts between Zeeman sublevels in an

{}^{87}

We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels in an

^{87}

Rb Bose--Einstein condensate using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin

F = 2

state due to the light being near-resonant to the D

_1

line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirms the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near-resonant dual-color light pulses with opposite quadratic shifts.

^{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 dynamic polarizability of

^{87}\mathrm{Rb}

atoms was measured using a guided-wave Bose-Einstein condensate interferometer. Taking advantage of the large arm separations obtainable in our device, a well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. The technique requires relatively low laser intensity and works for arbitrary optical frequencies. For off-resonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states.

We perform atom interferometry using the Zeeman sublevels of a spin-2 Bose-Einstein condensate of

^{87}

Rb. The observed fringes are strongly peaked, and fringe repetition rates higher than the fundamental Ramsey frequency are found in agreement with a simple theory based on spin rotations. With a suitable choice of initial states, the interferometer could function as a useful tool for magnetometry and studies of spinor dynamics in general.

{(}^{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.