Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

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

Shinya Yanagimachi, M. Kajiro, 守 町屋, Atsuo Morinaga

Published Mar 14, 2002• 28 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.65.042104

Related papers

Phase shift induced from the dc Stark effect in an atom interferometer comprised of four copropagating laser beams

Atsuo Morinaga, Masato Nakamura, Takayuki Kurosu +1 more

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 $^{3}P_{1}$ state and the $^{1}S_{0}$ state of calcium was obtained to be $\ensuremath{\alpha}(^{3}P_{1})\ensuremath{-}\ensuremath{\alpha}(^{1}S_{0})=(13.4\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{3}$. This value was consistent with that deduced from the Stark frequency shift.

Physical Review A•Jul 1, 1996•29 citations

Atomic multiwave interferometer for Aharonov-Casher-phase measurements

Min-Kang Zhou, Ke Zhang, Xiao‐Chun Duan +3 more

We present an atomic multiwave interferometer with magnetic sublevels to precisely determine the Aharonov-Casher (AC) geometric phase. Simulations show that this interferometer has sharper fringes than a normal two-wave interferometer, which means a higher phase resolution can be achieved. Moreover, atoms evolving in a single hyperfine structure state make the interferometer insensitive to the dc Stark phase shift. This dc Stark shift is one of the main noise sources in AC phase measurements. The constraint of the photon rest mass is also discussed when using this atomic interferometer to measure the Aharonov-Casher phase.

Physical Review A•Feb 24, 2016•6 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.

Physical Review A•Aug 1, 1993•31 citations

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

Tomoya Akatsuka, Yoshihiro Mori, 伸彦 曾根 +3 more

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 A•Aug 25, 2011•4 citations

Electric Aharonov-Bohm effect and multiple beam atom interference

Martin Weitz, M. Mel, Theodor W. Hänsch

Summary form only given. The field of atom interferometry is experiencing rapid progress. Atom interferometers have been used to determine topological phase shifts such as the Aharonov-Bohm or Aharonov-Casher effects. Both two beam and more recently multiple beam atom interferometers have been realized. We report on an investigation of the electric (or scalar) Aharonov-Bohm effect in a multiple beam Ramsey experiment. The topological phase shift leads to collapse and revival of the fringe pattern. In a first interaction region cesium atoms are optically pumped into a dark coherent superposition of the magnetic quantum numbers m/sub F/=-4, -2, 0, 2 and 4 of the 6S/sub 1/2/ (F=4) ground state. The coherent superposition is probed after a time T in a second interaction region. When the atoms are irradiated in between the Ramsey interactions by an additional linearly polarized light field 400 MHz blue detuned to the F=4/spl rarr/F'=4 transition of the cesium D1 line, the induced AC Stark shift increases quadratically with the magnetic quantum number. The laser field coupling to the induced atomic dipole moment causes-in the absence of any classical forces-an electric Aharonov-Bohm phase shift.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Measurement of the Zeeman-like ac Stark shift

Chang Yong Park, Heeso Noh, Chungmok Lee +1 more

We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the $D1$ and $D2$ transition frequencies, with the size of the detuning from the $D2$ resonance twice that from the $D1$ resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.

Physical Review A•Feb 9, 2001•28 citations
An atomic polarizing white-color interferometer composed of the wave packets in the m=+1m=+1m=+1 and m=\ensuremath−1m=\ensuremath{-}1m=\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 \ensuremathα2=2.623\ifmmode±\else\textpm\fi0.015kHz/(kV/cm)2{\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}\ensuremathα2​=2.623\ifmmode±\else\textpm\fi0.015kHz/(kV/cm)2 from the frequency shift between the m=+1m=+1m=+1 and m=\ensuremath−1m=\ensuremath{-}1m=\ensuremath−1 states.
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.
We present an atomic multiwave interferometer with magnetic sublevels to precisely determine the Aharonov-Casher (AC) geometric phase. Simulations show that this interferometer has sharper fringes than a normal two-wave interferometer, which means a higher phase resolution can be achieved. Moreover, atoms evolving in a single hyperfine structure state make the interferometer insensitive to the dc Stark phase shift. This dc Stark shift is one of the main noise sources in AC phase measurements. The constraint of the photon rest mass is also discussed when using this atomic interferometer to measure the Aharonov-Casher phase.
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{(}^{1}(1S0{\mathit{S}}_{0}S0​${\mathrm{\ensuremath{-}}}^{3}$P1{\mathit{P}}_{1}P1​) 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.
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${}^{\ensuremath{-}1}$.
Summary form only given. The field of atom interferometry is experiencing rapid progress. Atom interferometers have been used to determine topological phase shifts such as the Aharonov-Bohm or Aharonov-Casher effects. Both two beam and more recently multiple beam atom interferometers have been realized. We report on an investigation of the electric (or scalar) Aharonov-Bohm effect in a multiple beam Ramsey experiment. The topological phase shift leads to collapse and revival of the fringe pattern. In a first interaction region cesium atoms are optically pumped into a dark coherent superposition of the magnetic quantum numbers m/sub F/=-4, -2, 0, 2 and 4 of the 6S/sub 1/2/ (F=4) ground state. The coherent superposition is probed after a time T in a second interaction region. When the atoms are irradiated in between the Ramsey interactions by an additional linearly polarized light field 400 MHz blue detuned to the F=4/spl rarr/F'=4 transition of the cesium D1 line, the induced AC Stark shift increases quadratically with the magnetic quantum number. The laser field coupling to the induced atomic dipole moment causes-in the absence of any classical forces-an electric Aharonov-Bohm phase shift.
We demonstrate that when laser light is circularly polarized and properly detuned, the ac Stark shift of an alkali-metal atom in its ground state takes the form of a pure Zeeman shift. The condition is satisfied when the laser frequency is between the D1D1D1 and D2D2D2 transition frequencies, with the size of the detuning from the D2D2D2 resonance twice that from the D1D1D1 resonance. The direction of the effective magnetic field is along the laser propagation axis, and its magnitude is proportional to the vector polarizability of the atom and to the laser intensity. We use stimulated Raman spectroscopy on an optically pumped slow atomic beam from a magneto-optical trap to measure the vector polarizability and saturated absorption spectroscopy to show that the scalar polarizability vanishes at the particular detuning.