arXiv:2201.10435 · Physical Review A

Measurement of the Rb87 D -line vector tune-out wavelength

Adam Fallon, Edward Moan, E. A. Larson, Charles A. Sackett

Published Mar 29, 2022• 3 citations

Abstract

We report a precision measurement of a tune-out wavelength for $^{87}\mathrm{Rb}$ using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.

DOI: 10.1103/physreva.105.l030802

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Obtaining Atomic Matrix Elements from Vector Tune-Out Wavelengths Using Atom Interferometry

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Tune-out wavelength for the thulium atom near 576 nm

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Precision measurement of the Rb87 tune-out wavelength in the hyperfine ground state F=1 at 790 nm

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Polarizabilities and tune-out wavelengths of the hyperfine ground states of Rb87,85

Xia Wang, Jun Jiang, Lu-You Xie +2 more

arXiv:1610.08150Physical Review ANov 23, 201613 citations

Measurement of the tune-out wavelength for Cs133 at 880 nm

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arXiv:2110.00043Physical Review ANov 22, 202115 citations

Observation of vector and tensor light shifts in Rb87 using near-resonant, stimulated Raman spectroscopy

Qingqing Hu, Christian Freier, Yuan Sun +5 more

arXiv:1805.05704Physical Review AJan 29, 201826 citations

arXiv:2201.10435 · Physical Review A

Measurement of the Rb87 D -line vector tune-out wavelength

Adam Fallon, Edward Moan, E. A. Larson, Charles A. Sackett

Published Mar 29, 2022• 3 citations

arXiv HTML PDF

Abstract

We report a precision measurement of a tune-out wavelength for

^{87}\mathrm{Rb}

using circularly polarized light. A tune-out wavelength characterizes a zero in the electric polarizability of the atom. For circularly polarized light, the total polarizability depends on both the scalar and vector polarizability components. This shifts the location of the tune-out wavelength and makes it sensitive to different combinations of atomic dipole matrix elements than the scalar polarizability alone. Using

{\ensuremath{\sigma}}_{\ensuremath{-}}

polarized light with a purity of 0.9931(1), we observe a tune-out wavelength of 785.1522(3) nm, which agrees with theoretical expectations when small contributions from the core electrons and off-resonant valence states are taken into account.

DOI: 10.1103/physreva.105.l030802

Related papers

Obtaining Atomic Matrix Elements from Vector Tune-Out Wavelengths Using Atom Interferometry

Adam Fallon, Charles A. Sackett

Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. To date, tune-out wavelength measurements have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. To date, tune-out wavelength measurements have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.

arXiv:1603.09277AtomsMar 30, 201612 citations

Tune-out wavelength for the thulium atom near 576 nm

Ivan Pyrkh, Arjuna Rudnev, Daniil Pershin +12 more

We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of $575.646_{-0.014}^{+0.016}$ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to $575.646_{-0.004}^{+0.004}$ . Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.We report the theoretical prediction and measurement of a tune-out wavelength for the ground state of the thulium atom in a linearly polarized optical dipole trap with a wavelength of approximately 576 nm. The measurements were conducted using a combination of trap frequency and RF loss spectroscopy, thus making it possible to separate the scalar and tensor parts of the total polarizability without measurements in the range of negative total polarizability. The calculated tune-out wavelength is consistent with the measured one of $575.646_{-0.014}^{+0.016}$ nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to $575.646_{-0.004}^{+0.004}$. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.

physics.atom-phCross-listedarXiv:2602.20726Physical Review AFeb 25, 20260 citations

Precision measurement of the Rb87 tune-out wavelength in the hyperfine ground state F=1 at 790 nm

Felix Schmidt, Daniel Mayer, Michael Hohmann +3 more

We report on a precision measurement of the $D$ line tune-out wavelength of $^{87}\text{Rb}$ in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at $790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ , where the scalar ac Stark shifts of the ${D}_{1}$ and the ${D}_{2}$ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive ${m}_{F}=0$ state was determined to $790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}$ with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.We report on a precision measurement of the $D$ line tune-out wavelength of $^{87}\text{Rb}$ in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at $790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, where the scalar ac Stark shifts of the ${D}_{1}$ and the ${D}_{2}$ lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive ${m}_{F}=0$ state was determined to $790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}$ with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.

arXiv:1512.03578Physical Review AFeb 16, 201656 citations

Polarizabilities and tune-out wavelengths of the hyperfine ground states of Rb87,85

Xia Wang, Jun Jiang, Lu-You Xie +2 more

The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of $^{87,85}\mathrm{Rb}$ have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the $5{s}_{1/2},F=1,2$ states of $^{87}\mathrm{Rb}$ are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the $5{s}_{1/2},F=2$ state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the $5{s}_{1/2},F=2,3$ states of $^{85}\mathrm{Rb}$ are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels ${M}_{F}$ of each hyperfine level $F$ are also determined by considering the contributions of tensor polarizabilities.The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of $^{87,85}\mathrm{Rb}$ have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the $5{s}_{1/2},F=1,2$ states of $^{87}\mathrm{Rb}$ are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the $5{s}_{1/2},F=2$ state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the $5{s}_{1/2},F=2,3$ states of $^{85}\mathrm{Rb}$ are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels ${M}_{F}$ of each hyperfine level $F$ are also determined by considering the contributions of tensor polarizabilities.

arXiv:1610.08150Physical Review ANov 23, 201613 citations

Measurement of the tune-out wavelength for Cs133 at 880 nm

Apichayaporn Ratkata, Philip D. Gregory, Andrew D. Innes +6 more

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$ , ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$ , ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$ . At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

arXiv:2110.00043Physical Review ANov 22, 202115 citations

Observation of vector and tensor light shifts in Rb87 using near-resonant, stimulated Raman spectroscopy

Qingqing Hu, Christian Freier, Yuan Sun +5 more

We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the $^{87}\mathrm{Rb}$ atom $5s$ ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the $5s$ ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum $J$ is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the $^{87}\mathrm{Rb}$ atom $5s$ ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the $5s$ ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum $J$ is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.

arXiv:1805.05704Physical Review AJan 29, 201826 citations

We report a precision measurement of a tune-out wavelength for

^{87}\mathrm{Rb}

{\ensuremath{\sigma}}_{\ensuremath{-}}

575.646_{-0.014}^{+0.016}

nm in air. The existence of the zero in the polarizability for the Tm ground state was confirmed by the trap loss experiment, which also made it possible to refine the tune-out wavelength to

575.646_{-0.004}^{+0.004}

. Despite the presence of an imaginary part of the polarizability at some wavelengths, it was experimentally demonstrated that, with a proper choice of the dipole trap polarization, it was possible to achieve Bose-Einstein condensation of thulium atoms in the range from 575.348 to 575.689 nm, covering the tune-out wavelength.

We report on a precision measurement of the

D

line tune-out wavelength of

^{87}\text{Rb}

in the hyperfine ground state $\left|F=1,{m}_{F}=0,\ifmmode\pm\else\textpm\fi{}1\right\ensuremath{\rangle}$ manifold at

790\phantom{\rule{0.16em}{0ex}}\mathrm{nm}

, where the scalar ac Stark shifts of the

{D}_{1}

and the

{D}_{2}

lines cancel. This wavelength is sensitive to usually neglected contributions from vector and tensor ac Stark shifts, transitions to higher principle quantum numbers, and core electrons. The ac Stark shift is probed by Kapitza-Dirac scattering of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice in free space and controlled magnetic environment. The tune-out wavelength of the magnetically insensitive

{m}_{F}=0

state was determined to

790.01858(23)\phantom{\rule{0.16em}{0ex}}\mathrm{n}\mathrm{m}

with sub-pm accuracy. An in situ absolute polarization, and magnetic background field measurement is performed by employing the ac vector Stark shift for the ${m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ states. Comparing our findings to theory, we get quantitative insight into atomic physics beyond commonly used two-level atom approximations or the neglect of inner shell contributions.

The static and dynamic polarizabilities and the tune-out wavelengths of the ground state of Rb and the hyperfine ground states of

^{87,85}\mathrm{Rb}

have been calculated by using the relativistic configuration interaction plus core polarization (RCICP) approach. It is found that the first primary tune-out wavelengths of the

5{s}_{1/2},F=1,2

states of

^{87}\mathrm{Rb}

are 790.018187(193) and 790.032602(193) nm, respectively, where the calculated result for the

5{s}_{1/2},F=2

state is in good agreement with the latest high-precision measurement 790.032388(32) nm [R. H. Leonard et al., Phys. Rev. A 92, 052501 (2015)]. Similarly, the first primary tune-out wavelengths of the

5{s}_{1/2},F=2,3

states of

^{85}\mathrm{Rb}

are 790.023515(218) and 790.029918(218) nm, respectively. Furthermore, the tune-out wavelengths for the different magnetic sublevels

{M}_{F}

of each hyperfine level

F

are also determined by considering the contributions of tensor polarizabilities.

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the

{D}_{1}

, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and

{D}_{2}

, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for

^{133}\mathrm{Cs}

in the ground hyperfine state

(F=3,{m}_{F}=+3)

. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a

^{133}\mathrm{Cs}

Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

We present the derivation of the frequency-dependent scalar, vector, and tensor dynamical polarizabilities for the two hyperfine levels of the

^{87}\mathrm{Rb}

atom

5s

ground state. Based on the characterization of the dynamical polarizabilities, we analyze and measure the differential vector and tensor light shift between the

5s

ground-state sublevels with near-resonant, stimulated Raman transitions. These results clarify that the tensor polarizabilities for the ground states of alkali atoms are absent when the light field is far detuned from the atomic resonance and the total electronic angular momentum

J

is a good quantum number. In the near-resonant case, the light shifts are nontrivial and the determination of the frequency-dependent vector and tensor dynamic polarizabilities will help to achieve higher fidelities for applications of neutral atoms in quantum information and precision measurements.