Physical Review A

Comment on “Nondestructive light-shift measurements of single atoms in optical dipole traps”

Margaret E. Shea, Daniel J. Gauthier

Published Aug 11, 2017• 1 citation

Abstract

The light shift caused by an optical dipole force trap on a single $^{87}\mathrm{Rb}$ atom was recently studied by Shih and Chapman [Phys. Rev. A 87, 063408 (2013)] using a dipole-matrix-element-based approach. A separate study by Neuzner et al. [Phys. Rev. A 92, 053842 (2015)] considered the same system using a polarizability-based approach. We find that the results of these two studies do not agree, which we ascribe to an error in the theoretical part of Shih and Chapman's paper. We correct this error, offer an alternative formulation for the energy-level shift using the matrix-element-based approach, and find good agreement between our predictions and those obtained with the polarizability-based method. Furthermore, our predictions are in better agreement with Shih and Chapman's experimental results in comparison to their predictions. In contrast to the polarizability-based method, our formulation can be easily extended to different trapping wavelengths and atomic species.

DOI: 10.1103/physreva.96.027401

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Reply to “Comment on ‘Nondestructive light-shift measurements of single atoms in optical dipole traps’ ”

Chung-Yu Shih, Michael Chapman

This reply is in response to the comment by Shea and Gauthier on our paper [Phys. Rev. A 87, 063408 (2013)].Received 6 July 2017DOI:https://doi.org/10.1103/PhysRevA.96.027402©2017 American Physical Society

Physical Review AAug 11, 20170 citations

Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and the determination of atomic dipole matrix elements

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Experimental and Theoretical Study of Dynamic Polarizabilities in the 5S1/2 – 5D5/2 Clock Transition in Rubidium-87 and Determination of Electric Dipole Matrix Elements

Rhona Hamilton, Benjamin M. Roberts, Sarah K. Scholten +4 more

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Floquet theory for atomic light-shift engineering with near-resonant polychromatic fields

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Nondestructive light-shift measurements of single atoms in optical dipole traps

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arXiv:1304.3346Physical Review AJun 10, 201342 citations

Eliminating light shifts for single atom trapping

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Physical Review A

Comment on “Nondestructive light-shift measurements of single atoms in optical dipole traps”

Margaret E. Shea, Daniel J. Gauthier

Published Aug 11, 2017• 1 citation

Publisher

Abstract

The light shift caused by an optical dipole force trap on a single

^{87}\mathrm{Rb}

atom was recently studied by Shih and Chapman [Phys. Rev. A 87, 063408 (2013)] using a dipole-matrix-element-based approach. A separate study by Neuzner et al. [Phys. Rev. A 92, 053842 (2015)] considered the same system using a polarizability-based approach. We find that the results of these two studies do not agree, which we ascribe to an error in the theoretical part of Shih and Chapman's paper. We correct this error, offer an alternative formulation for the energy-level shift using the matrix-element-based approach, and find good agreement between our predictions and those obtained with the polarizability-based method. Furthermore, our predictions are in better agreement with Shih and Chapman's experimental results in comparison to their predictions. In contrast to the polarizability-based method, our formulation can be easily extended to different trapping wavelengths and atomic species.

DOI: 10.1103/physreva.96.027401

Related papers

Reply to “Comment on ‘Nondestructive light-shift measurements of single atoms in optical dipole traps’ ”

Chung-Yu Shih, Michael Chapman

Physical Review AAug 11, 20170 citations

Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and the determination of atomic dipole matrix elements

Jeff A. Sherman, A. Andalkar, Warren Nagourney +1 more

We have measured the ratio $R$ of the vector ac Stark effect (or light shift) in the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at $514.531\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ $m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at $1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ , $R=+0.4176(8)$ . These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.We have measured the ratio $R$ of the vector ac Stark effect (or light shift) in the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at $514.531\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ $m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at $1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, $R=+0.4176(8)$. These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.

arXiv:0808.1826Physical Review ANov 26, 200835 citations

Experimental and Theoretical Study of Dynamic Polarizabilities in the 5S1/2 – 5D5/2 Clock Transition in Rubidium-87 and Determination of Electric Dipole Matrix Elements

Rhona Hamilton, Benjamin M. Roberts, Sarah K. Scholten +4 more

The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$ -- $5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$ -- $5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$ -- $5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$--$5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$--$5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$--$5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.

arXiv:2212.10743Physical Review AppliedMay 18, 20239 citations

Floquet theory for atomic light-shift engineering with near-resonant polychromatic fields

Simon Coop, Silvana Palacios, Pau Gomez +3 more

Optical trapping of atoms employs high-intensity fields that necessarily alter atomic level structure. The calculation of light shifts by perturbation theory fails for scenarios that arise, for example, when the trapping light is near an excited-state transition or for polychromatic fields. We show here that non-perturbative methods based on Floquet’s theorem elegantly handle such scenarios. We compare our calculation to precision absorption spectroscopy on cold 87Rb atoms in a bichromatic optical dipole trap at 1560 + 1529 nm. Proximity to excited-state resonances induces highly nonlinear level shifts, providing a strong test of theory. The good theory-experiment agreement suggests a new method for accurate measurements of excited-state electric-dipole matrix elements and a precision tool for engineering custom atomic level structures.Optical trapping of atoms employs high-intensity fields that necessarily alter atomic level structure. The calculation of light shifts by perturbation theory fails for scenarios that arise, for example, when the trapping light is near an excited-state transition or for polychromatic fields. We show here that non-perturbative methods based on Floquet’s theorem elegantly handle such scenarios. We compare our calculation to precision absorption spectroscopy on cold 87Rb atoms in a bichromatic optical dipole trap at 1560 + 1529 nm. Proximity to excited-state resonances induces highly nonlinear level shifts, providing a strong test of theory. The good theory-experiment agreement suggests a new method for accurate measurements of excited-state electric-dipole matrix elements and a precision tool for engineering custom atomic level structures.

Optics ExpressDec 14, 201715 citations

Nondestructive light-shift measurements of single atoms in optical dipole traps

Chung-Yu Shih, Michael Chapman

We measure the ac Stark shifts of the $5{S}_{1/2},F=2\ensuremath{\rightarrow}5{P}_{3/2},{F}^{\ensuremath{'}}=3$ transitions of individual optically trapped ${}^{87}$ Rb atoms using a nondestructive detection technique that allows us to measure the fluorescent signal of one and the same atom for over 60 s. These measurements allow the efficient and rapid characterization of single-atom traps that is required for many coherent quantum information protocols. Although this method is demonstrated using a single-atom trap, the concept is readily extended to resolvable atomic arrays.We measure the ac Stark shifts of the $5{S}_{1/2},F=2\ensuremath{\rightarrow}5{P}_{3/2},{F}^{\ensuremath{'}}=3$ transitions of individual optically trapped ${}^{87}$Rb atoms using a nondestructive detection technique that allows us to measure the fluorescent signal of one and the same atom for over 60 s. These measurements allow the efficient and rapid characterization of single-atom traps that is required for many coherent quantum information protocols. Although this method is demonstrated using a single-atom trap, the concept is readily extended to resolvable atomic arrays.

arXiv:1304.3346Physical Review AJun 10, 201342 citations

Eliminating light shifts for single atom trapping

Nicholas R. Hutzler, Lee R. Liu, Yichao Yu +1 more

Microscopically controlled neutral atoms in optical tweezers and lattices have led to exciting advances in the study of quantum information and quantum many-body systems. The light shifts of atomic levels from the trapping potential in these systems can result in detrimental effects such as fluctuating dipole force heating, inhomogeneous detunings, and inhibition of laser cooling, which limits the atomic species that can be manipulated. In particular, these light shifts can be large enough to prevent loading into optical tweezers directly from a magneto-optical trap. We implement a general solution to these limitations by loading, as well as cooling and imaging the atoms with temporally alternating beams, and present an analysis of the role of heating and required cooling for single atom tweezer loading. Because this technique does not depend on any specific spectral properties, it should enable the optical tweezer platform to be extended to nearly any atomic or molecular species that can be laser cooled and optically trapped.Microscopically controlled neutral atoms in optical tweezers and lattices have led to exciting advances in the study of quantum information and quantum many-body systems. The light shifts of atomic levels from the trapping potential in these systems can result in detrimental effects such as fluctuating dipole force heating, inhomogeneous detunings, and inhibition of laser cooling, which limits the atomic species that can be manipulated. In particular, these light shifts can be large enough to prevent loading into optical tweezers directly from a magneto-optical trap. We implement a general solution to these limitations by loading, as well as cooling and imaging the atoms with temporally alternating beams, and present an analysis of the role of heating and required cooling for single atom tweezer loading. Because this technique does not depend on any specific spectral properties, it should enable the optical tweezer platform to be extended to nearly any atomic or molecular species that can be laser cooled and optically trapped.

arXiv:1605.09422New Journal of PhysicsFeb 2, 201750 citations

The light shift caused by an optical dipole force trap on a single

^{87}\mathrm{Rb}

We have measured the ratio

R

of the vector ac Stark effect (or light shift) in the

6{S}_{1∕2}

and

5{D}_{3∕2}

states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at

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

where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the

6{S}_{1∕2}

and

5{D}_{3∕2}

$m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at

1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

R=+0.4176(8)

. These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.

5{S}_{1/2}

5{D}_{5/2}

transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the

5{P}_{3/2}

5{D}_{5/2}

transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the

5{P}_{3/2}

5{D}_{5/2}

resonance, and the corresponding reduced E1 matrix element

1.80(6)e{a}_{0}

(experimental) and

1.96(15)e{a}_{0}

(theoretical). These values resolve a previous discrepancy between theory and experiment.

We measure the ac Stark shifts of the $5{S}_{1/2},F=2\ensuremath{\rightarrow}5{P}_{3/2},{F}^{\ensuremath{'}}=3$ transitions of individual optically trapped

{}^{87}

Rb atoms using a nondestructive detection technique that allows us to measure the fluorescent signal of one and the same atom for over 60 s. These measurements allow the efficient and rapid characterization of single-atom traps that is required for many coherent quantum information protocols. Although this method is demonstrated using a single-atom trap, the concept is readily extended to resolvable atomic arrays.