arXiv:1208.4291 · Physical Review Letters

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

Creston D. Herold, Varun Vaidya, Xiao Li, S. L. Rolston, J. V. Porto, Marianna S. Safronova

Published Dec 14, 2012• 95 citations

Abstract

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

DOI: 10.1103/physrevlett.109.243003

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arXiv:1208.4291 · Physical Review Letters

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

Creston D. Herold, Varun Vaidya, Xiao Li, S. L. Rolston, J. V. Porto, Marianna S. Safronova

Published Dec 14, 2012• 95 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.109.243003

Related papers

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

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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.

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In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift of the clock transition and the amplitude of the related parity-violating transition, and can be used as probes to test quantum electrodynamic effects, especially at the 10−3–10−4 level. We developed a universal experimental approach to precisely determine the dipole transition matrix elements by using the shelving technique, for the species where two transition channels are involved, in which the excitation pulses with increasing duration were utilized to induce shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited P1/22 state to the S1/22 ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this technique to a single Yb+ ion, and determined the 6p P1/22-5d D23/2 transition matrix element 2.9979(20) ea0, which indicates an order of magnitude improvement over existing reports. By combining our result with the 6p P1/22 lifetime of 8.12(2) ns, we extracted the 6s S1/22-6p P1/22 transition matrix element to be 2.4703(31) ea0. The accurately determined dipole transition matrix elements can serve as a benchmark for the development of high-precision atomic many-body theoretical methods.In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift of the clock transition and the amplitude of the related parity-violating transition, and can be used as probes to test quantum electrodynamic effects, especially at the 10−3–10−4 level. We developed a universal experimental approach to precisely determine the dipole transition matrix elements by using the shelving technique, for the species where two transition channels are involved, in which the excitation pulses with increasing duration were utilized to induce shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited P1/22 state to the S1/22 ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this technique to a single Yb+ ion, and determined the 6p P1/22-5d D23/2 transition matrix element 2.9979(20) ea0, which indicates an order of magnitude improvement over existing reports. By combining our result with the 6p P1/22 lifetime of 8.12(2) ns, we extracted the 6s S1/22-6p P1/22 transition matrix element to be 2.4703(31) ea0. The accurately determined dipole transition matrix elements can serve as a benchmark for the development of high-precision atomic many-body theoretical methods.

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We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb atoms. Recent progress in metrology exploits so-called “magic wavelengths,” whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb atoms. Recent progress in metrology exploits so-called “magic wavelengths,” whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically-trapped neutral atoms.

Physical Review LettersMar 29, 20101 citation

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 predict a sequence of magic-zero wavelengths for the Sr excited

5s5p~ ^3P_0

state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a best global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the

5s^2\ ^1S_0 - 5s5p\ ^3P_0

Sr clock transition between 350 nm and 500 nm which can also serve as precision benchmarks.

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the

6{S}_{1/2}

and

5{D}_{5/2}

states to 0.1% precision. We find $R={\ensuremath{\Delta}}_{S}/{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at 514.531 nm where ${\ensuremath{\Delta}}_{S,D}$ are the light shifts of the $m=\ifmmode\pm\else\textpm\fi{}1/2$ splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of

R

would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.

We predict a sequence of magic-zero wavelengths for the Sr excited

5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}

state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the $5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}\text{\ensuremath{-}}5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}$ Sr clock transition between 350 and 500 nm which can also serve as precision benchmarks.