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Journal of Physics B Atomic Molecular and Optical Physics

Ground-state hyperfine spectroscopy of 87 Rb atoms in a 1D optical lattice

Sooyoung Park, Meung Ho Seo, D. Cho

Published Sep 30, 2019• 3 citations

Abstract

Abstract We report our theoretical and experimental study on how the motional states of an atom trapped in a 1D optical lattice modify its hyperfine transition. We calculate and measure the inhomogeneously broadened line shape of a transition from the ∣ 5 S 1 / 2 , F = 1 , m F = 1 〉 state to the ∣ 5 S 1 / 2 , F = 2 , m F = 2 〉 state of 87 Rb atoms in a lattice with various elliptic polarizations, and find excellent agreement. The atoms are at a temperature below 10 μ K, and the well depth at an antinode is 100 μ K. For the line shape calculation, we develop an efficient formula that allows us to evaluate the Franck–Condon factor from the 3D motional states accurately with a motional quantum number of as high as 1600. Precise spectroscopic measurements are conducted using evaporatively cooled atoms in a 980 nm lattice formed by a Fabry–Perot cavity placed inside a two-layer magnetic shield. Our results show how the broadening and decoherence of a ground hyperfine transition are related with the motional states. Inversely, our results can be applied to develop schemes to manipulate the motional states by using an inhomogeneously broadened hyperfine transition. As an example, we discuss the radio-frequency induced evaporative cooling in an optical lattice with a fixed well depth.

DOI: 10.1088/1361-6455/ab4953

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Abstract We report our theoretical and experimental study on how the motional states of an atom trapped in a 1D optical lattice modify its hyperfine transition. We calculate and measure the inhomogeneously broadened line shape of a transition from the ∣ 5 S 1 / 2 , F = 1 , m F = 1 〉 state to the ∣ 5 S 1 / 2 , F = 2 , m F = 2 〉 state of 87 Rb atoms in a lattice with various elliptic polarizations, and find excellent agreement. The atoms are at a temperature below 10 μ K, and the well depth at an antinode is 100 μ K. For the line shape calculation, we develop an efficient formula that allows us to evaluate the Franck–Condon factor from the 3D motional states accurately with a motional quantum number of as high as 1600. Precise spectroscopic measurements are conducted using evaporatively cooled atoms in a 980 nm lattice formed by a Fabry–Perot cavity placed inside a two-layer magnetic shield. Our results show how the broadening and decoherence of a ground hyperfine transition are related with the motional states. Inversely, our results can be applied to develop schemes to manipulate the motional states by using an inhomogeneously broadened hyperfine transition. As an example, we discuss the radio-frequency induced evaporative cooling in an optical lattice with a fixed well depth.

We determine the absolute density of a sample of laser-cooled atoms in a two-level system by recording the absorption spectrum of the 85Rb 5S1/2 (F = 3, mf = 3) → 5P3/2 (F′ = 4, m′f = 4) transition. Trapped atoms were prepared in the (F = 3, mf = 3) ground state through optical-pumping techniques. We compare our results with an independent measure of the density that relies on a direct measurement of the number of atoms and size of the atomic sample. We also study the contributions of power broadening, laser line width, and Doppler broadening to the measured absorption spectrum. Our studies suggest that the natural line width (~6 MHz) can be measured to a precision of less than ~50 kHz if the laser line width is measured in real-time with a high-finesse Fabry–Perot cavity. PACS Nos.: 32.70.Cs, 32.70.Jz, 32.80.Pj, 42.62.Fi, 32.70.–n, 32.30.–r

Efficient high-fidelity ground-state cooling of motional degrees of freedom is crucial for applications in quantum simulation, computing, and metrology. Here, we demonstrate direct ground-state cooling of fermionic Yb 171 and bosonic Yb 174 atoms in two- and three-dimensional magic-wavelength optical lattices on the ultranarrow clock transition. Its high spectral resolution offers the potential for reaching extremely low temperatures. To ensure efficient cooling, we develop a chirped sideband cooling scheme, where we sweep the clock-laser frequency to mitigate the effects of spatial trap inhomogeneities. We further generalize the theoretical description of sideband spectra to higher-dimensional lattices for precise thermometry. We achieve 2D ground-state fractions of 97 % for Yb 171 with an average motional occupation of n ¯ ≃ 0.015 and provide a direct comparison with Yb 174 , reaching similar cooling performance. Applying the same scheme in 3D results in n ¯ ≃ 0.15 limited by layer-to-layer inhomogeneities in the vertical direction. These results demonstrate efficient motional ground-state cooling in optical lattices, especially for bosonic alkaline-earth(-like) atoms, where other methods are not applicable, opening the door to novel protocols for quantum science applications with neutral atoms.

We perform spectroscopy on the hyperfine splitting of

^{85}

Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then show how hyperfine spectroscopy can be used to study quantum dynamics of optically trapped atoms.

We develop a simple and practical scheme to apply sideband cooling to a cloud of rubidium atoms. A sample containing 4 × 10 70 87 Rb is trapped in a far red detuned optical lattice. Through optimizing the relevant parameters, i.e., laser detuning, magnetic field, polarization, and duration time, a temperature around 1.5 μK and phase space density close to 1/500 are achieved. Compared with polarization gradient cooling, the temperature decreases by around one order of magnitude. This technique could be used in high precision measurement such as atomic clocks and atom interferometer. It could also serve as a precooling means before evaporation cooling in a dipole trap, and may be a promising method of achieving quantum degeneracy with purely optical means.

We propose a way to eliminate the inhomogeneous broadening for a ground-state hyperfine transition of an alkali metal atom in an optical trap by using a properly polarized trapping field. The ac Stark shift contribution from the vector polarizability has opposite sign for a pair of ground hyperfine levels. It can be used to eliminate the inhomogeneous broadening from the difference in the scalar polarizbilities due to the hyperfine splitting. The size of the vector term is determined by the polarization state of the trapping field, and by controlling the polarization tightly one can achieve a very narrow linewidth. We estimate required tolerance in the polarization control to achieve 1-Hz linewidth for a specific case of a cesium atom. This proposal has significant implications for an electric dipole moment measurement using cesium atoms and quantum information processing using an optical lattice.

The dynamic Stark shift of an inhomogeneously broadened spectral transition has been studied. Our measurements show a shift in the observed 87 Rb ground-state hyperfine transition, which has a nonlinear dependence on light intensity when the conditions for inhomogeneous broadening are met. The nonlinearity is the result of light-intensity gradients in the signal volume, which produce an inhomogeneously broadened asymmetric microwave transition. We show that our measurements are in full agreement with the second-order perturbation-theory treatment of light-induced energy-level shifts when the effects of inhomogeneities are properly taken into consideration. The effects of inhomogeneous broadening must be carefully considered when one extracts oscillator strengths from light-shift data, or performs high-precision laser spectroscopy. Originator-supplied keywords include: AC stark effect, Atomic clocks, Atomic line shapes, Light shifts.