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arXiv:1702.02802

Strong light shifts from near-resonant and polychromatic fields: comparison of Floquet theory and experiment

Simon Coop, Silvana Palacios, Pau Gomez, Y. N. Martinez de Escobar, Thomas Vanderbruggen, Morgan W. Mitchell

Published Feb 9, 2017• 1 citation
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Abstract

We present a non-perturbative numerical technique for calculating strong light shifts in atoms under the influence of multiple optical fields with arbitrary polarization. We confirm our technique experimentally by performing spectroscopy of a cloud of cold $^{87}$Rb atoms subjected to $\sim$ kW/cm$^2$ intensities of light at 1560.492 nm simultaneous with 1529.269 nm or 1529.282 nm. In these conditions the excited state resonances at 1529.26 nm and 1529.36 nm induce strong level mixing and the shifts are highly nonlinear. By absorption spectroscopy, we observe that the induced shifts of the 5P3/2 hyperfine Zeeman sublevels agree well with our theoretical predictions.. We propose the application of our theory and experiment to accurate measurements of excited-state electric-dipole matrix elements.

DOI
10.48550/arxiv.1702.02802

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We present a non-perturbative numerical technique for calculating strong light shifts in atoms under the influence of multiple optical fields with arbitrary polarization. We confirm our technique experimentally by performing spectroscopy of a cloud of cold 87^{87}87Rb atoms subjected to ∼\sim∼ kW/cm2^22 intensities of light at 1560.492 nm simultaneous with 1529.269 nm or 1529.282 nm. In these conditions the excited state resonances at 1529.26 nm and 1529.36 nm induce strong level mixing and the shifts are highly nonlinear. By absorption spectroscopy, we observe that the induced shifts of the 5P3/2 hyperfine Zeeman sublevels agree well with our theoretical predictions.. We propose the application of our theory and experiment to accurate measurements of excited-state electric-dipole matrix elements.
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We perform nonperturbative calculations of resonant multiwave mixing of two high-intensity laser beams of different frequencies both for a general three-level system and for the 3 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​--3 2^{2}2P1/2{\mathit{P}}_{1/2}P1/2​ electronic resonance of the sodium atom. Our calculations proceed by direct numerical integration of the density-matrix equations and subsequent Fourier analysis of the calculated time-dependent density-matrix elements. We examine the case where two nearly degenerate input beams are each detuned many collisional linewidths from electronic resonance, and the frequency difference between the input beams is tuned through a ground-state resonance. Unlike previous high-intensity analyses, each input beam can be resonant with numerous transitions simultaneously; for a three-level system, we refer to this as an ``M-type'' system, in analogy with \ensuremath{\Lambda}- and V-type systems. Calculated four-, six-, and eight-wave-mixing spectra exhibit subharmonic resonances of the type observed experimentally by Trebino and Rahn [Opt. Lett. 12, 912 (1987)]. The three-level system is studied to gain insight into the physics of these subharmonic resonances. For more quantitative comparison with experiment, we use a model that includes the 16 Zeeman and hyperfine states in the 3 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​ and the 3 2^{2}2P1/2{\mathit{P}}_{1/2}P1/2​ levels, and accounts for arbitrary linear polarization of the input laser radiation. The relative intensities of the resonance features in the calculated multiwave-mixing spectra show good agreement with experiment. These resonance features broaden and shift as laser intensity increases, as predicted for four-wave-mixing processes in previous, less general high-intensity analyses. Both theory and experiment also show additional resonant features in the eight-wave-mixing spectra that appear at very high intensity.
We study the emergence of a collective optical response of a cold and dense 87Rb^{87}\mathrm{Rb}87Rb atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold atom clouds substantially deviate from those of thermal atomic ensembles, indicating strong light-induced resonant dipole-dipole interactions between the atoms. At high densities, the simulations also predict a significantly slower decay of light-induced excitations in cold than in thermal atom clouds. The role of dipole-dipole interactions is discussed in terms of resonant coupling examples and the collective radiative excitation eigenmodes of the system.
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 5S1/25{S}_{1/2}5S1/2​--5D5/25{D}_{5/2}5D5/2​ 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 5P3/25{P}_{3/2}5P3/2​--5D5/25{D}_{5/2}5D5/2​ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the 5P3/25{P}_{3/2}5P3/2​--5D5/25{D}_{5/2}5D5/2​ resonance, and the corresponding reduced E1 matrix element 1.80(6)ea01.80(6)e{a}_{0}1.80(6)ea0​ (experimental) and 1.96(15)ea01.96(15)e{a}_{0}1.96(15)ea0​ (theoretical). These values resolve a previous discrepancy between theory and experiment.
According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian He{\mathcal{H}}_{e}He​ which depends on the polarization and spectral profile of the incident light. In order to check the structure of He{\mathcal{H}}_{e}He​, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to He{\mathcal{H}}_{e}He​. We have been able to obtain experimentally in the ground state of 199Hg^{199}\mathrm{Hg}199Hg, 201Hg^{201}\mathrm{Hg}201Hg, and 87Rb^{87}\mathrm{Rb}87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of He{\mathcal{H}}_{e}He​ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.
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