Alignment-to-orientation conversion in the ground state of atomic Cs with linearly polarized laser excitation

In this study we explored the angular momentum alignment-to-orientation conversion occurring in various alkali metals -- K, Rb, Cs. We used a theoretical model that is based on Optical Bloch equations and uses the density matrix formalism. Our model includes the interaction of all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Additionally we simulated signals where the ground- or the excited-state coherent processes were switched off allowing us to determine the origins of obtained signals. We also performed experiments on Cs atoms with two laser beams: linearly polarised Cs D1 pump and circularly polarized Cs D2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. Full analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided.Comment: arXiv admin note: text overlap with arXiv:2006.1501

Scheme of the hyperfine levels and allowed transitions of the <em>D</em>₂ line of ⁸⁷Rb

<p><strong>Figure 1.</strong> Scheme of the hyperfine levels and allowed transitions of the <em>D</em>₂ line of ⁸⁷Rb.</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p

Relative transition strengths from the ground-state magnetic sublevels to the excited-state magnetic sublevels when the linearly polarized exciting radiation is decomposed into σ^± circularly polarized components for the F_g=2longrightarrow F_e=3 transition of the <em>D</em>₂ line

<p><strong>Figure 2.</strong> Relative transition strengths from the ground-state magnetic sublevels to the excited-state magnetic sublevels when the linearly polarized exciting radiation is decomposed into σ^± circularly polarized components for the F_g=2\longrightarrow F_e=3 transition of the <em>D</em>₂ line. The Lande factor <em>g_F</em> is given at the left of each particular hyperfine level.</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p

Geometry of the excitation and observation directions

<p><strong>Figure 3.</strong> Geometry of the excitation and observation directions.</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p

Decomposition of a magneto-optical signal into a superposition of signals from different velocity groups and at different magnetic fields

<p><strong>Figure 6.</strong> Decomposition of a magneto-optical signal into a superposition of signals from different velocity groups and at different magnetic fields. Left panel: the solid black line shows the magneto-optical signal as it would be observed in a vapour cell at room temperature. The dashed and dotted lines show the signals for the different velocity groups that make up the room temperature velocity distribution. Right panel: distribution of the atomic angular momentum at different values of the magnetic field <em>B</em> for the velocity groups in resonance at a (Doppler) detuning of 0, 5 and −5 MHz.</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p

LIF versus magnetic field value for the F_g=2longrightarrow F_e=3 transition of ⁸⁷Rb for different values of the laser power density <em>I</em>: (a) 0.14 mW cm⁻², (b) 1 mW cm⁻², (c) 10 mW cm⁻²

<p><strong>Figure 4.</strong> LIF versus magnetic field value for the F_g=2\longrightarrow F_e=3 transition of ⁸⁷Rb for different values of the laser power density <em>I</em>: (a) 0.14 mW cm⁻², (b) 1 mW cm⁻², (c) 10 mW cm⁻². The bottom right panel shows the contrast of the central minimum as a function of the laser power density. Filled circles correspond to experimentally measured values, whereas the solid line shows the result of a calculation. Note the different scales in (a), (b) and (c).</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p

Theoretical calculations of the LIF versus the magnetic field <em>B</em> for the F_g=2longrightarrow F_e=3 transition of ⁸⁷Rb with different physical effects taken into account: (a) all effects taken into account, (b) detuning effects only, (c) ground-state coherence effects only, (d) excited-state coherent effects only

<p><strong>Figure 5.</strong> Theoretical calculations of the LIF versus the magnetic field <em>B</em> for the F_g=2\longrightarrow F_e=3 transition of ⁸⁷Rb with different physical effects taken into account: (a) all effects taken into account, (b) detuning effects only, (c) ground-state coherence effects only, (d) excited-state coherent effects only. Note the different scales! The parameters used in the simulation were as follows: γ = 0.019 MHz, Δω_Laser = 2 MHz, σ_Doppler = 216 MHz, <em>D</em>_Step ≈ 1.73 MHz</p> <p><strong>Abstract</strong></p> <p>We present the results of an investigation of the different physical processes that influence the shape of nonlinear magneto-optical signals both at small magnetic field values (~100 mG) and at large magnetic field values (several tens of Gauss). We used a theoretical model that provided an accurate description of experimental signals for a wide range of experimental parameters. By turning various effects 'on' or 'off' inside this model, we investigated the origin of different features of the measured signals. We confirmed that the narrowest structures, with widths of the order of 100 mG, are related mostly to coherences among ground-state magnetic sublevels. The shape of the curves at other scales could be explained by taking into account the different velocity groups of atoms that come into and out of resonance with the exciting laser field. Coherent effects in the excited state can also play a role, although they mostly affect the polarization components of the fluorescence. The results of theoretical calculations are compared with experimental measurements of laser-induced fluorescence from the <em>D</em>₂ line of atomic rubidium as a function of the magnetic field.</p