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arXiv:2312.08370 · Physical Review A

State-insensitive wavelengths for light shifts and photon scattering from Zeeman states

Stuart J. Masson, Zhenjie Yan, Jacquelyn Ho, Yuehui Lu, Dan Stamper-Kurn, Ana Asenjo-Garcı́a

Published Jun 6, 2024• 1 citation
arXivHTMLPDF

Abstract

Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali-metal atoms and alkaline-earth-metal ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications.

DOI
10.1103/physreva.109.063105

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Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali-metal atoms and alkaline-earth-metal ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications.
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Nonlinear Zeeman (NLZ) shifts arising from magnetic-field mixing of the two hyperfine ground states in alkali-metal atoms lead to splitting of magnetic-resonance lines. This is a major source of sensitivity degradation and the so-called ``heading errors'' of alkali-metal-vapor atomic magnetometers operating in the geophysical field range $(B\ensuremath{\approx}0.2--0.7\phantom{\rule{0.3em}{0ex}}\mathrm{G})$. Here, it is shown theoretically and experimentally that NLZ shifts can be effectively canceled by light shifts caused by a laser field of appropriate intensity, polarization, and frequency, a technique that can be readily applied in practical situations.
We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by a vapor of alkali-metal atoms is independent of the population distribution among the Zeeman sublevels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancellation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan coefficients. One important application is the robust measurement of the hyperfine population.
We perform saturated absorption spectroscopy on the D2{D}_{2}D2​ line for room temperature rubidium atoms immersed in magnetic fields within the 0.05--0.13 T range. At those medium-high field values the hyperfine structure in the excited state is broken by the Zeeman effect, while in the ground-state hyperfine structure and Zeeman shifts are comparable. The observed spectra are composed by a large number of absorption lines. We identify them as saturated absorptions on two-level systems, on three-level systems in a V\mathsf{V}V configuration, and on four-level systems in an N\mathsf{N}N or double-N\mathsf{N}N configuration where two optical transitions not sharing a common level are coupled by spontaneous emission decays. We analyze the intensity of all those transitions within a unified simple theoretical model. We concentrate our attention on the double-N\mathsf{N}N crossovers signals whose intensity is very large because of the symmetry in the branching ratios of the four levels. We point out that these structures, present in all alkali-metal atoms at medium-high magnetic fields, have interesting properties for electromagnetically induced transparency and slow light applications.
The degree of linear polarization P L for two-photon absorption of alkali atoms in intermediate strength magnetic fields has been computationally investigated. Polarization spectra were obtained for n a s 2 S 1/2 to n b s 2 S 1/2 transitions with the photons in near resonance with intermediate 2 P j levels. Previous experiments and calculations in the absence of a magnetic held revealed a complete polarization reversal (P L approximately -100%) for frequencies near resonance between the 2 P 1/2 and 2 P 3/2 levels due to fine-structure coherence. Application of weak to intermediate strength fields induce additional depolarization features as a result of anomalous Zeeman splitting. The fine-structure depolarization feature disappears for strong fields (Paschen-Back regime), while the calculations predict that Zeeman depolarization persists though the transitions become forbidden. Magnetic-field-dependent polarization spectra can be measured in the laboratory with high precision and it should prove interesting to trace through the weak, intermediate, and strong field regimes.
We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.