[Paper Review] Nonlinear Zeeman effect, line shapes and optical pumping in electromagnetically induced transparency

Linjie Zhang, Shanxia Bao+5 more|arXiv (Cornell University)|Feb 16, 2017

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This study investigates nonlinear Zeeman effects, line shape asymmetries, and optical pumping in Rydberg electromagnetically induced transparency (EIT) in a room-temperature cesium vapor cell under magnetic fields up to 50 Gauss. Using quantum Monte Carlo wave-function simulations, the authors demonstrate that quadratic Zeeman shifts in the 6P₃/₂(Fₑ=5) state and the interplay between EIT and optical pumping cause significant spectral asymmetries, especially above 40 Gauss, with strong agreement between simulation and experiment.

ABSTRACT

We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50~Gauss and for several polarization configurations. The magnetic interactions of the $\vert 6S_{1/2}, F_g=4 angle$ ground, $\vert 6P_{3/2}, F_e=5 angle$ intermediate, and $\vert 33S_{1/2} angle$ Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the deep hyperfine Paschen-Back regimes, respectively. Starting in magnetic fields of about 5~Gauss, the spectra develop an asymmetry that becomes paramount in fields $\gtrsim40$~Gauss. We use a quantum Monte Carlo wave-function approach to quantitatively model the spectra. Simulated spectra are in good agreement with experimental data. The asymmetry in the spectra is, in part, due to level shifts caused by the quadratic Zeeman effect, but it also reflects the complicated interplay between optical pumping and EIT in the magnetic field. Relevance to measurement applications is discussed. %The simulations are also used to study optical pumping in the magnetic field and to investigate the interplay between optical pumping and EIT, which reduces photon scattering and optical pumping.

Motivation & Objective

• To understand the origin of spectral asymmetries in Rydberg EIT under magnetic fields in a room-temperature Cs vapor cell.
• To investigate the role of the quadratic Zeeman effect in the 6P₃/₂(Fₑ=5) intermediate state on EIT line shapes.
• To examine how optical pumping dynamics interact with EIT, particularly under Zeeman splitting and laser polarization variations.
• To develop and validate a quantum Monte Carlo wave-function (QMCWF) model that quantitatively reproduces experimental spectra.
• To assess the implications of these effects for precision electric field measurements in magnetized environments, such as plasma diagnostics.

Proposed method

• Conducted Zeeman spectroscopy on a ladder-type Rydberg EIT system in a Cs vapor cell with magnetic fields up to 50 Gauss.
• Employed counter-propagating probe and coupling lasers at 852 nm and 510 nm, respectively, with precise frequency stabilization.
• Used a quantum Monte Carlo wave-function (QMCWF) approach to simulate the time evolution of the atomic density matrix under laser and magnetic field interactions.
• Tracked optical pumping dynamics by monitoring the average magnetic quantum number ⟨m_I + m_J⟩ and photon scattering rates across velocity classes.
• Varied laser polarization configurations (σ⁺/σ⁻, σ⁻/σ⁺) to probe polarization-dependent asymmetries and Rabi frequency differences.
• Compared simulated spectra and optical pumping maps with experimental data to validate the model, particularly at 5 G and 40 G fields.

Experimental results

Research questions

• RQ1 What causes the pronounced spectral asymmetry in Rydberg EIT lines at magnetic fields above 40 Gauss?
• RQ2 How does the quadratic Zeeman effect in the 6P₃/₂(Fₑ=5) state influence EIT line shapes and peak intensities?
• RQ3 To what extent does optical pumping efficiency differ between red- and blue-detuned Zeeman features in the EIT spectrum?
• RQ4 How do different laser polarization configurations (e.g., σ⁺/σ⁻ vs. σ⁻/σ⁺) affect the observed asymmetry and satellite peak formation?
• RQ5 Can a quantum Monte Carlo wave-function approach accurately model the interplay between EIT, optical pumping, and Zeeman shifts in a thermal vapor cell?

Key findings

• Spectral asymmetry in Rydberg EIT becomes prominent at magnetic fields as low as 5 Gauss and is most pronounced above 40 Gauss, primarily due to the quadratic Zeeman effect in the 6P₃/₂(Fₑ=5) state.
• The QMCWF simulations reproduce experimental spectra with good quantitative agreement, confirming that asymmetries arise from both level shifts and optical pumping dynamics.
• Optical pumping efficiency is significantly reduced on EIT resonances, with ⟨m_I + m_J⟩ dropping from ~3.48 to 3.16 at peak A and from ~3.84 to 3.66 at peak A′, indicating strong suppression of population transfer.
• The simulations reveal that photon scattering and optical pumping maps are asymmetric with respect to coupling laser detuning Δ_C and atomic velocity v, especially at higher fields.
• At 40 Gauss, the σ⁺-polarized probe experiences significantly higher background absorption than σ⁻-polarized probe, reflecting polarization-dependent asymmetry due to the quadratic Zeeman effect.
• The appearance of distinct Type-II satellite peaks (e.g., B, C, D) on the blue side of the main EIT peak A, with no counterparts on the red side, is attributed to lower Rabi frequencies and magnetic field-dependent frequency shifts of ~112 MHz at 40 Gauss.