Nonlinear Zeeman effect, line shapes and optical pumping in electromagnetically induced transparency

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 $\vert 6S_{1/2}, F_g=4 \rangle$ ground, $\vert 6P_{3/2}, F_e=5 \rangle$ intermediate, and $\vert 33S_{1/2} \rangle$ 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.

• The paper demonstrates that the nonlinear Zeeman effect induces significant asymmetry in Cs vapor EIT spectra through robust optical pumping dynamics.
• The experimental setup uses a ladder-type scheme and QMCWF simulations to assess both linear and quadratic magnetic interactions.
• Results show that magnetic fields as low as tens of Gauss cause notable spectral shifts and variations in photon scattering rates.

Nonlinear Zeeman Effect in Rydberg EIT Systems

The paper "Nonlinear Zeeman effect, line shapes and optical pumping in electromagnetically induced transparency" explores the influence of magnetic fields on electromagnetically induced transparency (EIT) in Rydberg atoms, particularly the nonlinear Zeeman effect and its asymmetric impact on spectral lines due to optical pumping dynamics. The study presents experimental and simulation results for a cesium vapor cell subjected to varying magnetic fields, illustrating the complex spectral behavior due to intertwined optical pumping and quantum interference.

Experimental Setup and Methodology

The authors implement a ladder-type EIT system using Cs vapor, transitioning through $\vert 6S_{1/2}, F_g=4 \rangle$, $\vert 6P_{3/2}, F_e=5 \rangle$, and $\vert 33S_{1/2} \rangle$ Rydberg states. The experiment is performed in a controlled setting with magnetic fields up to 50 Gauss, using precise laser locking for stability. The analysis accounts for linear and quadratic Zeeman effects across the varying regimes of ground, intermediate, and Rydberg states. The research leverages quantum Monte Carlo wave-function (QMCWF) methods for simulating the atomic interactions, effectively capturing the photon scattering rates involved.

Theoretical Framework

The theoretical model integrates hyperfine structures and magnetic interactions into the Hamiltonian, using the $\{ |m_I, m_J \rangle \}$ basis to compute interactions among various quantum states. The nonlinear Zeeman effect is detailed extensively with respect to perturbations in magnetic sub-states, demonstrating the necessity to consider both linear and quadratic components. The QMCWF approach provides computational efficiency for large quantum systems like Cs, which have complex state distributions due to the combination of nuclear and electronic spin effects.

Spectral Analysis and Results

Experiments elucidate how EIT spectra split and develop asymmetries as the magnetic field increases. Spectral peaks initially symmetric begin to shift non-uniformly due to quadratic Zeeman interactions, and satellite lines emerge prominently at stronger fields. The study finds substantial agreement between the experimental data and QMCWF simulations, validating the sophisticated interplay of magnetic effects and optical pumping. The research highlights that spectral asymmetry at fields as low as a few tens of Gauss mainly stems from the quadratic Zeeman effect of the intermediate state.

Optical Pumping and EIT Interplay

Optical pumping dynamics are crucial; the Zeeman effect modulates atomic populations in various sublevels, impacting the strength and shape of EIT lines. The model suggests significant variation in photon scattering rates primarily at probe-transition resonances, indicative of differing optical pumping efficacy across velocity classes. Simulated data display asymmetrical behavior in scattering rates and pumping efficiency, dependent on whether probe or coupler transitions are induced, providing deeper insight into the optical pumping dynamics in magnetic fields.

Polarization Effects

Further experiments with alternative polarization configurations (e.g., $\sigma^{+}/\sigma^{-}$) reveal similar asymmetric behavior at high magnetic fields, underscoring the role of polarization in modulating atomic interactions and spectral positions. The asymmetric background absorption and emergence of "Type-II" transitions, with marked lower Rabi frequencies due to spin overlap differences between states, are consistent across polarization types.

Conclusion

This paper effectively bridges experimental findings with advanced simulations to demonstrate the non-intuitive effects of magnetic fields on EIT in Rydberg systems. The insights into Zeeman effects at moderate fields contribute substantially to future endeavors in electric field sensing and diagnostics in magnetized environments. Understanding these aspects is pivotal for precise measurement applications in quantum sensors and may guide ongoing developments in quantum information systems leveraging Rydberg atom properties.