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arXiv:1002.1628 · Physical Review A

All-optical reconstruction of atomic ground-state population

Paz London, Ofer Firstenberg, M. Shuker, A. Ron

Published Apr 27, 2010• 2 citations
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Abstract

The population distribution within the ground state of an atomic ensemble is of great significance in a variety of quantum-optics processes. We present a method to reconstruct the detailed population distribution from a set of absorption measurements with various frequencies and polarizations, by utilizing the differences between the dipole matrix elements of the probed transitions. The technique is experimentally implemented on a thermal rubidium vapor, demonstrating a population-based analysis in two optical-pumping examples. The results are used to verify and calibrate an elaborated numerical model, and the limitations of the reconstruction scheme, which result from the symmetry properties of the dipole matrix elements, are discussed.

DOI
10.1103/physreva.81.043835

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The population distribution within the ground state of an atomic ensemble is of great significance in a variety of quantum-optics processes. We present a method to reconstruct the detailed population distribution from a set of absorption measurements with various frequencies and polarizations, by utilizing the differences between the dipole matrix elements of the probed transitions. The technique is experimentally implemented on a thermal rubidium vapor, demonstrating a population-based analysis in two optical-pumping examples. The results are used to verify and calibrate an elaborated numerical model, and the limitations of the reconstruction scheme, which result from the symmetry properties of the dipole matrix elements, are discussed.
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A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized D1{D}_{1}D1​ line as pumping radiation, instead of a mixture of the two DDD lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.
A method for reconstructing the quantum state of a system of atoms or spins is proposed. The QQQ distribution is derived from the measured population in the ground state of a system that has interacted with an external field. Using multipole operators the QQQ function is inverted to derive the density matrix.
This paper investigates stimulated emission and absorption near resonance for a driven system of interacting two-level atoms. Microscopic kinetic equations for the density matrix elements of N-atom states including atomic motion are built, taking into account atom-field and atom-atom interactions. Analytical solutions are given for the resulting macroscopic equations in different limits, for a system composed of a strong coherent “pump” field and a weak counter-propagating “probe” field. It was shown that the existence of a dipole-dipole (long-range) interaction between atoms separated by distance less than the pump wave-length can cause the formation of periodic polarization and population structures (gratings in time and space) in the pumped medium without a probe field. The magnitude of pump induced population grating can have a strong dependence on the relation between the pump field detuning and the polarization decay rate. The “interaction” between pump and probe induced polarization/population gratings through a dipole-dipole interaction mechanism causes the absorption line shape asymmetry. Under certain conditions, this asymmetry is revealed in increasing probe gain for the “red”-shifted (relative to pump) probe and suppressing the gain for the “blue”-shifted probe field when pump is “red”-shifted relative to the ensemble averaged resonant frequency. The theoretical results are consistent with experimental data for the probe gain or absorption as the function of frequency and the dependance of the gain on atomic density for sodium vapor when the pump laser is tuned near the D 2 line. Here the dependance of gain on particle density was explained in the terms of the long-range interaction between the atoms.
Cs) atoms by applying circularly polarized light at an optimal frequency for electronic transitions from ground to excited states. To enhance control over sublevel populations following optical pumping, we incorporate a radiofrequency (RF) field. This integrated approach enables us to achieve a tailored distribution of atomic sublevel populations with high efficiency. Utilizing the Lindblad master equation, we provide a comprehensive framework for analyzing these dynamics, examining relaxation rates, repopulation processes, and the evolution of cesium Zeeman sublevels. Our findings underscore the effectiveness of the Lindblad master equation in accounting for external field effects and environmental interactions, significantly improving the accuracy and generalizability of optical pumping models. This method holds substantial promise for various applications in optical experiments, including magnetometry and quantum computing, paving the way for future advancements in these fields.