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Japanese Journal of Applied Physics

Optical Nutation in Cold 85Rb Atoms

Unyob Shim, S. B. Cahn, Anantharaman Kumarakrishnan, Tycho Sleator, Jin‐Tae Kim

Published Jan 1, 2005• 5 citations
Publisher

Abstract

We have observed optical nutation in cold 85Rb atoms with a negligible Doppler broadening. The optical nutation of a two-level atom arranged by optical pumping has been studied as a function of detuning frequency and Rabi frequency. The change of the nutation signal caused by magnetic substate degeneracy has also been observed for σ and π excitations. This can be explained by optical nutation beatings from different transition probabilities among magnetic sublevels. Absolute transition probabilities with σ and π transitions and a branching ratio between them have been measured.

DOI
10.1143/jjap.44.168

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We have observed optical nutation in cold 85Rb atoms with a negligible Doppler broadening. The optical nutation of a two-level atom arranged by optical pumping has been studied as a function of detuning frequency and Rabi frequency. The change of the nutation signal caused by magnetic substate degeneracy has also been observed for σ and π excitations. This can be explained by optical nutation beatings from different transition probabilities among magnetic sublevels. Absolute transition probabilities with σ and π transitions and a branching ratio between them have been measured.
We have analyzed the magnetic field dependencies of the intensities of all the optical transitions between magnetic sublevels of hyperfine levels, excited with σ + , π , and σ − polarized light, for the D 1 and D 2 lines of 87 R b and 85 R b atoms. Depending on the type of transition and the quantum numbers of the involved levels, the Hamiltonian matrices are of 1 × 1 , 2 × 2 , 3 × 3 , or 4 × 4 dimension. As an example, analytical expressions are presented for the case of 2 × 2 dimension matrices for the D 1 line of both isotopes. Eigenvalues and eigenkets are given, and the expression for the transition intensity as a function of B has been determined. It is found that some π transitions of 87 R b and 85 R b get completely canceled for certain, extremely precise, values of B . No cancellation occurs for σ + or σ − transitions of the D 1 line. For matrices with a size over 2 × 2 , analytical formulas are heavy, and we have performed numerical calculations. All the B values canceling σ + , π , and σ − transitions of the D 1 and D 2 lines of 87 R b and 85 R b are calculated, with an accuracy limited by the precision of the involved physical quantities. The experimental implementation feasibility and its possible outcome are addressed. We believe the experimental realization will allow an increase in the precision of the physical quantities involved, in particular the upper state atomic level energy.
Optical nutation under Raman excitation accompanied by considerable (up to inverted) population changes was observed. The Raman-active 6P1/2–6P3/2 transition of thallium atoms was excited by picosecond pulses of a dye and an Nd : YAG laser. Transition polarization and upper level population were probed by delayed pulses at a fixed time by means of coherent Raman scattering and third harmonic generation schemes, respectively. Optical nutation manifested itself in corresponding changes of anti-Stokes and third harmonic signal energies as functions of the product of the pump pulses energies. As a result of the a.c. Stark shift, the nutation picture strongly depended on the sign of wavenumber detuning from the transition wavenumber. Copyright © 2000 John Wiley & Sons, Ltd.
An optical pumping device, consisting of only 85Rb lamp and 87Rb absorption bulb, is used. The 0-0 transition resonance signal of 87Rb ground state is found to be greater than that in the conventional optical pumping device, in which the 87Rb lamp, 85Rb filter and 87Rb absorption bulb are used. In a definite temperature range, a negative resonance signal is observed. Up to now, it has not been explained yet. The line-width and optical frequency shift are measured. The possibility of applying this device in 87Rb atomic frequency standard is discussed.
Optical pumping makes atom system be partial polarization but magnetic resonance produces depolarization,which is the basic process for investigation of the responsibility to optical pumping for Rb isotope.With improvement on experimental technology,the magnetic resonance signal,also with optical pumping signal,from 85Rb and 87Rb can be completely separated.The relation between detecting signal and physics parameters for optical pumping is drawn out by assuming a model of three energy levels.Results from data analysis indicate the responsibility to optical pumping for 87Rb and 85Rb will be accurately described with unitary relaxation mechanism,respectively.The relaxation time has partly reflected the difference of transition probabilities between energy levels of 87Rb and 85Rb.
We present analytical solutions for the populations of the D 1 transition line of 85 Rb atoms. The time evolution of the populations of the magnetic sublevels in the excited state at the weak intensity limit exhibits several kinds of homogeneous or inhomogeneous second-order differential equations. General solutions of the differential equations result in an analytical form of the population in each magnetic sublevel as a function of the elapsed time, laser intensity, and laser frequency detuning.
Optical nutation at the Raman-active transition 6P 1/2−6P 3/2 of thallium atoms (ω R /2πc=7793 cm −1) under resonant Raman excitation by a biharmonic picosecond pulsed field, giving rise to substantial motion of the population, is detected. Optical nutation appears as an oscillatory behavior of the energy of the anti-Stokes scattering of probe pulses, which follow with a fixed delay, as a function of the product of the energies of the excitation pulses. As a result of the dynamic Stark effect, which decreases the frequency of the transition under study, resonance excitation conditions are satisfied for negative initial detunings of the Raman excitation frequency from resonance. The Raman scattering cross section for the transition under study is estimated by comparing the experimental data with the calculations.