Optical pumping effect in absorption imaging of F=1 atomic gases

We report our study of the optical pumping effect in absorption imaging of $^{23}$Na atoms in the $F=1$ hyperfine spin states. Solving a set of rate equations for the spin populations in the presence of a probe beam, we obtain an analytic expression for the optical signal of the $F=1$ absorption imaging. Furthermore, we verify the result by measuring the absorption spectra of $^{23}$Na Bose-Einstein condensates prepared in various spin states with different probe beam pulse durations. The analytic result can be used in the quantitative analysis of $F=1$ spinor condensate imaging and readily applied to other alkali atoms with $I=3/2$ nuclear spin such as $^{87}$Rb.Comment: 6 pages, 4 figure

Modulation Transfer Spectroscopy of the D1 Transition of Potassium: Theory and Experiment

We report on a study of modulation transfer spectroscopy of the $4\textrm{S}_{1/2}\rightarrow 4\textrm{P}_{1/2}$ ($D_{1}$) transition of naturally abundant potassium in a room-temperature vapour cell. This transition is critical for laser cooling and optical pumping of potassium and our study is therefore motivated by the need for robust laser frequency stabilisation. Despite the absence of a closed transition, the small ground-state hyperfine splitting in potassium results in strong crossover features in the $D_{1}$ modulation transfer spectrum. To emphasise this we compare the $D_{1}$ and $D_{2}$ spectra of potassium with those of rubidium. Further, we compare our experimental results with a detailed theoretical simulation, examining different pump-probe polarization configurations to identify the optimal signals for laser frequency stabilisation. We find good agreement between the experiment and the theory, especially for the $\textrm{lin} \parallel \textrm{lin}$ polarization configuration

Spontaneous Symmetry Breaking of Population between Two Dynamic Attractors in a Driven Atomic Trap: Ising-class Phase Transition

We have observed spontaneous symmetry breaking of atomic populations in the dynamic phase-space double-potential system, which is produced in the parametrically driven magneto-optical trap of atoms. We find that the system exhibits similar characteristics of the Ising-class phase transition and the critical value of the control parameter, which is the total atomic number, can be calculated. In particular, the collective effect of the laser shadow becomes dominant at large atomic number, which is responsible for the population asymmetry of the dynamic two-state system. This study may be useful for investigation of dynamic phase transition and temporal behaviour of critical phenomena.Comment: 4 pages, 4 figure

Analytical Solutions of Temporal Evolution of Populations in Optically-Pumped Atoms with Circularly Polarized Light

We present an analytical calculation of temporal evolution of populations for optically pumped atoms under the influence of weak, circularly polarized light. The differential equations for the populations of magnetic sublevels in the excited state, derived from rate equations, are expressed in the form of inhomogeneous second-order differential equations with constant coefficients. We present a general method of analytically solving these differential equations, and obtain explicit analytical forms of the populations of the ground state at the lowest order in the saturation parameter. The obtained populations can be used to calculate lineshapes in various laser spectroscopies, considering transit time relaxation