Analytical solutions for the subsidiary maxima in multiple slit interference

Optical Review - We present analytical solutions for the subsidiary maxima in multiple slit interference up to eleven slits. For the number of slits N, there exist $$N-2$$ subsidiary maxima between...     

Analytic solutions of the susceptibility for Doppler-broadened two-level atoms

We derive the rigorous analytic solutions for the susceptibility of Doppler-broadened two-level atoms, valid for arbitrary laser intensities. As is usually the case with real atoms, we observe that, when the homogeneous linewidth is much narrower than the Doppler width, the real part of the susceptibility is given by the product of an imaginary error function and a Gaussian, whereas the imaginary part consists simply of a Gaussian function. By employing the analytic results, in particular, we study the effects of optical pumping and saturation on the atomic susceptibility. We also find that the real (imaginary) part of the susceptibility is weakly (strongly) dependent on such parameters as the laser intensity or the optical pumping rate. The availability of analytic solutions for the simple laser-atom interaction may provide convenient tools for its understanding as well as application to more general and realistic situations.     

Spin polarization in a freely evolving sample of cold atoms

We have implemented and optimized a technique of spin polarization by optical pumping in a caesium atomic fountain, gaining a nearly fivefold increase in the useful cold atom signal in detection. This allows an improvement of the fountain clock stability without compromising its accuracy. We present a detailed study of optical pumping in a freely evolving cloud of cold caesium atoms: we have investigated theoretically and experimentally the dynamics of the pumping process and the associated heating due to random photon scattering. The heating limits the potential gain in the fountain signal due to an additional cloud expansion. A high degree of spin polarization was achieved with accumulation of up to 97 % of the population in a single magnetic (m _F  = 0) sublevel of the ground state. Factors affecting the achievable spin polarizations, such as the purity of the pumping light polarization and the shadowing effect in the cloud, were considered. This technique may also be used in atom interferometers and for other alkali metal systems.     

Spontaneous symmetry breaking of population in a nonadiabatically driven atomic trap: an Ising-class phase transition

We have observed spontaneous symmetry breaking of the population of Brownian particles between two moving potentials in the spatiotemporally symmetric system. Cold atoms preferentially occupy one of the dynamic double-well potentials, produced in the parametrically driven dissipative magneto-optical trap far from equilibrium, above a critical number of atoms. We find that the population asymmetry, which may be interpreted as the biased Brownian motion, can be qualitatively described by the mean-field Ising-class phase transition. This in situ study may be useful for investigation of dynamic phase transition or temporal behavior of critical phenomena.     

Nonequilibrium dynamics of parametrically excited cold atoms via magnetic field-gradient modulation

We propose that the driven cold atomic system whose trap potential is periodically perturbed via parametric modulation of the magnetic field-gradien is a novel system to investigate the complex dynamics in nonlinear dynamical systems. We calculate the atomic trajectories and basins of attraction by varying the modulation amplitude and the modulation frequency. The calculation results show parametric resonance similar to those in Kim et. al.'s work [Opt. Commun. 236 (2004) 349] on cold atoms under parametric modulation of trap laser intensities in the case of small modulation amplitude or low modulation frequency. As the modulation amplitude or the modulation frequency is increased, the nonlinear effects are enhanced so that the dynamics of the system shows a wide variety of nonlinear behaviors, such as period doubling and chaos. We experimentally demonstrate the parametric resonance when the magnetic field gradient is parametrically modulated, which evidences the realization of the proposed system. We expect that this system is useful for understanding the stochastic phenomena occurring between complex basins of attraction, such as fluctuation induced transitions across the complex basin boundaries.     

Output characteristics of a simple FP-LD/FBG module

We propose a simple laser diode module that consists of a Fabry–Perot laser diode (FP-LD) and a fiber Bragg grating (FBG) for a compact, stable and low-cost wavelength division multiplexing light source. The spectral bandwidth of the laser output from the FP-LD/FBG module was measured to be 0.024 nm. The side mode suppression ratio (SMSR) was 44.42 dB at the injected electric current of 14 mA and at 25 °C. Both the BER characteristics and the eye diagram were measured, and they confirmed that the present laser diode module could be used as an alternative configuration for a low-cost light source.     

Comment on “On the analytical solution of the optical Bloch equations”

In a recent paper [P.J. Colmenares and J.L. Paz, Opt. Commun. 284 (2011) 5171], analytical solutions of the optical Bloch equations are presented. This paper follows the same procedures as presented in the paper by the authors [H.R. Noh and W. Jhe, Opt. Commun. 283 (2010) 2353] but concludes that their results are substantially different from the results of the authors. We find that the discrepancy results from the wrong initial conditions employed by those authors for one of the Bloch vector components (w), whose initial value must be 1 not 0. We also find that if proper initial conditions are used, there are no discrepancies between the two results.     

Analytic solutions of the optical Bloch equations

We present analytic solutions of optical Bloch equations. We found that the solutions exhibit two different types of the behavior: one is oscillatory, and the other is a simple decay. The boundary dividing the two different types of solutions is exactly calculated in a two-dimensional space of the laser detuning and Rabi frequency. We also obtained simple analytic solutions for special conditions.     

High-order resonances in a parametrically excited magneto-optical trap

We present analytical and numerical study of high-order parametric resonance in a driven magneto-optical trap of cold atoms. We have obtained the general solutions for parametric resonance of arbitrary order. In particular, the amplitude and phase of atomic limit-cycle motion is expressed as a function of the modulation amplitude and frequency. Moreover, the atomic dynamics for high-order parametric resonance is investigated in terms of the Hamiltonian approach, which is useful in studying transitions between attractors. We find that the analytical results are in good agreement with the numerical calculations.