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Journal of the Optical Society of America B

Characterization of a forced damped harmonic oscillator in a magneto-optical trap of 133 Cs atoms

Jaeuk Baek, Sanglok Lee, Min-Hwan Lee, Geol Moon

Published May 23, 2023• 4 citations
Publisher

Abstract

We report the characterization of the forced damped harmonic oscillations of 133 Cs atoms in a magneto-optical trap, which was realized by modulating the intensity of the lasers counterpropagating along the anti-Helmholtz coil axis. Trap parameters such as trap frequency, damping coefficient, and magnitude of the driving force were determined from the resonant vibrational amplitude of the 133 Cs atomic cloud depending on the modulation frequency of the modulated laser intensity. The experimental results were compared with the theoretical ones based on the simple two-level and multi-level atom models, considering all possible transition lines used to trap the 133 Cs atom, and were found to be consistent with their theoretical counterparts. Furthermore, we theoretically examined the effect of the repumping laser on trap parameters.

DOI
10.1364/josab.489096

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We report a simple method for trap parameter measurement by realizing forced harmonic oscillation in a magneto-optical trap (MOT). Through the resonance curve of the vibrational amplitude of the harmonic oscillation on the driving frequency of the laser intensity, we measured the damping coefficient and trap frequency of trapped atoms in the MOT under various conditions and compared them with those obtained from the parametric resonance. In particular, we report a significant effect of a transverse laser on one-dimensional harmonic oscillation. This effect is expected to explain the discrepancies in other previous experiments between the experimental and theoretical results.
Abstract We report the first observation of motional excitation induced by parametric resonance of cold 133^{133}133Cs atoms in a dual-species magneto-optical trap (MOT) simultaneously trapping 133 Cs and 85 Rb atoms. By modulating the cooling laser’s intensity at approximately twice the resonant frequency of the trap, the atoms inside the trap separate into two atomic clouds, oscillating with a π phase difference due to the trap potential’s nonlinearity, resulting in a finite oscillation length. This behavior reflects general nonlinear dynamics and is described as a Hopf bifurcation or limit cycle motion. The measured oscillation amplitude was compared with theoretical calculations derived from simple Doppler cooling theory, changing modulation amplitude, magnetic field gradient, and saturation parameter. In addition, we investigate the noise-induced switching dynamics by measuring the temporal evolution of atomic populations localized in each of the two attractors under resonant symmetry lifting induced by an effective bias field. Notably, this dual-species MOT system is expected to provide a new platform for studying nonlinear and nonequilibrium dynamics between cold rubidium and cesium atomic ensembles. PACS numbers: 37.10.Vz, 37.10.De, 37.10.Gh
We demonstrate parametric resonance in a magneto-optical trap. When we modulate the intensity of the cooling laser at about twice the resonant frequency of the trap, the atoms in the trap are divided into two parts and oscillate with 180 degree phase difference with the finite length due to nonlinearity of the trap potential. These are the effects of general nonlinear dynamics, called the Hopf bifurcation, or limit cycle motion. The amplitude and the phase of the oscillations are measured and compared with the theoretical calculations based on simple Doppler cooling theory. The experimental results are in excellent agreement with the simulation results based on the simple Doppler cooling theory.
We present a method to measure the trap frequency or the spring constant of a magneto-optical atom trap via the parametric resonance. When the intensity of the cooling laser is modulated at around twice its resonant trap frequency, the trapped atoms are parametrically excited and divided into two groups oscillating with the motional phase difference of $\ensuremath{\pi}$. We find that one can measure the natural trap frequency as the modulation amplitude is decreased down to its threshold value. The experimental results are in good agreement with the three-dimensional Doppler cooling theory based on the rate equation model.
Alkaline-earth-metal atoms present an ideal platform for exploring magneto-optic trap (MOT) dynamics, enabling unique and definitive tests of laser cooling and trapping mechanisms. We have measured the trapping beam intensity, detuning, magnetic-field gradient, trap density, and lifetime dependence of the spring constant $\ensuremath{\kappa}$ and damping coefficient $\ensuremath{\alpha}$ for a ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ 88Sr{}^{88}\mathrm{Sr}88Sr MOT by fitting the oscillatory response of the atom cloud to a step-function force. We find that the observed behavior of $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ provide a unified and consistent picture of trap dynamics that agrees with Doppler cooling theory at the level of 1010%.10 Additionally, we demonstrate that the trapped atom temperature can be determined directly from measured value of $\ensuremath{\kappa}$ and the trap size, in excellent agreement with free-expansion temperature measurements. However, the experimentally determined temperature is much higher than Doppler cooling theory, implying significant additional heating mechanisms.
Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.