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Journal of the Korean Physical Society

Parametric excitation of a cold atom in an optical polarization-modulated magneto-optical trap

Min-Hwan Lee, Dooyoung Kim, Sanghyun Park, Jaeuk Baek, Geol Moon

Published Oct 10, 2025• 0 citations
Publisher

Abstract

Abstract This paper presents a novel method for achieving parametric excitation in an optical polarization-modulated magneto-optical trap for a two-level atom. The proposed method has a unique mechanism that is different from that of the existing methods, which modulate the laser intensity, magnetic field gradient, or laser detuning, because the excitation realized through the polarization modulation originates from the competition between the repulsive and attractive forces on a two-level atom. The theoretical calculation is based on the simple Doppler cooling theory, and we derive atomic motion in a rotating frame and coupled equation for motional amplitude and phase, in detail. PACS numbers: 37.10.Vz, 37.10.De, 37.10.Gh

DOI
10.1007/s40042-025-01486-4

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Abstract This paper presents a novel method for achieving parametric excitation in an optical polarization-modulated magneto-optical trap for a two-level atom. The proposed method has a unique mechanism that is different from that of the existing methods, which modulate the laser intensity, magnetic field gradient, or laser detuning, because the excitation realized through the polarization modulation originates from the competition between the repulsive and attractive forces on a two-level atom. The theoretical calculation is based on the simple Doppler cooling theory, and we derive atomic motion in a rotating frame and coupled equation for motional amplitude and phase, in detail. PACS numbers: 37.10.Vz, 37.10.De, 37.10.Gh
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.
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.
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
The double structure potential predicted in the atomic cloud of a magneto-optical trap by one- (Doppler part) and two-photon process (sub-Doppler part) is experimentally observed and studied through the parametric excitation with the modulation of cooling laser intensities. Modulating the intensity of the cooling laser at around twice its resonant frequency of Doppler part, the atoms in Doppler part are divided and they oscillate reciprocally with finite amplitude due to the nonlinearity of the trap, and the others in sub-Doppler part are not influenced. By the modulation, we can investigate the sub-Doppler part spatially without Doppler part and also measure the temperature of sub-Doppler part independently.
Magnesium atoms are cooled in a magneto-optical trap (MOT) using the 3s2 S0 → 3s3p P1 resonance transition. Magnesium is a simple atom which offers a unique possibility for comparison to the Doppler theory of laser cooling. We measure trap parameters as a function of laser-intensity, -detuning and magnetic field gradient. We find the main features well accounted for by Doppler theory, but temperature measurements gave significant higher values than predicted by the Doppler theory. We also observe radiation pressure effects within the MOT that limit the maximum achievable density. Comparing our results to predictions by models in the literature shows a good agreement. Recently we have improved our set-up and now trap about 150 × 106 atoms.
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.