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Observation of Parametric Resonance Phenomenon in a Cold Cesium Atoms

Dooyoung Kim, Jaeuk Baek, Minsu Kim, J K Ju, Hyogi Kim, Minjae Gwak, Donghyeon Yu, 장시원, Min-Hwan Lee, Geol Moon

Published Jun 11, 2026• 0 citations
Publisher

Abstract

Abstract We report the first observation of motional excitation induced by parametric resonance of cold $^{133}$Cs 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

DOI
10.21203/rs.3.rs-9841982/v1

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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 have made a nonlinear dynamics study of a parametrically driven magneto-optical trap. When the trapping potential is modulated at around twice the trap frequency above a threshold, the limit cycle is manifested as two separate collective atomic packets oscillating with opposite phases and finite amplitudes, determined by the balance of the nonlinearity and the damping of the trap. In particular, we directly observe in situ the subcritical Hopf bifurcation, which suddenly converts the combined motions of a limit cycle and a stable attractor into a limit cycle motion. The experimental results are in quantitative agreement with the numerical results based on the simple Doppler cooling theory.
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
The results of characterization of cold cloud of cesium (Cs) atoms trapped in a magneto-optical trap (MOT) have been presented. The MOT is a part of the Physics package of the Cs Fountain Clock being developed at National Physical Laboratory (NPL), India. The number of atoms, size and temperature of the cloud have been measured and calculated. It is also been investigated how the number of trapped atoms changes with the trapping laser’s beam intensity, detuning and magnetic-field gradient of the trap.
Abstract We describe a three-dimensional (3D) magneto-optical trap (MOT) capable of simultaneously capturing 85Rb and 133Cs atoms. Unlike conventional setups, our system utilizes two separate laser systems that are combined before entering the vacuum chamber, enabling the simultaneous trapping of two different atomic species. We trapped 85Rb and 133Cs atoms using relatively low total power: 8 mW cooling and 4 mW repump for 85Rb, and 7.5 mW cooling and 1.5 mW repump for 133Cs. The number of trapped atoms was 1.6 × 108 for 85Rb and 1.4 × 108 for 133Cs. The optical depths were 3.71 for 85Rb and 3.45 for 133Cs. The temperature of trapped atoms was ∼200 μK for 85Rb and ∼200 μK for 133Cs. Our 3D MOT setup allows full horizontal optical access to the trapped atomic ensembles without spatial interference from the trapping or repump laser beams. Our vacuum system is also quite simple, avoiding much of the complexity typically encountered in similar dual-species systems. However, the red detuning of the cooling laser used for atomic trapping in our system is relatively small, leaving room for further optimization. This system offers a versatile platform for exploring complex phenomena in ultracold atom physics, such as Rydberg molecule formation and interspecies interactions.
We have investigated the noise-induced transition of cold atoms between double or triple phase-space attractors that are produced in the parametrically driven magneto-optical trap. The transition rates between two dynamic attractors, directly measured for various modulation frequencies and amplitudes, are in good agreement with calculations from the dynamic version of Kramers' theory and Monte Carlo simulations. For the triple attractors, the transition rates are measured indirectly through the steady-state population and the results are also in agreement with simulations. Our experiment may be useful for study of nonlinear dynamic problems involving transitions between states far from equilibrium.