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Physical Review A

Measurements of trap parameters of a magneto-optical trap by parametric resonance

Kihwan Kim, Heung‐Ryoul Noh, Wonho Jhe

Published Mar 23, 2005• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.71.033413

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ. 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.
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.
We have measured the trap frequency as well as the damping coefficient of a magneto-optical trap by using a transient oscillation method. The dependence of such trap properties on the various experimental parameters such as the cooling laser intensity, detuning, and magnetic field gradient is investigated. We find that the measured trap frequency is in excellent agreement with the simple rate-equation analysis based on the Doppler cooling theory. In contrast, the damping coefficient is about twice as large as the calculated one, which is attributed to the existence of the sub-Doppler trap near the trap center.
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 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 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.