# Parametric Excitation of Ultracold Sodium Atoms in an Optical Dipole Trap

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## Abstract

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## 1. Introduction

## 2. Experimental Setup

## 3. Theoretical Simulation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Experimental apparatus of the science chamber and a part of the Zeeman slower. The science chamber is an octagonal chamber with 12 viewports. Magneto-optical trap (MOT) cooling beams (yellow arrows) and repump beams (blue line in yellow arrows) are coupled together. The Zeeman slowing beam (brown arrow) is used to decelerate the ejected atoms (yellow ball). A focused ODT (red arrow) along a cooling beam captures the atoms. The orange arrows represent the image beams.

**Figure 2.**Experimental sequence of parametric excitation of atoms in the ODT. The axes are not to scale.

**Figure 3.**The experimental spectrum of the losses associated to parametric excitation of the ODT modulated by a sine wave (black data), a triangle wave (red data) and a square wave (blue data). The modulation depth is 0.15. Gaussian fits were used to determine the resonance center position. The measured resonance positions are 2.47 (±0.19) kHz, ∼4.89 (±0.15) kHz and ∼7.31 (±0.27) kHz, corresponding to the frequencies of ${\omega}_{0}$, $2{\omega}_{0}$, and $3{\omega}_{0}$, respectively.

**Figure 4.**Experimental result (data points) and theoretical fitting (colorful solid lines) of the evolution of the trapped atom population. The modulation frequencies are $2{\omega}_{0}$ and the modulation depths are 0.15. The green points show an experimental trap loss measurement without modulation as a comparison.

**Figure 5.**Decimal logarithms of the simulated population of the lowest level vs. the relative frequency $\omega /{\omega}_{0}$ of the modulation signal at the instant $t=50\phantom{\rule{0.277778em}{0ex}}$ms, within the model described above: black—the sinusoidal modulation signal, red—the triangular modulation signal, blue—the square modulation signal.

**Figure 6.**Simulated time evolution of the lowest level population vs time (s) at the frequency $\omega =2\phantom{\rule{0.166667em}{0ex}}{\omega}_{0}$ of the modulation signal, within the model described above: black—the sinusoidal modulation signal, red—the triangular modulation signal, blue—the square modulation signal.

**Figure 7.**Decimal logarithms of the simulated population of the lowest level vs the relative frequency $\omega /{\omega}_{0}$ of the modulation signal at the instant $t=50\phantom{\rule{0.277778em}{0ex}}$ms, within the pure harmonic (i.e., with ${\omega}_{3}=0$) model described above: black—the sinusoidal modulation signal, red—the triangular modulation signal, blue—the square modulation signal.

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**MDPI and ACS Style**

Zheng, N.; Liu, W.; Wu, J.; Li, Y.; Sovkov, V.; Ma, J. Parametric Excitation of Ultracold Sodium Atoms in an Optical Dipole Trap. *Photonics* **2022**, *9*, 442.
https://doi.org/10.3390/photonics9070442

**AMA Style**

Zheng N, Liu W, Wu J, Li Y, Sovkov V, Ma J. Parametric Excitation of Ultracold Sodium Atoms in an Optical Dipole Trap. *Photonics*. 2022; 9(7):442.
https://doi.org/10.3390/photonics9070442

**Chicago/Turabian Style**

Zheng, Ningxuan, Wenliang Liu, Jizhou Wu, Yuqing Li, Vladimir Sovkov, and Jie Ma. 2022. "Parametric Excitation of Ultracold Sodium Atoms in an Optical Dipole Trap" *Photonics* 9, no. 7: 442.
https://doi.org/10.3390/photonics9070442