# Continuous Acceleration Sensing Using Optomechanical Droplets

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Existence of Optomechanical Droplets

## 4. Continuous Acceleration Sensing Using Optomechanical Droplets

^{−2}. For accelerations much smaller than this, a limiting factor will be the heating of the BEC due to spontaneous light scattering. This will become significant when the interaction time becomes significantly larger than ${r}_{s}^{-1}$, where ${r}_{s}$ is the rate at which photons are incoherently scattered by the BEC. In [56], it is shown that

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the single mirror feedback (SMF) configuration showing a BEC interacting with a forward propagating optical field (F) and a retroreflected/backward propagating optical field (B) while undergoing an acceleration (a) in the $x-$direction. The optical image of the BEC is detected after transmission through the BEC, propagation in free space to a mirror of reflectivity, R, at a distance d from the BEC, and further propagation over distance d.

**Figure 2.**Evolution of the BEC density, $|\mathrm{\Psi}(\overline{x},\overline{t}){|}^{2}$, and optical intensity at the image plane, $|{F}_{\mathrm{trans}}(\overline{x},\overline{t}){|}^{2}$, calculated from the BEC–SMF model, Equations (1)–(3), using an initial condition where the BEC density is a Gaussian function of position with width ${\sigma}_{\overline{x}}=0.562$. Parameters used are ${\overline{\omega}}_{r}=1.14\times {10}^{-5}$, ${b}_{0}=100$, $\Delta =-10000$, $R=0.99$ and ${p}_{0}=10{p}_{\mathrm{th}}=2.28\times {10}^{-6}$.

**Figure 3.**Evolution of the BEC density, $|\mathrm{\Psi}(\overline{x},\overline{t}){|}^{2}$, and optical intensity at the image plane, $|{F}_{\mathrm{trans}}(\overline{x},\overline{t}){|}^{2}$, calculated from the accelerating BEC–SMF model, Equation (2), (3) and (8), showing a uniformly accelerating droplet. Parameters used are identical those in Figure 2 with the exception of the acceleration parameter, which here is $\overline{a}=1.0\times {10}^{-5}$.

**Figure 4.**Plot of position of central optical intensity maximum, ${\overline{x}}_{\mathrm{max}}$, against ${\overline{t}}^{2}$ from Figure 3.

**Figure 5.**Evolution of the BEC density, $|\mathrm{\Psi}(\overline{x},\overline{t}){|}^{2}$, and optical intensity at the image plane, $|{F}_{\mathrm{trans}}(\overline{x},\overline{t}){|}^{2}$, calculated from the accelerating BEC–SMF model, Equation (2), (3) and (8), with no mirror feedback ($R=0$). All other parameters are identical to those in Figure 3.

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**MDPI and ACS Style**

Robb, G.R.M.; Walker, J.G.; Oppo, G.-L.; Ackemann, T.
Continuous Acceleration Sensing Using Optomechanical Droplets. *Atoms* **2024**, *12*, 15.
https://doi.org/10.3390/atoms12030015

**AMA Style**

Robb GRM, Walker JG, Oppo G-L, Ackemann T.
Continuous Acceleration Sensing Using Optomechanical Droplets. *Atoms*. 2024; 12(3):15.
https://doi.org/10.3390/atoms12030015

**Chicago/Turabian Style**

Robb, Gordon R. M., Josh G. Walker, Gian-Luca Oppo, and Thorsten Ackemann.
2024. "Continuous Acceleration Sensing Using Optomechanical Droplets" *Atoms* 12, no. 3: 15.
https://doi.org/10.3390/atoms12030015