# Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum

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## Abstract

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## 1. Introduction

## 2. Experimental Setup with Improved Precision

#### 2.1. Sources of Error

#### 2.2. Sensitivity Estimation

## 3. Possibilities to Measure Thermal Effects in the Casimir Force

## 4. Prospective Constraints on Non-Newtonian Gravity and Axion-Like Particles

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Simplified two-dimensional schematic representation of our setup with included improvements proposed in the main text. The material composition of the surfaces is shown separately on the left.

**Figure 2.**Estimated experimental uncertainties for the present and improved versions of the setup as a function of separation between the two parallel plates. (

**a**) Pressure measurements using the upper interferometer. (

**b**) Pressure gradient measurements using the lower interferometer.

**Figure 3.**(

**a**) The magnitude of the Casimir pressure between two parallel Au plates and (

**b**) the pressure gradient are shown as functions of separation by the red and blue solid lines computed at $T=300\phantom{\rule{3.33333pt}{0ex}}$K using the plasma and Drude extrapolations of the optical data, respectively. The same quantities computed at $T=0$ are shown by the dashed lines. The region of separations from 5 to 10 $\mathsf{\mu}$m is shown in the insets using the homogeneous scale.

**Figure 4.**The relative thermal corrections to (

**a**) the Casimir pressure between two parallel Au plates and (

**b**) its gradient is shown as functions of separation by the red and blue lines computed at $T=300\phantom{\rule{3.33333pt}{0ex}}$K using the plasma and Drude extrapolations of the optical data, respectively.

**Figure 5.**Constraints on the parameters of Yukawa-type interaction obtained from two Casimir-less experiments, from measuring the difference in lateral forces, from the torsion pendulum experiment and from the Cavendish-type experiments are shown by the top and bottom blue lines, green, black and gray lines, respectively. The proposed constraints which could be obtained from the Cannex test of the quantum vacuum when measuring (

**a**) the Casimir pressure and (

**b**) its gradient are indicated by the red lines.

**Figure 6.**Constraints on the axion-to-nucleon coupling constant obtained from the improved Casimir-less experiment, the Cavendish-type experiment, measurements of the effective Casimir pressure, and the lateral Casimir force are shown by the blue, gray, black, and green lines, respectively. The proposed constraints which could be obtained from the Cannex test of the quantum vacuum when measuring (

**a**) the Casimir pressure and (

**b**) its gradient are indicated by the red lines.

**Table 1.**Values for the experimental parameters and uncertainties for the setup in its present configuration and after the proposed improvements.

Parameter | Present Value | Improved Value | |
---|---|---|---|

Separation uncertainty $\delta {a}_{\mathrm{cal}}$ | 2.0 | 0.5 | nm |

Mass calibration error $\delta {m}_{\mathrm{eff}}$ | 1.0 | 0.01 | % |

Area uncertainty $\delta A$ | $5\times {10}^{-4}$ | $5\times {10}^{-4}$ | cm${}^{2}$ |

Applied AC voltages uncertainty | 10 | 1 | $\mathsf{\mu}$$\mathrm{V}$ |

Frequency measurement error | ${10}^{-5}$ | $4\times {10}^{-7}$ | Hz |

Vibration amplitude at ${f}_{0}$ | 300 | 20 | nm |

Patches ${V}_{\mathrm{rms}}$ | 1.28 | 0.64 | V |

Patches $\langle {\ell}^{2}\rangle $ | 7.3 | 2.4 | $\mathsf{\mu}$$\mathrm{m}$${}^{2}$ |

Tilt angle $\delta \alpha $ | 3.0 | 0.1 | $\mathsf{\mu}$$\mathrm{rad}$ |

Temperature stability | 3.0 | 0.5 | mK |

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**MDPI and ACS Style**

Klimchitskaya, G.L.; Mostepanenko, V.M.; Sedmik, R.I.P.; Abele, H.
Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum. *Symmetry* **2019**, *11*, 407.
https://doi.org/10.3390/sym11030407

**AMA Style**

Klimchitskaya GL, Mostepanenko VM, Sedmik RIP, Abele H.
Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum. *Symmetry*. 2019; 11(3):407.
https://doi.org/10.3390/sym11030407

**Chicago/Turabian Style**

Klimchitskaya, Galina L., Vladimir M. Mostepanenko, René I. P. Sedmik, and Hartmut Abele.
2019. "Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum" *Symmetry* 11, no. 3: 407.
https://doi.org/10.3390/sym11030407