#
Optical Pumping of TeH^{+}: Implications for the Search for Varying m_{p}/m_{e}

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## Abstract

**:**

## 1. Introduction

## 2. Molecular Structure

#### 2.1. Magnetic Dipole Moments

## 3. Internal State Cooling

#### 3.1. ${X}_{1}{0}^{+}$ − ${X}_{2}1$ Coupling

#### 3.2. Rotational Cooling on $X-b{0}^{+}$ at 600 nm

#### 3.2.1. Vibrational Repumping

#### 3.3. Rotational Cooling on $X-a2$ at 1300 nm

#### 3.3.1. CW Assist

#### 3.4. Vibrational Cooling

## 4. Rate Equation Simulation

## 5. State Preparation during Spectroscopy Cycle

## 6. $\mathit{\mu}$ Variation Measurement

#### 6.1. Single-Ion TeH${}^{+}$ Measurement

#### 6.2. Multi-Ion Spectroscopy

#### 6.3. Homonuclear Molecule Benchmarks

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Relevant spontaneous emission channels and partial lifetimes of TeH${}^{+}$. Line thicknesses (not to scale) represents the branching ratios of each excited state.

**Figure 4.**Rotational cooling scheme using $\mathrm{X}\to \mathrm{b}{0}^{+}$ at 600 nm. Straight arrows show transitions driven by lasers, with arrow width indicating laser linewidth. Both the X${}_{1}{0}^{+}$− X${}_{2}1$ coupling and the X${}_{2}1$→ b${0}^{+}$ lasers are capable of driving M1 transitions that preserve parity. The wavy arrow indicates the spontaneous emission channel to the dark state.

**Figure 5.**Rotational cooling scheme using $\mathrm{X}\to \mathrm{a}2$ at 1300 nm. Straight arrows show transitions driven by lasers, with arrow width indicating laser linewidth. Yellow arrows indicate CW-assist lasers. The wavy arrow indicates the spontaneous emission channel to the dark state.

**Figure 6.**Vibrational cooling. Straight arrows indicate transitions covered by lasers, and wavy arrows indicate spontaneous emission channels.

**Figure 7.**Simulation results for the $|{\mathrm{X}}_{1}{0}^{+},v=0,J=0\rangle $ population versus cooling time, beginning from a 293 K thermal distribution.

**Figure 8.**Simulation results for statistical uncertainty using various state preparation schemes, a single TeH${}^{+}$ ion and for one day of averaging. Squares represent the projection noise-limited outcome, corresponding to instantaneous state preparation with 100% fidelity. ‘Optical’ indicates results for rotational cooling at 600 nm, with vibrational repump (VR) included. ‘IR’ refers to rotational cooling at 1300 nm, with two CW-assist lasers included. Diamonds indicate results without vibrational cooling, and circles indicate results with each cycle ending with vibrational cooling (VC) followed by rotational cooling.

**Figure 9.**The total number of photon scatters from $|\mathrm{b}{0}^{+},v=0,J=0\rangle $ as a function of time, in the two-laser fluorescence state detection scheme described in the text.

**Table 1.**Properties of vibrational transitions $v=0\to {v}^{\prime}=n$. ${T}_{\mathrm{VC}}$ is the simulated optimal cooling time for vibrational cooling. $\mathsf{\Omega}/\left(2\pi \right)$ and $S/\left(2\pi \right)$ are in units of THz.

n | $\mathit{\tau}$ (ms) | $\mathsf{\Omega}/\left(2\mathit{\pi}\right)$ | $\mathit{S}/\left(2\mathit{\pi}\right)$ | ${\mathit{T}}_{\mathbf{VC}}$ (ms) |
---|---|---|---|---|

1 | 210 | 62 | 30 | 0 |

2 | 110 | 120 | 58 | 1.0 |

3 | 85 | 180 | 83 | 1.2 |

4 | 70 | 230 | 110 | 1.4 |

5 | 61 | 290 | 130 | 1.6 |

6 | 53 | 340 | 140 | 1.7 |

7 | 47 | 380 | 160 | 1.9 |

8 | 41 | 430 | 170 | 2.0 |

**Table 2.**Benchmark candidates for $\mu $ variation measurement. The upper vibrational states n that maximize the absolute sensitivities are calculated from molecular constants [52] and achievable precision for zero dead time, $C=0.6$, an averaging time $T=1$ day, and a coherence time of 6 s [53]. $\mathsf{\Omega}/\left(2\pi \right)$ and $S/\left(2\pi \right)$ are in units of THz.

n | $\mathsf{\Omega}/\left(2\mathit{\pi}\right)$ | $\mathit{S}/\left(2\mathit{\pi}\right)$ | ${\mathit{\sigma}}_{\mathit{y}}^{\left(\mathit{\mu}\right)}\left(1\mathbf{day}\right)/{10}^{-19}$ | |
---|---|---|---|---|

N${}_{2}^{+}$ | 33 | 1700 | 540 | 6.7 |

O${}_{2}^{+}$ | 28 | 1200 | 390 | 9.1 |

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**MDPI and ACS Style**

Stollenwerk, P.R.; Kokish, M.G.; De Oliveira-Filho, A.G.S.; Ornellas, F.R.; Odom, B.C. Optical Pumping of TeH^{+}: Implications for the Search for Varying *m _{p}*/

*m*.

_{e}*Atoms*

**2018**,

*6*, 53. https://doi.org/10.3390/atoms6030053

**AMA Style**

Stollenwerk PR, Kokish MG, De Oliveira-Filho AGS, Ornellas FR, Odom BC. Optical Pumping of TeH^{+}: Implications for the Search for Varying *m _{p}*/

*m*.

_{e}*Atoms*. 2018; 6(3):53. https://doi.org/10.3390/atoms6030053

**Chicago/Turabian Style**

Stollenwerk, Patrick R., Mark G. Kokish, Antonio G. S. De Oliveira-Filho, Fernando R. Ornellas, and Brian C. Odom. 2018. "Optical Pumping of TeH^{+}: Implications for the Search for Varying *m _{p}*/

*m*"

_{e}*Atoms*6, no. 3: 53. https://doi.org/10.3390/atoms6030053