#
Toward a New Generation of Compact Transportable Yb^{+} Optical Clocks

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## Abstract

**:**

## 1. Introduction

## 2. First Generation of a Transportable ${}^{171}{\mathrm{Yb}}^{+}$ Clock at the Lebedev Institute

## 3. Results

#### 3.1. Ion Trap

#### 3.2. Clock Laser

#### 3.3. Optical Frequency Comb

#### 3.4. Spectroscopy of the Quadrupole Clock Transition

## 4. Comparison with Tm Optical Clock

## 5. New Solutions for Compact Clock Modules

#### 5.1. Clock Laser with Low Sensitivity to Vibrations

#### 5.2. Compact OFC

#### 5.3. Planar Ion Trap with Elements of Integrated Photonics

#### 5.4. Outlook

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

UTC | Coordinated Universal Time |

TAI | International Atomic Time |

OFC | Optical Frequency Comb |

AC | Alternating Current |

PDH | Pound–Drever–Hall |

RF | Radio Frequency |

DC | Direct Current |

ECDL | External Cavity Diode Laser |

FWHM | Full-Width Half-Maximum |

ULE | Ultra-Low Expansion Glass |

CTE | Coefficient of Thermal Expansion |

PLL | Phase-Locked Loop |

NALM | Nonlinear Amplifying Loop Mirror |

DDS | Direct Digital Synthesis |

PZT | Lead Zirconate Titanate |

PM | Polarization Maintaining |

EDFA | Erbium-Doped Fiber Amplifier |

PC | Personal Computer |

EOM | Electo-optic Modulator |

AOM | Acousto-optic Modulator |

PMT | Photomultiplier Tube |

PIC | Integrated Photonic Circuits |

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**Figure 1.**The first generation of a transportable single ${}^{171}{\mathrm{Yb}}^{+}$ clock at the Lebedev Institute.

**Figure 4.**Scheme of clock laser module. PID — fast proportional–integral–derivative controller; ULE — reference optical cavity in a vacuum chamber; AOM, EOM — acousto- and electro-optical modulators; $\lambda /2$ — zero-order half-wave plate.

**Figure 5.**Modified Allan deviation ${\sigma}_{beat}$ of the beat-note signal between 871 nm and OFC, stabilized by 1140 nm laser system. Linear drift of 348 mHz s${}^{-1}$ is subtracted.

**Figure 8.**The clock transition excitation probability; $\pi $–pulse duration is 30 ms: (blue points) experimental data and (red line) the approximation by a sinc function.

**Figure 9.**The next design of reference cavity with a part of the support system (bottom view; CAD drawing).

**Figure 10.**The planar ion trap with the surface electrodes from the side view with comparison to a 3D rod electrode trap (

**left**) and the top view (

**right**).

**Figure 11.**Schematic picture of the focusing grating coupler (

**left**) and the planar trap with light delivery and detection using the PIC grating couplers (

**right**) [43].

**Table 1.**The comparison between the developed transportable ${}^{171}$Yb${}^{+}$ single-ion clock and the stationary ${}^{69}$Tm optical lattice clock via the developed OFC.

Averaging Time | Signal Accumulation Time | ${\mathit{\sigma}}_{\mathbf{Tm}}$ | ${\mathit{\sigma}}_{\mathbf{conversion}}$ | ${\mathit{\sigma}}_{\mathbf{beat}}$ | ${\mathit{\sigma}}_{\mathbf{result}}$ |
---|---|---|---|---|---|

1 s | 100 s | $2.7\xb7{10}^{-15}$ | $8.5\xb7{10}^{-15}$ | $3.7\xb7{10}^{-15}$ | $8.9\xb7{10}^{-15}$ |

100 s | 10,000 s | $6.1\xb7{10}^{-16}$ | $2.1\xb7{10}^{-16}$ | $1.1\xb7{10}^{-15}$ | $9.4\xb7{10}^{-16}$ |

1000 s | 24 h | $1.2\xb7{10}^{-16}$ | $3.0\xb7{10}^{-17}$ | $5.0\xb7{10}^{-16}$ | $4.9\xb7{10}^{-16}$ |

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**MDPI and ACS Style**

Khabarova, K.; Kryuchkov, D.; Borisenko, A.; Zalivako, I.; Semerikov, I.; Aksenov, M.; Sherstov, I.; Abbasov, T.; Tausenev, A.; Kolachevsky, N.
Toward a New Generation of Compact Transportable Yb^{+} Optical Clocks. *Symmetry* **2022**, *14*, 2213.
https://doi.org/10.3390/sym14102213

**AMA Style**

Khabarova K, Kryuchkov D, Borisenko A, Zalivako I, Semerikov I, Aksenov M, Sherstov I, Abbasov T, Tausenev A, Kolachevsky N.
Toward a New Generation of Compact Transportable Yb^{+} Optical Clocks. *Symmetry*. 2022; 14(10):2213.
https://doi.org/10.3390/sym14102213

**Chicago/Turabian Style**

Khabarova, Ksenia, Denis Kryuchkov, Alexander Borisenko, Ilia Zalivako, Ilya Semerikov, Mikhail Aksenov, Ivan Sherstov, Timur Abbasov, Anton Tausenev, and Nikolay Kolachevsky.
2022. "Toward a New Generation of Compact Transportable Yb^{+} Optical Clocks" *Symmetry* 14, no. 10: 2213.
https://doi.org/10.3390/sym14102213