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# Scalable all-optical cold damping of levitated nanoparticles

## Abstract

Motional control of levitated nanoparticles relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of the measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce an all-optical cold damping scheme based on the spatial modulation of trap position, which has the advantage of being scalable to multiple particles. The scheme relies on programmable optical tweezers to provide full independent control over the trap frequency and position of each tweezer. We show that the technique cools the centre-of-mass motion of particles along one axis down to 17 mK at a pressure of 2 × 10−6 mbar and demonstrate its scalability by simultaneously cooling the motion of two particles. Our work paves the way towards studying quantum interactions between particles; achieving three-dimensional quantum control of particle motion without cavity-based cooling, electrodes or charged particles; and probing multipartite entanglement in levitated optomechanical systems.

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• ### Tuneable Gaussian entanglement in levitated nanoparticle arrays

npj Quantum Information Open Access 28 December 2022

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## Data availability

Source data for Figs. 1b, 24 and Extended Data Figs. 14 are available via the ETH Zürich Research Collection at https://doi.org/10.3929/ethz-b-000569410.

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## Acknowledgements

This research was supported by the Swiss National Science Foundation (SNF) through the NCCR-QSIT programme (grant no. 51NF40-160591; L.N.), European Union’s Horizon 2020 research and innovation programme under grant nos. 863132 (iQLev; L.N.) and 951234 (Q-Xtreme; L.N.), and ETH Grant ETH-47 20-2 (M.F.). The funders had no role in the study design, data collection and analysis, decision to publish or preparation of the manuscript. We thank our colleagues at the Photonics Laboratory at ETH Zürich, U. Delic and A. Omran, for valuable input and discussions.

## Author information

Authors

### Contributions

J.V., Z.Z., J.P. and D.W. performed the measurements and analysed the data. J.V. and L.N. conceptualized the experiments with input from F.v.d.L and M.F. All the authors discussed the results and contributed to writing the manuscript.

### Corresponding author

Correspondence to Jayadev Vijayan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Nanotechnology thanks Klaus Hornberger, Tongcang Li and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data

### Extended Data Fig. 1 Detection schemes used in the experiment.

Light scattered by the particle in the forward direction is detected on the QPD which performs measurement-based cold damping of the particle motion. The back-scattered light is detected on photodiodes that perform parametric cooling of the particle motion. Additionally, the back-scattered light is also used in a heterodyne detection scheme that can overcomes the scalability limitations of the forward detection. At the moment, it is used as a tool to detect multiple particles as they are loaded into the chamber. A green laser is used to illuminate the particles for taking high resolution images, such as in Fig. 4a of the main text.

### Extended Data Fig. 2 Linear feedback circuit.

A) A schematic of the cold damping feedback loop from the detected signal Vil to the spatial displacement of the tweezer Δy. B) Estimated tweezer displacement Δy (green circles) for different gains applied at the function generator GFG. The dashed line is a square root fit to the data.

### Extended Data Fig. 3 Damping rates from ring-down and reheating measurements.

The feedback damping rate (green circles) is independent of pressure whereas the gas damping rate (red circles) increases with pressure. As in the main text, the gain is fixed to a low value of γfb = 2π × 42 Hz, corresponding to GFG = 5 kHz/V.

### Extended Data Fig. 4 Calibration of feedback gain.

Due to differences in the detection efficiency of the motional signal from particle 1 (red circles) and 2 (blue circles), the gain applied at the function generator GFG is adjusted to get the same γfb. Dashed lines are a linear fit to the data.

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Reprints and Permissions

Vijayan, J., Zhang, Z., Piotrowski, J. et al. Scalable all-optical cold damping of levitated nanoparticles. Nat. Nanotechnol. 18, 49–54 (2023). https://doi.org/10.1038/s41565-022-01254-6

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• DOI: https://doi.org/10.1038/s41565-022-01254-6

• ### Scalable optical levitation

• P. F. Barker

Nature Nanotechnology (2023)

• ### Tuneable Gaussian entanglement in levitated nanoparticle arrays

• Anil Kumar Chauhan
• Ondřej Černotík