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# Quantum control of a nanoparticle optically levitated in cryogenic free space

## Abstract

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1,2,3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4,5,6,7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.

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## Data availability

Source data for Figs. 1b, 2, 3 and for Extended Data Figs. 27 are available in the ETH Zurich Research Collection (https://doi.org/10.3929/ethz-b-000480147).

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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) and the R’Equip programme (grant no. 206021-189605), and by the European Union’s Horizon 2020 research and innovation programme under grant no. 863132 (iQLev). We are grateful to F. van der Laan for his contributions to the particle characterization procedure. We thank O. Wipfli and C. Fischer for their suggestions in designing the cryogenic vacuum chamber, J. Piotrowski and D. Windey for their advice with the trap assembly, and Y. Li for her work on the control software. We thank our colleagues P. Back, E. Bonvin, J. Gao, A. Militaru, R. Reimann, J. Vijayan and J. Zielinska for input and discussions.

## Author information

Authors

### Contributions

F.T., M.L.M. and M.R. conducted the experiments and co-wrote the manuscript with M.F., who directed the project with L.N.

### Corresponding author

Correspondence to Lukas Novotny.

Competing interests The authors declare no competing interests.

Peer review information Nature thanks Dalziel Wilson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Experimental setup.

We optically trap a nanoparticle inside a cryogenic vacuum chamber using a telecom laser. In the forwards direction, we employ a libration and position detection system. In the backwards direction, we place both a homodyne and a heterodyne photodetector. AOM, acousto-optic modulator; DAQ, data acquisition card; EOM, electro-optic modulator; λ/2, half-wave plate; LO, local oscillator; PBS, polarizing beam-splitter; R, reflection; T, transmission.

### Extended Data Fig. 2 Postselecting the data.

The compression cycles of the cryocooler are visible in our interferometric signal at baseband (idc[t] in grey). We identify the cycles (red dotted lines) and postselect 300-ms-long intervals (indicator function in orange) of the time traces containing the particle motion (exemplary for ihom[t] in blue).

### Extended Data Fig. 3 Transfer function of the electronic feedback chain.

a, b, Measured magnitude (a) and phase (b) response of the experimentally used delay filter. The dotted, dashed, and dot-dashed vertical lines mark the location of the resonance frequency of motion along the z, x, and y axes, respectively.

### Extended Data Fig. 4 Detection noise characterization.

Variance of the laser noise as a function of local oscillator power in homodyne detection. The variance, expressed in dB, is normalized to the variance of the electronic noise floor of the detector (grey). The dotted blue line provides a guide for the eye for the linear dependence between variance and power of the beam.

### Extended Data Fig. 5 Sideband asymmetry in out-of-loop heterodyne measurements.

a, b, Stokes (a) and anti-Stokes (b) sidebands, at different electronic feedback gains, normalized to the estimated background level (grey line). Each sideband pair is simultaneously fitted to a theoretical model. c, Mechanical occupations (green squares) at different feedback gains. The black solid line is a theoretical model based on an ideal delay filter with parameters estimated from the in-loop spectra. The error bars are obtained by propagating the fit uncertainties (1 s.d.) of the areas.

### Extended Data Fig. 6 Sideband cross-correlations in out-of-loop heterodyne measurements.

a, b, Real (a) and imaginary (b) parts of cross-spectra, at different electronic feedback gains. Each pair is simultaneously fitted to a theoretical model and the results are shown as black lines. The grey line marks the zero as a reference. c, d, Fitted mechanical resonance frequency (c) and effective linewidth (d) at different electronic gains. e, Extracted mechanical occupations as a function of fitted effective linewidths. The black line is a theoretical model based on an ideal delay filter and on parameters estimated from the in-loop spectra. The error bars are obtained by the fit uncertainties (1 s.d.).

### Extended Data Fig. 7 Fit results.

a, Reference displacement spectrum measured by the homodyne detector at the smallest feedback gain, with a fit to a model (black line). In light red we show the spectral features excluded from the fits. b, Fitted feedback gain, γeff, as a function of the experimentally tunable electronic gain gel. Coloured dots come from fitting the corresponding spectra shown in Fig. 3a. The black squares are the full-width at half-maximum extracted from the computed actual displacement spectra. The grey line is a guide for the eye, and represents the expected linear relation.

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Tebbenjohanns, F., Mattana, M.L., Rossi, M. et al. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 595, 378–382 (2021). https://doi.org/10.1038/s41586-021-03617-w

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