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# Disorder-assisted assembly of strongly correlated fluids of light

## Abstract

Guiding many-body systems to desired states is a central challenge of modern quantum science, with applications from quantum computation1,2 to many-body physics3 and quantum-enhanced metrology4. Approaches to solving this problem include step-by-step assembly5,6, reservoir engineering to irreversibly pump towards a target state7,8 and adiabatic evolution from a known initial state9,10. Here we construct low-entropy quantum fluids of light in a Bose–Hubbard circuit by combining particle-by-particle assembly and adiabatic preparation. We inject individual photons into a disordered lattice for which the eigenstates are known and localized, then adiabatically remove this disorder, enabling quantum fluctuations to melt the photons into a fluid. Using our platform11, we first benchmark this lattice melting technique by building and characterizing arbitrary single-particle-in-a-box states, then assemble multiparticle strongly correlated fluids. Intersite entanglement measurements performed through single-site tomography indicate that the particles in the fluid delocalize, whereas two-body density correlation measurements demonstrate that they also avoid one another, revealing Friedel oscillations characteristic of a Tonks–Girardeau gas12,13. This work opens new possibilities for the preparation of topological and otherwise exotic phases of synthetic matter3,14,15.

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## Data availability

The experimental data presented in this manuscript are available from the corresponding author upon request, due to the proprietary file formats used in the data collection process.

## Code availability

The source code for simulations throughout are available from the corresponding author upon request.

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## Acknowledgements

This work was supported by ARO MURI grant W911NF-15-1-0397, AFOSR MURI grant FA9550-19-1-0399 and by NSF Eager grant 1926604. Support was also provided by the Chicago MRSEC, which is funded by NSF through grant DMR-1420709. G.R. and M.G.P. acknowledge support from the NSF GRFP. A.V. acknowledges support from the MRSEC-funded Kadanoff–Rice Postdoctoral Research Fellowship. Devices were fabricated in the Pritzker Nanofabrication Facility at the University of Chicago, which receives support from Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-1542205), a node of the National Science Foundation’s National Nanotechnology Coordinated Infrastructure.

## Author information

Authors

### Contributions

The experiments were designed by B.S., A.V., G.R., J.S. and D.I.S. The apparatus was built by B.S., A.V. and G.R. The collection of data was handled by B.S., A.V. and G.R. All authors analysed the data and contributed to the manuscript.

### Corresponding author

Correspondence to Brendan Saxberg.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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### Peer review information

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## Extended data figures and tables

### Extended Data Fig. 1 Adiabaticity Curves for All $$\bar{n}$$ Fillings.

Adiabaticity is given by the average number of photons that return to the originally excited sites as a function of ramp length. Here, we measure adiabaticity curves for the highest energy eigenstate for all $$\bar{n}$$ fillings, revealing the minimum ramp length needed to be adiabatic when preparing these many-body states. As particle number increases, we start to suffer more from loss and no longer fully recover the initial starting population.

### Extended Data Fig. 2 Profiles for $$\bar{n}$$ Fillings.

Density profiles for the highest energy eigenstates, corresponding to fluid ground states, for filling $$\bar{n}$$=$$\frac{1}{7}$$ through $$\frac{6}{7}$$. For 5 and 6 particles, our results suffer from particle loss.

### Extended Data Fig. 3 Entanglement for $$\bar{n}$$ Fillings.

Measure of entanglement vs disorder, for filling $$\bar{n}$$=$$\frac{1}{7}$$ through $$\frac{6}{7}$$. Error bars reflect S.E.M.; here they are smaller than markers.

## Supplementary information

### Supplementary Information

Supplementary Sections A–J, Table 1, Figs. 1–7 and references.

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Saxberg, B., Vrajitoarea, A., Roberts, G. et al. Disorder-assisted assembly of strongly correlated fluids of light. Nature 612, 435–441 (2022). https://doi.org/10.1038/s41586-022-05357-x

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• DOI: https://doi.org/10.1038/s41586-022-05357-x