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Spectral engineering of cavity-protected polaritons in an atomic ensemble

Nature Physics volume 19, pages 1104–1109 (2023)Cite this article

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Abstract

Multiple quantum emitters coupled to a single cavity mode appear in many situations, including quantum technologies and polaritonic chemistry. The ideal case of identical emitters is modelled in terms of symmetric states, and understood in terms of polaritons. In the practically relevant case of an inhomogeneous frequency distribution, this simple picture breaks down and new features emerge. Here we observe the transition from a disordered regime to a polaritonic one with only two resonances, using the high degree of control in a strongly coupled cold-atom system where the ratio between coupling strength and frequency inhomogeneities can be tuned. The polaritons are much narrower than the frequency distribution, as predicted in the context of cavity protection. We find that the concentration of photonic weight of the coupled light–matter states is a key parameter for this transition and demonstrate that a simple parameter based on the statistics of transmission count spectra provides an experimental proxy for this theoretical quantity. Moreover, we realize a dynamically modulated Tavis–Cummings model to produce a comb of narrow polariton resonances protected from disorder, with potential applications to quantum networks.

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Fig. 1: Experimental setup of the cold-atom cavity interface with tunable inhomogeneous frequency distribution.
Fig. 2: Cavity protection effect.
Fig. 3: Transition from the unprotected to protected regime.
Fig. 4: Modulation of polariton eigenfrequencies.

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Code availability

The data that support the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.7308847.

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Acknowledgements

We thank G. Pupillo and J. Schachenmayer for discussion within the ANR project CLIMAQS. This project has received funding from Agence Nationale de la Recherche (ANR) (SAROCEMA project, ANR-14-CE32-0002) and European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme via grant agreement no. 671133 (EQUEMI project). It has been supported by Region Ile-de-France in the framework of DIM SIRTEQ. S.S. acknowledges funding from the European Union under the Marie Skłodowska-Curie Individual Fellowship Programme H2020-MSCA-IF-2014 (project no. 658253).

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Author notes

  1. Sylvain Schwartz

    Present address: DPHY, ONERA, Université Paris-Saclay, Palaiseau, France

  2. These authors contributed equally: Mohamed Baghdad, Pierre-Antoine Bourdel, Sylvain Schwartz.

Authors and Affiliations

  1. Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France

    Mohamed Baghdad, Pierre-Antoine Bourdel, Sylvain Schwartz, Francesco Ferri, Jakob Reichel & Romain Long

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Contributions

M.B., F.F. and R.L. built the experimental setup. M.B., P.-A.B., S.S., F.F. and R.L. performed the measurements and analysed the data. P.-A.B., S.S., J.R. and R.L. interpreted the results and wrote the manuscript with input from all the authors.

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Correspondence to Romain Long.

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Nature Physics thanks Zhenjie Yan 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 Simulated atomic frequency distribution for different trap depths.

For each trap depth U0, the temperature T used in the simulation corresponds to the typical experimental value based on time-of-flight measurements. When U0 increases, the mean frequency of the distribution decreases linearly – as expected with red-detuned off-resonant light – and the width Δω of the distribution increases. At low trap depth U0 = 310 ± 10 μK, the distribution has mainly one lobe, corresponding to the \(\left\vert F=2\right\rangle \to \left\vert {F}^{{\prime} }=3\right\rangle\) transition. For larger trap depths, two-photon couplings at 1559 nm mix the excited state hyperfine levels and two extra lobes appear in the distributions, at lower frequencies, corresponding roughly to transitions \(\left\vert F=2\right\rangle \to \left\vert {F}^{{\prime} }=2\right\rangle\) and \(\left\vert F=2\right\rangle \to \left\vert {F}^{{\prime} }=1\right\rangle\). This illustrates the tunability of the inhomogeneous distribution with the intensity of the trapping field.

Extended Data Fig. 2 Single-shot experimental spectrum.

As we probe the coupled system in the low excitation regime, we collect few photons in transmission and the spectrum is discretized (orange dots). For each spectrum, we compute the fraction Fout of photons (identified with black triangles) that lies outside of a frequency window Δf/2π (green colored area), centered on each peak distribution (red and blue dashed lines).

Extended Data Fig. 3 Robustness of Fout with respect to the size of the exclusion window.

Here, we show Fout for several values of Δf/2π chosen to define the exclusion window, together with the simulated sum of the two highest PW, SPW, as in Fig. 3 of the main text (red dots). The result is rather robust: when Δf/2π decreases, the shape of Fout remains the same and is shifted upwards as expected. Data are presented as mean values ± s.e.m. obtained with an average of 55 spectra per point.

Supplementary information

Supplementary Information

Supplementary sections I–III, figs. 1 and 2 and tables I and II.

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Baghdad, M., Bourdel, PA., Schwartz, S. et al. Spectral engineering of cavity-protected polaritons in an atomic ensemble. Nat. Phys. 19, 1104–1109 (2023). https://doi.org/10.1038/s41567-023-02035-1

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