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Bosonic stimulation of atom–light scattering in an ultracold gas

Nature Physics volume 19, pages 210–214 (2023)Cite this article

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Abstract

For bosons, the transition rate into an already occupied quantum state is enhanced by its occupation number: the effect of bosonic stimulation. Bosonic stimulation of light scattering was predicted more than 30 years ago but has proven elusive to direct observation. Here we investigate this effect in an ultracold gas of bosons. We show that the bosonic enhancement factor for a harmonically trapped gas is bounded by a universal constant above the phase transition to a Bose–Einstein condensate and depends linearly on the condensate fraction just below the phase transition. We observe bosonic enhanced light scattering both above and below the phase transition, and we show how interactions can alter the bosonic stimulation and optical properties of the gas. Lastly, we demonstrate that, for a multi-level system prepared in a single internal state, the bosonic enhancement is reduced because it occurs only for Rayleigh scattering but not for Raman scattering.

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Fig. 1: Schematic of bosonic stimulation in light scattering.
Fig. 2: Bosonic stimulation of light scattering in a trapped 23Na gas across the phase transition.
Fig. 3: Bosonic enhancement of light scattering above and below the BEC phase transition.
Fig. 4: Bosonic enhancement for Rayleigh and Raman scattering.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request and through Zenodo42.

Code availability

The codes that support the findings of this study are available from the corresponding authors upon reasonable request and through Zenodo43.

Change history

  • 20 January 2023

    In the version of this article initially published, the term “light scattering” was missing from the beginning of the abstract and is now amended in the HTML and PDF versions of the article.

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Acknowledgements

We thank Z. Hadzibabic, J. de Hond and P. Barral for comments on the manuscript. This work is supported by NSF through the Center for Ultracold Atoms and grant no. 1506369, and from a Vannevar-Bush Faculty Fellowship.

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Authors and Affiliations

  1. Research Laboratory of Electronics, MIT-Harvard Center for Ultracold Atoms, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yu-Kun Lu, Yair Margalit & Wolfgang Ketterle

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  1. Yu-Kun Lu
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Contributions

All authors contributed to the concepts of the experiment, Y.-K.L. and Y.M. performed the experiment, Y.-K.L. analysed the data and performed the theoretical calculations. Y.-K.L., Y.M. and W.K. wrote the paper.

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Correspondence to Yu-Kun Lu.

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Extended data

Extended Data Fig. 1 Linearity check for light scattering.

Scattered photons are measured for different probe beam powers. The blue (red) data points represent a cloud with (without) BEC. The absence of nonlinearity shows that we are working in the perturbative regime. Data points here are each averaged over 3 samples.

Extended Data Fig. 2 Light scattering after compressing the cloud.

The photon scattering signal was measured for different final trap depths. The dashed line represents the signal observed for a non-degenerate cloud with no bosonic enhancement. Each data point was averaged over 6 samples.

Extended Data Fig. 3 Bosonic enhancement factor for an ideal gas in a 3D box potential for different recoil momenta κ.

At the phase transition point, the bosonic enhancement factor diverges as 1/κ.

Extended Data Fig. 4 Bosonic enhancement factor for an ideal gas in a 3D harmonic trapping potential for different recoil momenta κ.

The enhancement factor is bounded at and above the phase transition, but will diverge as 1/κ2 below the phase transition.

Extended Data Fig. 5 The density distribution of the condensate and thermal cloud for different models.

In the calculations we used the following values: scattering length of a = 85a0 (a0 is the Bohr radius), trap frequency ω = 2π × 2.7kHz, atom number N = 4 × 105 and condensate fraction of 30%.

Extended Data Fig. 6 Comparison between different models above the phase transition.

(a) Predictions for the Bose enhancement factor for different models. (b) Fitting of the models to the experimental data. The only free parameter is the overall scaling. In the calculations we used the following parameters: scattering length a = 85a0 (a0 is the Bohr radius), atom number N = 4 × 105 and dimensionless recoil momentum κ = 0.51.

Extended Data Table 1 Bosonic enhancement factor for different exponent x in the density of states.

In the limit of zero recoil momentum, the enhancement factor is bounded for x ≤ 0 and x > 1 while diverging for 0 < x ≤ 1.

Extended Data Table 2 χ2 values for fits using different models.

The χ2 values are normalized in such a way that it becomes dof = 13 for the full interacting model. As a comparison, the probability for χ2 (dof=13) to be larger than 18.5 is 10%.

Supplementary information

Supplementary Information

Supplementary discussion and Fig. 1.

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Lu, YK., Margalit, Y. & Ketterle, W. Bosonic stimulation of atom–light scattering in an ultracold gas. Nat. Phys. 19, 210–214 (2023). https://doi.org/10.1038/s41567-022-01846-y

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