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Driven-dissipative non-equilibrium Bose–Einstein condensation of less than ten photons

Abstract

In a Bose–Einstein condensate, bosons condense in the lowest-energy mode available and exhibit high coherence. Quantum condensation is inherently a multimode phenomenon, yet understanding of the condensation transition in the macroscopic limit is hampered by the difficulty in resolving populations of individual modes and the coherences between them. Here, we report non-equilibrium Bose–Einstein condensation of 7 ± 2 photons in a sculpted dye-filled microcavity, where the extremely small particle number and large mode spacing of the condensate allow us to measure occupancies and coherences of the individual energy levels of the bosonic field. Coherence of the individual modes is found to generally increase with increasing photon number. However, at the break-down of thermal equilibrium we observe phase transitions to a multimode condensate regime wherein coherence unexpectedly decreases with increasing population, suggesting the presence of strong intermode phase or number correlations despite the absence of a direct nonlinearity. Experiments are well-matched to a detailed non-equilibrium model. We find that microlaser and Bose–Einstein statistics each describe complementary parts of our data and are limits of our model in appropriate regimes, providing elements to inform the debate on the differences between the two concepts1,2.

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Acknowledgements

We thank R. Oulton for enlightening discussions. We are grateful to the UK Engineering and Physical Sciences Research Council for supporting this work through fellowship no. EP/J017027/1 (to R.A.N.) and the Controlled Quantum Dynamics CDT EP/L016524/1 (B.T.W. and H.J.H.). D.H. thanks the DFG cluster of excellence ‘Nanosystems Initiative Munich’. L.C.F., A.A.P.T and J.M.S. acknowledge support from the Leverhulme Trust.

Author information

B.T.W. carried out the experiments with assistance from R.A.N., and both analysed the data. L.C.F., A.A.P.T., J.M.S. and D.H. fabricated the mirrors and assessed their performance. H.J.H. and R.A.N. and worked out the theory with assistance from F.M. R.A.N. conceived the experiment, and wrote the manuscript with input from all authors.

Competing interests

The authors declare no competing interests.

Data availability

The data underlying this manuscript, source code to reproduce the figures and any further details are available from the corresponding author upon reasonable request.

Correspondence to Robert A. Nyman.

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Fig. 1: Sculpted dye-filled microcavity allowing mode-resolved characterization of condensation threshold.
Fig. 2: The break-down of thermalization.
Fig. 3: Phase coherence measured for various delay times through a Mach–Zehnder interferometer using a spectrometer.
Fig. 4: Coherence time of the ground state.