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Quantum phase transitions of light

Abstract

The ability to conduct experiments at length scales and temperatures at which interesting and potentially useful quantum-mechanical phenomena emerge in condensed-matter or atomic systems is now commonplace. In optics, though, the weakness with which photons interact with each other makes exploring such behaviour more difficult. Here we describe an optical system that exhibits strongly correlated dynamics on a mesoscopic scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our results predict that at zero temperature the system will undergo a characteristic Mott insulator (excitations localized on each site) to superfluid (excitations delocalized across the lattice) quantum phase transition. Moreover, the ability to couple light to and from individual cavities of this system could be useful in the realization of tuneable quantum simulators and other quantum-mechanical devices.

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Figure 1: A proposed implementation of the photonic condensed-matter analogue.
Figure 2: Eigenspectrum for a single atom in a high-Q cavity, as a function of the atom–cavity detuning, centred around zero (En ω).
Figure 3: Boundaries between Mott lobes in the limit of low tunnelling (small κ) as a function of μ and Δ.
Figure 4: Slices showing the superfluid order parameter, ψ, as a function of the photon hopping frequency, κ, and the chemical potential, μ, for different detunings.
Figure 5: Plateaux with constant density, ρ, indicating regions with definite-number state excitations, as a function of the chemical potential, μ, and photon hopping frequency, κ, for detuning, Δ=0.

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Acknowledgements

The authors would like to acknowledge useful discussions with P. Eastham, M. Friesen, D. Jamieson, R. Joynt, R. Kalish, P. Littlewood, A. Martin, M. Makin, G. Milburn, J. Salzman and H. Wiseman. C.T. is funded by a USA National Science Foundation Math and Physical Sciences Distinguished International Postdoctoral Research Fellowship. This work was supported by the Australian Research Council, the Australian Government and by the US National Security Agency (NSA), Advanced Research and Development Activity (ARDA) and the Army Research Office (ARO) under Contract Nos. W911NF-04-1-0290 and W911NF-05-1-0284.

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A.D.G. and J.H.C. conceived the original concept, which was developed by C.T. and L.C.L.H. C.T. initiated the quantum many-body analysis and A.D.G. and C.T. carried out the mean-field calculations. All authors contributed to writing the paper, and checking and interpreting the results.

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Correspondence to Andrew D. Greentree.

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The authors declare no competing financial interests.

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Greentree, A., Tahan, C., Cole, J. et al. Quantum phase transitions of light. Nature Phys 2, 856–861 (2006). https://doi.org/10.1038/nphys466

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