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Hong–Ou–Mandel interference of two phonons in trapped ions


The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong–Ou–Mandel effect1. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose–Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong–Ou–Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right2,3,4, and could have implications for the quantum simulation of bosonic particles5,6 and analogue quantum computation via boson sampling7.

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Figure 1: Conceptual diagrams of phonon hopping dynamics and two-phonon interference.
Figure 2: Experimental results for phonon dynamics.
Figure 3: Measurement of fidelity of the state.


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We thank Y. Yamamoto for suggestions made at the early stages of this study, and K. Hayasaka for comments on the manuscript. This work was supported by JSPS KAKENHI, grant number 26400418.

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Authors and Affiliations



S.U., K.T. and A.N. designed this study. A.N. and R.H. conducted the experiment. R.H. wrote an early version of the manuscript. K.T. revised and completed the manuscript.

Corresponding author

Correspondence to Kenji Toyoda.

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The authors declare no competing financial interests.

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Toyoda, K., Hiji, R., Noguchi, A. et al. Hong–Ou–Mandel interference of two phonons in trapped ions. Nature 527, 74–77 (2015).

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