Invited
Effective Magnetic Fields for Photons and Phonons through Optomechanical Interactions

We demonstrate nonreciprocal transport of both light and sound, mediated by radiation pressure interactions. We show how optomechanical interactions and suitable symmetry breaking creates one-way propagation mimicking that of electrons in magnetic fields.

Reciprocity is a symmetry that characterizes the transport of light and sound waves in the vast majority of systems. Creating nonreciprocal behaviour requires suitable ways of breaking the system’s time-reversal symmetry. This can yield functionality such as isolation and circulation, useful for the routing of classical and quantum information, and could also allow exploring topological physics for photons and phonons. While the breaking of time-reversal symmetry is usually achieved with a magnetic field, the weakness of magneto-optic interactions makes miniaturization to chip-scale devices challenging. A possible route to nonreciprocity without a magnetic field relies on a spatiotemporal modulation of the refractive index, which is straightforwardly achieved in optomechanical systems. The mutual interaction between light and mechanical motion then allows to create effective magnetic fields for either degree of freedom [1]. We exploit these effects to create nonreciprocal functionality such as gyration, isolation, and circulation for on-chip transport of both light and sound. We show how these systems can be used as building blocks to study quantum Hall physics in bosonic systems.

We explain how in multimode optomechanical systems, the radiation pressure of an optical control field can break the symmetry of propagation of probe photons. We demonstrate optical isolation and circulation with ~10 dB contrast and low insertion loss in a high-quality ring resonator [2,3]. A general theory reveals the minimal requirements to create nonreciprocity in a wide class of optomechanical systems that involve a pair of optical modes parametrically coupled to a mechanical mode. The underlying principle is related to a nonreciprocal phase incurred during photon-phonon transfer that is induced by the control field. This mechanism can be directly related to the Aharonov-Bohm effect for electrons, where a magnetic vector potential gauge field imprints a nonreciprocal phase on wave propagation. In an analogous fashion, we create gauge fields for nanomechanical transport (sound) in systems that couple multiple mechanical resonators to a single optical cavity. We develop photonic crystal systems in which mechanical transport is mediated by radiation pressure forces. Suitable laser driving then induces nonreciprocal transport of phonons between different resonators. We show how these effects can be scaled to optomechanical lattices in order to induce a nanomechanical quantum Hall effect, including the emergence of topologically protected edge states showing unidirectional transport.

[1] E. Verhagen and A. Alù, Nat Phys. 13, 922 (2017).

[2] F. Ruesink et al., Nat. Commun. 7, 13662 (2016).

[3] F. Ruesink et al., Nat. Commun. 9, 1798 (2018).