One-way States and Topology in Driven Nonlinear Mechanical Resonators

In this talk, I will explore both the theoretical and experimental opportunities that mechanical resonators provide for engineering one-way (nonreciprocal) and topological states.

I will show how to create artificial magnetic fields in mechanical resonators using radiation pressure. Modulating the optical density in an optomechanical nanocavity unlocks Aharonov-Bohm interference, signalling the break-down of time-reversal symmetry akin to electrons in a magnetic field [1]. Next, I will show how parametric pumping, which squeezes mechanical fluctuations, allows a non-Hermitian counterpart to the Aharonov-Bohm effect [2], enabling precise control of symmetries, spectral degeneracies (e.g. exceptional points), and chiral (one-way) amplification. Furthermore, I will cover how interfering two-mode squeezing and hopping interactions enable nonreciprocal transport without breaking time-reversal symmetry [3], linked to non-Hermitian topology in a bosonic Kitaev model [4]. Finally, I will extend the discussion to broader classes of driven-dissipative nonlinear systems and introduce a topological classification framework based on vector flow topology in phase space. By tuning driving parameters (e.g., amplitudes, detunings), I will reveal both local and global topological phase transition, such as flow chirality and connectivity flips, and present confirming experimental evidence [5].

References: [*equal contribution]

[1] Mathew, J. P. *, del Pino, J. *, & Verhagen, E. (2020). Synthetic gauge fields for phonon transport in a nano-optomechanical system. Nature Nanotechnology, 15, 198–202.

[2] del Pino, J. *, Slim, J.J. *, & Verhagen, E. (2022). Non-Hermitian chiral phononics through optomechanically induced squeezing. Nature, 606, 82–87. [*equal contribution]

[3] Wanjura, C.C. *, Slim, J.J. *, del Pino, J., et al. (2023). Quadrature nonreciprocity in bosonic networks without breaking time-reversal symmetry. Nature Physics, 19, 1429–1436. [*equal contribution]

[4] Slim, J. J., Wanjura, C. C., Brunelli, M., del Pino, J., Nunnenkamp, A., & Verhagen, E. (2024). Optomechanical realization of the bosonic Kitaev chain. Nature, 627(8005), 767–771.

[5] Villa, G. *, del Pino, J. *, Dumont, V., Rastelli, G., Michałek, M., Eichler, A., & Zilberberg, O. (2024). Topological classification of driven-dissipative nonlinear systems. arXiv preprint arXiv:2406.16591.