From chiral squeezing to nonlinear topology in optomechanics
Javier del Pino1,3, Jesse J. Slim3, Ewold Verhagen3, Jan Košata1, Toni L. Heugel1 and Oded Zilberberg2
1Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
2Department of Physics, University of Konstanz, 78464 Konstanz, Germany
3Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands
Synthetic gauge fields can be harnessed to engineer unconventional transport and localise bosonic states by breaking time-reversal symmetry and mimicking electrons' behaviour in electromagnetic fields. Optomechanical systems address optically mechanical modes via modulated radiation pressure, enabling spring constant tuning and strong mechanical interactions that imprint nonreciprocal Peierls phases – akin to the Aharonov-Bohm effect for electrons [1].
Here we demonstrate how optomechanical cavities unlock synthetic magnetic fields for many-mode oscillator networks, offering a route toward acoustic chirality and non-Hermitian topological states [2]. These ideas are tested within state-of-the-art nanobeam photonic crystals that support localised optical resonances coupled to multiple coherent mechanical overtones. Phase control of intensity-modulated driving in a single cavity then unlocks a versatile, optically-tunable nanomechanical network featuring arbitrary-range interactions that span a synthetic dimension (Fig. 1a). Our study analyses the emergence of chiral phononic propagation in single mechanical loops with nonreciprocal Aharonov-Bohm (AB) link phases. In addition, we demonstrate the interplay of AB interference and gain by inducing parametric interactions through radiation pressure, through control of non-Hermitian physics, including exceptional points and non-reciprocal phononic amplification (Fig. 1b). We finally overview our efforts [3] in exploiting optomechanical nonlinearities, natural in our systems, to control bifurcations into self-oscillating phases via nonreciprocal control phases.
Our findings open new prospects for bosonic transport and non-Hermitian topological phases for mechanical modes at the nanoscale. They ultimately illustrate the potential of optomechanical systems toward quantum chiral acoustic networks and strongly nonlinear systems with broken Hermiticity and time-reversal symmetry.
Figure 1: (a) (left) A modulated cavity field c couples three resonators ai in a loop with complex beam-splitter couplings Jijeiφij, which phases add up to a synthetic flux Φ. (right) Time evolution of resonator amplitudes |ai| for trivial and nontrivial flux. (b) (left) Graph associated with a dimer subject to parametric driving with complex amplitudes ηi eiθi, unwrapping “particle-hole” loops threaded by effective synthetic fluxes. Experimental fingerprints of control of exceptional points through effective fluxes.
[1] Mathew J. P.* , del Pino, J.* , Verhagen E. (2020). Synthetic gauge fields for phonon transport in a nano-optomechanical system (*equal contribution) - [Nature Nanotechnology volume 15, pages 198 - 202]
[2] del Pino, J.*, Slim, Jesse J.* and Verhagen, E. (2021). Non-Hermitian chiral phononics through optomechanically-induced squeezing. (*equal contribution) [Nature – in press- arXiv: 2110.14710]
[3] Košata, Jan*, del Pino, J.*, Heugel, Toni L. and Zilberberg, Oded (2022). HarmonicBalance.jl: a Julia suite for interacting nonlinear dynamics. (*equal contribution) [arXiv:2202.00571]