Research

Nonlinear Dynamics and Non-Equilibrium Phases of Matter

Can we map and predict complex dynamical phases beyond the linear regime?

What kinds of topology emerge in systems with nonlinearity and strong driving?

Nonlinear effects arise naturally in mechanical, optical, and electronic systems driven far from equilibrium. Even weak nonlinearities can produce solitons, limit cycles, phase transitions, and multistability at large amplitudes.

Understanding this behaviour requires more than energy levels or band structures. We classify nonequilibrium phases of matter through the geometry and topology of their dynamical flows: how systems settle into patterns, switch between states, and respond to perturbations.

We develop frequency-domain tools based on harmonic balance to find steady and periodic behaviour without simulating many initial conditions. These methods are particularly useful for discovering and analysing limit cycles—self-sustained oscillations that break time-translation symmetry.

Applications include neuromorphic computing, nanomechanical frequency combs, topological solitons, and quantum error correction. More broadly, this work reveals how topology constrains nonlinear dynamics and the transitions between nonequilibrium phases.

This research has been presented and applied in the following works:

• A. S. Gómez and J. del Pino – [Phys. Rev. Research 8, 023319 (2026)]
• G. Villa †, J. del Pino †, V. Dumont, G. Rastelli, M. Michałek, A. Eichler, and O. Zilberberg – [Sci. Adv. 11, eadt9311 (2025)]
• M. Fu, O. Ameye, F. Yang, J. Košata, J. del Pino, O. Zilberberg, and E. Scheer – [Phys. Rev. Research 7, 033127 (2025)]
• L. Catalini, J. del Pino, S. S. Kumar, V. Dumont, G. Margiani, O. Zilberberg, and A. Eichler – [Phys. Rev. Research 7, 033058 (2025)]
• J. del Pino, J. Košata, and O. Zilberberg – [Phys. Rev. Research 6, 033180 (2024)]
• P. Álvarez, D. Pittilini, F. Miserocchi, S. Raamamurthy, G. Margiani, O. Ameye, J. del Pino, O. Zilberberg, and A. Eichler – [Phys. Rev. Lett. 132, 207401 (2024)]
• V. Borovik, P. Breiding, J. del Pino, M. Michałek, and O. Zilberberg – [J. Math. Pures Appl. 182, 195–222 (2024)]
• G. Margiani, J. del Pino, T. L. Heugel, N. E. Bousse, S. Guerrero, T. W. Kenny, O. Zilberberg, D. Sabonis, and A. Eichler – [Phys. Rev. Research 5, L012029 (2023)]
• J. Košata †, J. del Pino †, T. L. Heugel, and O. Zilberberg – [SciPost Phys. Codebases 6 (2022)]

† Equal contribution

Open-Source Software: HarmonicBalance.jl

I co-develop HarmonicBalance.jl with Orjan Ameye and Jan Košata. The open-source Julia package finds and analyses steady states, limit cycles, stability, and phase diagrams in nonlinear driven systems.

GitHub Documentation Paper Learn more

Artificial Gauge Fields and Nonreciprocal Transport

Can we make light or sound behave as if they feel a magnetic field?

What happens when we break time symmetry to make energy flow in one direction?

How can gain, loss, and topology work together to control signals in quantum systems?

Gauge fields describe how particles interact and play a central role in condensed-matter physics. In the quantum Hall effect, for example, a magnetic field breaks time-reversal symmetry and produces robust, directional topological edge states.

In driven resonator systems, we engineer artificial gauge fields that break time-reversal symmetry for neutral excitations such as photons and phonons. Carefully designed modulations generate effects analogous to the Aharonov–Bohm phase and enable nonreciprocal transport, in which energy flows preferentially in one direction.

Combining artificial gauge fields with parametric interactions, gain, and loss creates non-Hermitian dynamics with no direct counterpart in conventional materials. This interplay enables unidirectional amplification, control of exceptional points, and new ways to manipulate signals and quantum states.

This physics has been demonstrated and explored in several recent works:

• J. J. Slim, J. del Pino, and E. Verhagen – [Nat. Commun. 16, 7471 (2025)]
• J. J. Slim †, C. Wanjura †, M. Brunelli, J. del Pino, E. Verhagen, and A. Nunnenkamp – [Nature 627, 767–771 (2024)]
• C. Wanjura †, J. J. Slim †, J. del Pino, M. Brunelli, E. Verhagen, and A. Nunnenkamp – [Nat. Phys. 19, 1429–1436 (2023)]
• J. del Pino and O. Zilberberg – [Phys. Rev. Lett. 130, 171901 (2023)]
• J. del Pino †, J. J. Slim †, and E. Verhagen – [Nature 606, 82–87 (2022)]
• J. P. Mathew †, J. del Pino †, and E. Verhagen – [Nat. Nanotechnol. 15, 198–202 (2020)]
• R. Duggan †, J. del Pino †, E. Verhagen, and A. Alù – [Phys. Rev. Lett. 123, 023602 (2019)]

† Equal contribution

Quantum Optics with Organic Molecules

How does strong coupling to confined light reshape molecular dynamics?

Can optical cavities control vibrations, relaxation, and spectroscopy?

Organic molecules combine electronic excitations with rich vibrational environments. When they couple strongly to a confined optical mode, they form polaritons: hybrid light–matter states whose dynamics can differ sharply from those of either component alone.

We develop quantum and tensor-network descriptions of collective strong coupling, non-Markovian dynamics, and molecular vibrations. This work also explores how these effects appear in Raman scattering and ultrafast emission, and how they can enable new optical devices.

Selected works, in reverse chronological order:

• R. E. F. Silva, J. del Pino, F. J. García-Vidal, and J. Feist – [Nat. Commun. 11 (2020)]
• J. del Pino, F. A. Y. N. Schröder, A. W. Chin, J. Feist, and F. J. García-Vidal – [Phys. Rev. Lett. 121, 227401 (2018)]
• J. del Pino, F. A. Y. N. Schröder, A. W. Chin, J. Feist, and F. J. García-Vidal – [Phys. Rev. B 98, 165416 (2018)]
• J. del Pino, F. J. García-Vidal, and J. Feist – [Phys. Rev. Lett. 117, 277401 (2016)]
• J. del Pino, J. Feist, and F. J. García-Vidal – [J. Phys. Chem. C 119, 29132–29137 (2015)]
• J. del Pino, J. Feist, and F. J. García-Vidal – [New J. Phys. 17, 053040 (2015)]