Research

Current research directions and recent work.

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 are at the heart of how we understand forces in nature—they describe how particles interact, from electromagnetism to the strong and weak nuclear forces. In condensed matter systems, external gauge fields like magnetic fields play a key role in shaping the behavior of electrons. A famous example is the quantum Hall effect, where applying a magnetic field to a two-dimensional electron gas leads to current flowing only along the edges, in one direction, while the bulk remains insulating. This remarkable behavior results from breaking time-reversal symmetry and gives rise to topological edge states that are robust against imperfections.

One exciting direction in driven resonator systems is the design of artificial gauge fields—synthetic magnetic fields that act –break time-reversal symmetry– on neutral particles like photons or phonons. In contrast to electrons, these systems do not naturally react to magnetic field, so directional effects like the Aharonov-Bohm phase must be engineered through clever modulations in time or space. This opens the door to nonreciprocal transport, where energy flows preferentially in one direction, a key ingredient for next-generation quantum devices.

Artificial gauge fields can also be combined with parametric interactions (e.g. modulating the resonator frequency in time) to access non-Hermitian effects. These appear in systems where there is gain and loss, breaking the usual rules of Hermitian dynamics. When combined with artificial gauge fields this leads to striking directional behavior. In particular, the interplay of both ingredients enables amplification in one direction only, a phenomenon not possible with non-Hermiticity alone. Other effects include the control over exceptional points, where modes coalesce and signal response becomes highly sensitive. These phenomena have no analog in traditional condensed matter systems and offer new ways to control signal flow and potentially, quantum states.

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

† Equal contribution

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 are everywhere—they show up naturally in mechanical, optical, and electronic systems, especially when pushed out of equilibrium. Even small nonlinearities can lead to rich and unexpected behavior for high state amplitudes: solitons, limit cycles, phase transitions, or multistability. These are not rare exceptions—they are essential features of how many physical systems evolve and organize, from fluid turbulence and biological rhythms to quantum materials.

Understanding this behavior goes beyond linear theory. Instead of focusing on energy levels or band structures, we need to describe how systems evolve in time—how they settle into patterns, switch between states, or react to disturbances. This calls for a new way to classify non-equilibrium phases of matter, based not on static properties but on the geometry and topology of their dynamical flow.

To tackle these challenges, we use tools that work in the frequency domain. One of them is harmonic balance, which finds steady or periodic behaviors without simulating time evolution from many initial conditions. It is especially useful for uncovering limit cycles—self-sustained oscillations that break time-translation symmetry. These states are common and robust, but often hard to find or count. Our work develops tools to uncover and analyze them. For more information and tools related to Harmonic Balance, see: https://jdelpino.github.io/repositories/

These methods support applications in neuromorphic computing, where networks of nonlinear oscillators can emulate models like Ising or Boltzmann machines. They also shed light on the formation of frequency combs in nanomechanical systems—regular trains of vibrations with rich structure. More broadly, this approach opens new paths to understand how topology shapes nonlinear dynamics, revealing robust patterns like topological solitons, and suggesting future uses in areas such as quantum error correction.

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

† Equal contribution