Our research goal is to explore and foster a positive (and possibly strange) feedback loop between two domains:
The physics and applications of complex dynamical systems (mostly high-dimensional optical waves) and
Computer science (mostly artificial intelligence and machine learning)
The lab is, in other words, interested in concepts, devices, algorithms, and phenomena that symbiotically combine physics and computer science, such as quantum information, physics-informed machine learning, control, embodied intelligence, and robotics. As applied physicists, we try to maintain a firm footing in experiments and applications, with multimode photonic systems serving as the main testbed, motivator, and beneficiary of new ideas.
What sorts of inventions or discoveries may arise in this exploration? To get a better idea, scroll down for examples of some of our current, more specific projects. Ultimately, however, we're seeking long-term outcomes like the following:
High-dimensional advanced light tools: systems based on lasers and quantum light sources that use photons tailored in many degrees of freedom (space, time, polarization, frequency) to optimally sense, control, or modify the material world.
Photonic brains: computing and learning machines that process and interact with data using light, realizing artificial intelligence and machine learning much faster, and with vastly lower energy consumption than digital electronics.
Phobots: photonic (or phononic) systems -- robots -- that use computers and high-dimensional wave-based actuators and sensors to interact with, and learn about complex physical systems, such quantum materials, chemical processes, and fluids.
Physical programming: Methods and platforms to "program" the functionality and form of real, messy physical systems - even ones that are nonlinear, quantum, and/or far from equilibrium.
(Some of our) Current projects
Conventional deep neural networks (DNNs) consist of sequences of mathematical transformations of data. These sequential transformations have adjustable parameters ('weights and biases') which are learned in a supervised fashion using an algorithm called backpropagation. This procedure, usually called deep learning, uses DNNs to approximate desired mathematical functions.
A proof-of-concept PNN: a metal plate driven by a speaker can be used to perform machine learning. See the published paper for more details. Experiment performed by Martin Stein, PhD student at Cornell, during 2020-2021.
Physical neural networks replace the mathematical transformations in DNNs with adjustable physical processes, such as light propagating in microstructured materials, or the time evolution of driven multimode mechanical oscillators (like the speaker-driven metal plate shown on the left). With some simple tricks, we can train these physical devices in the same fashion as DNNs. But whereas DNNs are taught to perform desired mathematical functions, PNNs are taught to perform desired physical functions.
The complex physical functions learned by PNNs may be useful for performing machine learning calculations very efficiently, or very quickly. But because they process data directly, natively in the physical domain (e.g., as photons or acoustic vibrations), they may also be useful for computational imaging or sensing systems, or for realizing new kinds of functional physical machines.
We are exploring different strategies and substrates for PNNs, as well as a diverse range of applications of them.
Representative questions include:
What happens when the physical processes used in a PNN involve quantum mechanical phenomena, such as entanglement and squeezing?
Are there ways we can cause PNNs to learn on their own, i.e., autonomously?
What physical processes make for the best PNNs, and just how efficient or fast could they perform machine learning calculations?
Multimode nonlinear optical waves
Freeman Dyson famously argued that scientific progress is driven by a combination of new ideas and new tools. Our astounding, intricate hands and eyes were our first tools, providing the interface from brain to world that allowed homo sapiens to become engineers, scientists, and artists. New scientific tools can extend our hands and eyes, providing unique and unprecedented capabilities that in turn enable scientists to explore previously inaccessible regimes of nature. These explorations inevitably lead to discoveries, inventions, and applications that were simply impossible before. Over the past decades, advanced light sources based on nonlinear optics have provided the basis for many such ability-expanding tools. Today, there is hardly any domain of science which does not rely in one fashion or another on lasers, or on related tools like parametric down-conversion, mode-locked optical combs, or supercontinuum. These light sources provide truly awe-inspiring forms of light, such as femtosecond duration pulses with terawatts of peak power. But these unique capabilities still often resemble hammers more than hands.
We believe therefore that the breakthroughs of tomorrow will be enabled not only by better photonic hammers, but even more by photonic hands: light sources and devices that are not only more powerful, but also more multifaceted, more adaptable, and more nuanced. For this, we will need to achieve rich control of coherent multimode photons: light with many degrees of freedom in space, time, and frequency, and with multitudinous classical and quantum correlations. We are thus motivated to learn how to design and control multimode nonlinear optical systems. To do this, we make use of intensive numerical simulations, complexity-mitigating machine learning techniques and analytic theory, and experiments and prototypes based on reconfigurable photonic devices, including multimode fibers and integrated waveguides, spatial light modulators, and multimode laser cavities.
But multimode nonlinear optical systems are not only tools to develop tools: They are also tools to develop new ideas and concepts, those other key drivers of scientific progress. In particular, these systems provide an almost ideal playground, a laboratory microcosm within which to explore high-dimensional nonlinear and quantum physics, both near and far from equilibrium.
Thus, just as biologists use cell cultures or laboratory mice to efficiently explore biological complexity, we use multimode nonlinear optical platforms as "model systems" to allow us to efficiently develop new, universal strategies for data-driven control, high-dimensional design, and reduced modelling. These techniques should ultimately have broad utility in automated discovery, and in the design, control, and understanding of complex nonlinear and quantum dynamical systems. This in turn will lead to new tools, such as new kinds of computers, lasers, and robots, as well as advances in the physics and engineering of fluids, chemical processes, and complex materials.