Projects overview
Quantum Optimal Control Theory
Optimal quantum control theory deals with how to find pulses to steer a quantum system in a desired direction, i.e., to a particular target state, or to perform a specific gate, etc. In our work, we have incorporated ideas from machine learning to radically increase the scope of problems that can be solved using optimal quantum control theory.
We published our ideas in this paper and used them to optimize trajectories for the tractor atom interferometer (see Quantum Sensing section below).
The code is also available as part of a Julia framework for quantum optimal control (see QuantumControl.jl), which includes propagator implementations for efficient simulations of open and closed quantum systems. Part of the framework has been published here.
Novel Quantum Control Techniques
Working alongside experimentalists is not only fun, but it also brings challenges. Specific experimental imperfections or limitations often require adapting known control schemes, and sometimes, we must develop new techniques!
This was the case when we introduced the concept of dynamical elimination (the name is a mix of dynamical decoupling and adiabatic elimination of far-detuned states, so is the idea).
The goal was to overcome the limitations of STIRAP to bring robustness to variations (or drifts) of the experimental parameters in the low pulse area regime. Thanks to that, now we have a new way of creating two-photon transitions with applications beyond the original experimental challenge.
Currently, I keep myself busy working on other applications of this concept.
Quantum Sensing
This is the main topic of my postdoctoral work. As an overview I will divide it in different subprojects.
- Spin squeezing optimization. We worked alongside the group of Prof. Vladan Vuletic at MIT to optimize the generation of spin-squeezed states using both pulse sequences and adiabatic methods.
- Tractor atomic interferometer (TAI). We are working with Prof. Georg Raithel's group at the University of Michigan, Ann Arbor, on a new interferometric device, the TAI. The idea is to split and interfere atoms in programmable paths and leverage long interrogation times. The paths will be designed by optimal quantum control. The device could function as an accelerometer or a gyroscope, depending on the trajectories.
- Quantum sensing using NV centers We are incorporating new quantum control solutions into an NV center setup alongside Prof. Budker's group. We have used STIRAP to improve long-term stability of a diamond-based gyroscope and also introduced a new technique called dynamical elimination (see above).
I have also worked with some young UMD researchers. We demonstrated with Zhifan Zhou (Paul Lett's group, formerly at Ron Folman's group) enhanced quantum sensing using non-cyclic geometric phases. And I worked with JJ Oon (formerly at Ron Walsworth's group) the details of what happens at the breakdown of average Hamiltonian theory.
Quantum information and quantum optics
A fundamental no-go theorem of quantum mechanics is that quantum states cannot be perfectly discriminated (unless the states are completely orthogonal). The intuition is that if you measure a particle to be spin-up, you cannot tell if it was in the spin-up state before the measurement or in a superposition of spin-up and down, and you just happened to get spin-up as the measured outcome. However, you can tell if the only options for the initial states are spin-up or spin-down.
Our work exploits this fundamental property to look for radar spoofing and derive the optimal states and success probabilities. The idea is that you encode a quantum state randomly from an alphabet of quantum states in the radar signal. When the signal gets to a target, it can decide to spoof the signal (send a false reflection back). However, that false reflection must contain the same quantum state, which is impossible to determine accurately. Thus, the spoofer only has some chance to get it right.
Additionally, radar operators have the same problem. It is also impossible to tell if the signal was spoofed. However, we were able to show, considering coherent and squeezed states of light, that there is a quantum advantage, i.e., one is more likely to detect spoofing using quantum mechanics than without it.
This was the thesis project of one of my former master's students, Tomás P. Espinoza.
Quantum models of simple molecules
Quantum control has evolved alongside quantum chemistry. Coherent control ideas like pump–dump schemes, phase interference, and STIRAP showed that chemical reactions can be controlled with light pulses. Later, access to pulse shapers gave rise to optimal control. More recently, those ideas became crucial to enable quantum technologies.
In my career, I followed a similar pathway. During my PhD, I worked with Prof. Ignacio Sola from Universidad Complutense of Madrid, modelling the H2+ molecule fully quantum mechanically. We were able to show that this particular molecule does not align with electric fields, as most molecules do. It actually anti-aligns when it is excited and dissociates. Later, we were able to design pulses to stabilize its excited state.
Complex Systems
Before I dove into quantum control, I became fascinated by complex systems. I learned how simple rules lead to emergent phenomena and how minor rule tweaks cascade into dramatic changes. I have researched across many directions, ranging from simple models of proto-living systems to predicting soccer match outcomes using complex networks. For example, I recently mentored Nikolas N. Encina (Universidad de Chile, undergrad) about using reinforcement learning to model the evacuation of agents from a room. We discovered that trained agents are more socially aware and avoid collisions significantly better.
Another example is a series of works about simulating routing systems in cities. The inspiration came from a professor at the Universidad de Chile who follows Waze profusely. We showed that it's bad for city traffic if everyone does that, and it's healthy for the city and its energy consumption to sometimes take a wrong turn. Then, we went on to find analogies between city traffic and thermodynamics (including phase-transitions).
The black car is trying to follow the route formed by the red numbers. This is a simplified version of the simulation.