Research and Projects

Our areas of study are quantum simulation and quantum computing, with an emphasis on the many-body interacting-electron problem, due to its fascinating and fruitful physics and its relevance in superconductors, quantum computers, and novel materials. One of the objectives of our research is to understand the fundamental physics governing electron behavior in lattices by stripping the system down to its very simplest form. To accomplish this, we develop and use numerical methods for quantum simulations of systems where electrons interact strongly and traditional analytic methods fail. Understanding properties of such toy models has also been a subject of intensive research with atoms loaded in optical lattices. In these quantum simulators, different internal states of atoms represent the possible spin states of electrons +1/2 (up) and -1/2 (down). These atoms are loaded into lattices made with laser beams and are well described by mathematical models that capture the basic ingredients of quantum materials. One of the directions in this line of research is going beyond the simple spin up/spin down paradigm and study systems with larger spins. These systems display interesting magnetic patterns and exhibit richer, more exotic physics. Although for condensed matter research the internal states of atoms represent the spin degrees of freedom of the electrons, these can also be used to represent states of qubits and utilized as a platform for quantum computing and sensing. We can encode information in sequences of qubits, and we perform computations on them. Thus, our research also enables other applications in the field of quantum information.

Collaborators

Machine learning for strongly correlated materials

Team Leader - Postdoc project

Although knowledge of phase transitions is generally obtained by studying order parameters, in some cases these might not be well defined or hard to measure (either experimentally or numerically).

In this project we aim to understand if signatures of different phases of matter and crossovers can be detected using supervised and unsupervised learning techniques. In particular, how to extract valuable physics from projective measurements such as those used in quantum gas microscopes.

Learn more about the algorithm and analysis code

Determinant Quantum Monte Carlo - How we do the physics
Density Matrix Renormalization Group - How we do the physics
Structural complexity - How we analyze the data and understanding the physics

Interacting fermions with SU(N) symmetry

Team Leader - PhD project

What do insulation, magnetism and superconductivity have in common? All of these diverse and interesting properties of materials arise from the behavior of electrons in a lattice.

I seek to understand this behavior by stripping the system down to its very simple form named the Hubbard model, which accurately describes ultracold atomic systems that serve as quantum simulators of macroscopic materials.

Learn more about the projects

Universal thermodynamics of an SU(N) Fermi-Hubbard model
Observation of antiferromagnetic correlations in an ultracold SU(N) Hubbard model
Thermodynamics and magnetism in the 2D to 3D crossover of the Hubbard model

Learn more about the algorithm and analysis code

Determinant Quantum Monte Carlo - How we do the physics
Data cleaning - How we read the output and format it for easier manipulation
Analysis and plotting - How we analyze data and generate figures

Fermi Hubbard Optical Tweezer

Team Member

Although optical lattices have been of enormous use to simulate condensed matter systems, they are restricted to simple geometries such as squares.

In contrast, recent lattices formed by optical tweezer have the ability to not only construct a wide variety of geometries, but also have single-site control capabilities.

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I seek to numerical simulate the dynamics of atoms trapped in such tweezers, which are stroboscopically turned on and off while experiments are performed. The dynamics encode information such as the heating rate of the atoms in the lattice, which is relevant for experiments.

Learn more about the numerical techniques

Discrete Variable Representations (DVR) - How we diagonalize the matrices
Time evolution - How we simulate the dynamics of the system
Analysis and plotting - How we analyze data and generate figures

Loop observables and classical Monte Carlo

Undergraduate Research Advisor

Eventhough classical models do not suffer from the consequences of anticommutation and commutation relationships, computing the partition function and correlation functions is not a trivial task.

For this purpose, we employ classical Monte Carlo techniques to study lattice models. One of the most studied ones is the Ising model, which has an analytical solution in two dimensions, but not in three.

We study generalizations of the Ising model in 3D with different lattice geometries and couplings. For this, we do not limit ourselves to n-point correlators, but loop observables, which depend on their topology, i.e. whether they are continuously shrinkable to a point, or non-shrinkable. Some if these models have an analytic solution for complex values of the coupling constants, and the existence of phases where these loop observables are quantized at fractional values. We aim to determine if similar phases can be found for all coupling constants that are all real.

Learn more about the numerical techniques and analysis code

Classical Monte Carlo - How we perform the simulation
Loop observables - What quantities we compute and how they depend on length.
Analysis and plotting - How we analyze data and generate figures