Research Highlights/Interests

The research in our group falls along the following general themes:

Quantum protocols

[Conformal Quench] One of the emerging goals in science today is the development of quantum simulators and quantum computers. The challenges on this front include, for instance: i) how can we stabilize quantum memories, and correct for errors from decoherence and dissipation? ii) how can we prepare quantum states of matter in specific eigenstates and with certain entanglement features? iii) what are feasible channels to implementing universal quantum gates? These questions are also motivating an entirely new approach towards studying quantum dynamics in non-equilibrium settings. There is immense potential for novel research combining both numerical and analytical techniques to make progress on such questions. In this regard, we are recently working towards new protocols to create ground states of interacting quantum systems that could be used in ultracold atoms, protocols to stabilize quantum bits in topological superconductors, and new error correction codes. Our research goals are also motivated by new experimental developments in the engineering of artificial quantum systems.

Quantum thermalization, many-body localization and non-equilibrium phases of quantum matter

[Scaling] The principles of thermodynamics (as well as our usual intuition from the macroscopic world) suggests that when two bodies at different temperatures are brought together, they equilibrate to the same intermediate temperature by exchanging heat and matter. Many-body localization is a quantum phase that defies this very basic expectation. A transition between equilibrating and non-equilibrium matter is much like a quantum phase transition, but one that now occurs for all eigenstates simultaneously as opposed to just occurring in the ground state. Understanding such a transition is a key theoretical goal because it has the possibility of revealing the role of quantum mechanics in thermalization and macroscopic dynamics at a level never understood before. Many-body localization is also the backbone for developing phases of matter that only exist in out-of-equilibrium conditions, such as time-crystals, or exhibit topological order at all energy densities. We are interested in both purely theoretical questions, as well as opportunities for exploring potential applications of such novel physics.

Novel spectroscopic probes

[Scaling] A variety of interesting physical phenomena show up in scaling properties of correlation functions and require measurement across a set of length- and/or time-scales. These phenomena cannot be measured by traditional probes that measure charge or heat transport across the length of a sample, and typically at low frequencies. For instance, recent research suggests that there may be fundamental bounds on viscous transport (which has consequences for transport at finite length scales) that are saturated in the limit of strong interactions. These scale-dependent features often carry important signatures about the system and interactions. One important avenue for exploring such physics experimentally is using Nitrogen-Vacancy (NV) centers, which are a type of defect in diamond that can be thought of as a tiny polarized magnetic moment. We recently proposed experiments to measure hydrodynamic transport coefficients among other properties in low-dimensional materials, and have worked with experimentalists to identify a phononic Cerenkov effect in graphene. We aim to continue working with experimentalists both at McGill and elsewhere to explore the potential of such devices and more that allow for a direct probe of novel dynamical features in quantum systems.