Friday Quantum Seminar

Although lattice gauge theories are primarily considered in particle physics, they are also a valuable platform to study strongly correlated quantum systems in condensed-matter physics. Particularly interesting is the study of confinement, which can arise when dynamical charges are coupled to gauge fields. In this talk, I will present our recent work on a one-dimensional Z2 lattice gauge theory (LGT), where dynamical matter is coupled to Z2 gauge field [1].

Authors: Billy Braasch and William K. Wootters

The study of topological phases of matter and the invariants that define them has become a central pursuit of condensed matter physics. In particular, crystalline systems are known to host a large set of topological invariants, but the physical response properties associated to them are still not fully understood.

Recent optical probes have used excitons, electron-hole bound states, to probe correlated insulating phases of two-dimensional semiconducting materials. Motivated by these experiments, we investigate these composite particles involving Mott physics. In this talk, we will discuss the formalism of two types of Mott excitons: Intraband exciton with both charges from a single band Hubbard model, and interband exciton with only one charge in the Mott.

Quantum state and unitary $t$-designs play an important role in several applications, including tomography, randomized benchmarking, state discrimination, cryptography, sensing, and fundamental physics. In this work, we generalize the notion of state designs to infinite-dimensional, separable Hilbert spaces. We first prove that under the definition of continuous-variable (CV) state $t$-designs from [Comm. Math. Phys 326, 755-771 (2014)], no state designs exist for $t\geq2$. Similarly, we prove that no CV unitary $t$-designs exist for $t\geq 2$.

Hybridizing light and matter by means of cavities can be used as a tool to influence material properties.  In my talk I will discuss a model for strongly correlated fermions close to a quantum phase-transition coupled to a single mode of an optical cavity. Close to the critical point, light and matter degrees of freedom hybridize, which can be observed in an increase in their entanglement.

The non-equilibrium dynamics of quantum many-body systems is a notoriously difficult topic of study, but one in which much progress is currently being made. Lieb-Robinson bounds have proven to be a valuable tool for obtaining both rigorous results and physical intuition. In this talk, after an introduction to the physical content of Lieb-Robinson bounds and a description of various applications, we discuss our recent work constructing bounds for systems with quenched disorder in 1D.

Motivated by the recent progress of quantum chaos and quantum information scrambling, the growth of an operator under the Heisenberg evolution has attracted a lot of attentions. I will first introduce a recently proposed perspective on the operator growth problem from the Lanczos algorithm point of view and the associated “Krylov complexity”.

Topological mixed quantum states in or out of equilibrium can arise in open quantum systems. Their linear responses are generally non-quantized, even though quantized topological invariants can be defined. In this talk, I will present a real-time U(1) topological gauge field action capable of reconciling this paradoxical phenomenology. In addition to non-quantized linear responses, this action encodes quantized non-linear responses associated with mixed state topology.

Arrays of neutral atoms promise to enable a variety of goals across quantum science, including quantum information processing, metrology, and many-body physics. While there have been recent significant improvements in quantum control, coherence times, and entanglement generation, one outstanding limitation is the efficient implementation of dissipation or measurement.