Friday Quantum Seminar

(Pizza and refreshments will be served after the talk.)

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be generalized at the microscopic level. In this work, we show that the generalized cluster state introduced in arXiv:1408.6237 is an SPT protected by categorical symmetry.

Quantum Spin Liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z2 topological order, arrays of neutral atoms with Rydberg interactions have emerged as a promising platform to realize a spin liquid. In this work, we propose a way to realize the deconfined phase of U(1) gauge theory in 3 spatial dimensions from Rydberg interactions on a pyrochlore lattice.

Abstract: 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].

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.