Quantum circuit complexity of one-dimensional topological phases

Topological quantum states cannot be created from product states with local quantum circuits of constant depth and are in this sense more entangled than topologically trivial states, but how entangled are they? Here we quantify the entanglement in one-dimensional topological states by showing that local quantum circuits of linear depth are necessary to generate them from product states. We establish this linear lower bound for both bosonic and fermionic one-dimensional topological phases and use symmetric circuits for phases with symmetry. We also show that the linear lower bound can be saturated by explicitly constructing circuits generating these topological states. The same results hold for local quantum circuits connecting topological states in different phases.Comment: published versio

Out-of-time-ordered correlators in many-body localized systems

In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread only within a finite distance. Is it possible to detect the logarithmic light cone generated by a local perturbation from the response of a local operator at a later time? We numerically calculate various correlators in the random-field Heisenberg chain. While the equilibrium retarded correlator A(t = 0)B(t > 0) is not sensitive to the unbounded information propagation, the out-of-time-ordered correlator A(t = 0)B(t > 0)A(t = 0)B(t > 0) can detect the logarithmic light cone. We relate out-of-time-ordered correlators to the Lieb-Robinson bound in many-body localized systems, and show how to detect the logarithmic light cone with retarded correlators in specially designed states. Furthermore, we study the temperature dependence of the logarithmic light cone using out-of-time-ordered correlators

Transverse-electric Brewster effect enabled by nonmagnetic two-dimensional materials

Discovered in the 19th century, the Brewster effect is known to occur for transverse-magnetic waves in regular optical dielectrics; however, it is believed to arise for transverse-electric (TE) waves only in systems with magnetic responses, i.e., nonunity effective relative permeability. This paper introduces a scheme to realize the TE Brewster effect in a homogeneous dielectric interface without magnetic responses, by adding ultrathin two-dimensional (2D) materials such as graphene. In particular, the effect remains even for waves approaching normal incidence, spanning from terahertz to visible frequencies. In contrast to the conventional Brewster effect, the graphene-assisted TE Brewster effect is asymmetric, and can be achieved only when the incidence is from the higher-refractive-index side. Moreover, graphene layers can tailor a total-internal-reflection dielectric interface into zero reflection, accompanied by perfect absorption. This control over TE waves enabled by ultrathin 2D materials may lead to a variety of applications, such as atomically thin absorbers, polarizers, and antireflection coating.Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (W911NF-13-D-0001)Solid-State Solar-Thermal Energy Conversion Center (DESC0001299

All-angle negative refraction of highly squeezed plasmon and phonon polaritons in graphene-boron nitride heterostructures

A fundamental building block for nanophotonics is the ability to achieve negative refraction of polaritons, because this could enable the demonstration of many unique nanoscale applications such as deep-subwavelength imaging, superlens, and novel guiding. However, to achieve negative refraction of highly squeezed polaritons, such as plasmon polaritons in graphene and phonon polaritons in boron nitride (BN) with their wavelengths squeezed by a factor over 100, requires the ability to flip the sign of their group velocity at will, which is challenging. Here we reveal that the strong coupling between plasmon and phonon polaritons in graphene-BN heterostructures can be used to flip the sign of the group velocity of the resulting hybrid (plasmon-phonon-polariton) modes. We predict all-angle negative refraction between plasmon and phonon polaritons, and even more surprisingly, between hybrid graphene plasmons, and between hybrid phonon polaritons. Graphene-BN heterostructures thus provide a versatile platform for the design of nano-metasurfaces and nano-imaging elements.Comment: 16 pages; 3 figure