Topological order in the insulating Josephson junction array

Realization of all-band-flat photonic lattices

Flatbands play an important role in correlated quantum matter and have promising applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such methods can only obtain a few flatbands with most bands remaining dispersive. Here we realize all-band-flat photonic lattices of an arbitrary size by precisely controlling the coupling strengths between lattice sites to mimic those in Fock-state lattices. This allows us to go beyond the perturbative regime of strain engineering and group all eigenmodes in flatbands, which simultaneously achieves high band flatness and large usable bandwidth. We map out the distribution of each flatband in the lattices and selectively excite the eigenmodes with different chiralities. Our method paves a way in controlling band structure and topology of photonic lattices.

Superconducting Qubit Based on Twisted Cuprate Van der Waals Heterostructures

Van-der-Waals assembly enables the fabrication of novel Josephson junctions featuring an atomically sharp interface between two exfoliated and relatively twisted Bi_{2}Sr_{2}CaCu_{2}O_{8+x} (Bi2212) flakes. In a range of twist angles around 45°, the junction provides a regime where the interlayer two-Cooper pair tunneling dominates the current-phase relation. Here we propose employing this novel junction to realize a capacitively shunted qubit that we call flowermon. The d-wave nature of the order parameter endows the flowermon with inherent protection against charge-noise-induced relaxation and quasiparticle-induced dissipation. This inherently protected qubit paves the way to a new class of high-coherence hybrid superconducting quantum devices based on unconventional superconductors.

Solvothermal Synthesis of Lateral Heterojunction Sb2Te3/Bi2Te3 Nanoplates

A lateral heterojunction of topological insulator Sb2Te3/Bi2Te3 was successfully synthesized using a two-step solvothermal method. The two crystalline components were separated well by a sharp lattice-matched interface when the optimized procedure was used. Inspecting the heterojunction using high-resolution transmission electron microscopy showed that epitaxial growth occurred along the horizontal plane. The semiconducting temperature-resistance curve and crossjunction rectification were observed, which reveal a staggered-gap lateral heterojunction with a small junction voltage. Quantum correction from the weak antilocalization reveals the well-maintained transport of the topological surface state. This is appealing for a platform for spin filters and one-dimensional topological interface states.

Protected Josephson Rhombus chains

We have studied the low-energy excitations in a minimalistic protected Josephson circuit which contains two basic elements (rhombi) characterized by the π periodicity of the Josephson energy. Novel design of these elements, which reduces their sensitivity to the offset charge fluctuations, has been employed. We have observed that the lifetime T1 of the first excited state of this quantum circuit in the protected regime is increased up to 70  μs, a factor of ∼100 longer than that in the unprotected state. The quality factor ω01T1 of this qubit exceeds 106. Our results are in agreement with theoretical expectations; they demonstrate the feasibility of symmetry protection in the rhombus-based qubits fabricated with existing technology.

Bosonic Mott insulator with Meissner currents

We introduce a generic bosonic model exemplifying that (spin) Meissner currents can persist in insulating phases of matter. We consider two species of interacting bosons on a lattice. Our model exhibits separation of charge (total density) and spin (relative density): the charge sector is gapped in a bosonic Mott insulator phase with total density one, while the spin sector remains superfluid due to interspecies conversion. Coupling the spin sector to the gauge fields yields a spin Meissner effect reflecting the long-range spin superfluid coherence. We investigate the resulting phase diagram and describe other possible spin phases of matter in the Mott regime possessing chiral currents as well as a spin-density wave phase. The model presented here is realizable in Josephson junction arrays and in cold atom experiments.

Physical implementation of protected qubits

We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.

Uniformly frustrated XY model without a vortex-pattern ordering

The uniformly frustrated XY model with f=1/3 on a dice lattice is shown to possess an accidental degeneracy of its ground states so well developed that the difference between the free energies of fluctuations does not lead to the stabilization of a particular vortex pattern down to zero temperature. Nonetheless, at low temperatures the system is characterized by a finite helicity modulus whose vanishing (at a finite temperature) is related to the dissociation of half-vortex pairs.

Fluctuations and vortex-pattern ordering in the fully frustrated XY model on a honeycomb lattice

The accidental degeneracy of various ground states of a fully frustrated XY model with a honeycomb lattice is shown to survive even when the free energy of the harmonic fluctuations is taken into account. The reason for that consists in the existence of a hidden gauge symmetry between the Hamiltonians describing the harmonic fluctuations in all these ground states. A particular vortex pattern is selected only when anharmonic fluctuations are taken into account. However, the observation of vortex ordering requires relatively large system size L>>Lc > or approximately equal to 10(5).