Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals

We determine conditions on the filling of electrons in a crystalline lattice to obtain the equivalent of a band insulator -- a gapped insulator with neither symmetry breaking nor fractionalized excitations. We allow for strong interactions, which precludes a free particle description. Previous approaches that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an essential way, and cannot be applied to the physically interesting case of spin-orbit coupled systems. Here we introduce two approaches, the first an entanglement based scheme, while the second studies the system on an appropriate flat `Bieberbach' manifold to obtain the filling conditions for all 230 space groups. These approaches only assume time reversal rather than spin rotation invariance. The results depend crucially on whether the crystal symmetry is symmorphic. Our results clarify when one may infer the existence of an exotic ground state based on the absence of order, and we point out applications to experimentally realized materials. Extensions to new situations involving purely spin models are also mentioned.Comment: 9 pages + 5 page appendices, 4 figures, 2 tables; v4: a typo in Figure 4 is correcte

Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals

While band insulators are usually described in wavevector space in terms of fully filled bands, they are sometimes also described in terms of a complementary Wannier picture in which electrons occupy localized, atom-like orbitals. Under what conditions does the latter picture break down? The presence of irremovable quantum entanglement between different sites can obstruct a localized orbital description, which occurs in systems like Chern and topological insulators. We collectively refer to such states as Quantum Band Insulators (QBIs). Here we report the theoretical discovery of a filling-enforced QBI - that is, a free electron insulator in which the band filling is smaller than the minimum number dictated by the atomic picture. Consequently such insulators have no representation in terms of filling localized orbitals and must be QBIs. This is shown to occur in models of certain cubic crystals with non-symmorphic space groups. Like topological insulators, filling-enforced QBIs require spin-orbit coupling. However, in contrast, they do not typically exhibit protected surface states. Instead their nontrivial nature is revealed by studying the quantum entanglement of their ground state wavefunction.Comment: 4.5 pages + 7.5 page Appendices, 2+4 figures; v3: Corrected Fig. 5 in Appendix B; added discussion on surface states (Fig. 6

A proposal for a scalable universal bosonic simulator using individually trapped ions

We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap

Majorana fermions in ferromagnetic chains on the surface of bulk spin-orbit coupled ss-wave superconductors

Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a platform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled $s$-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, $n$, can be either one or two, and should be revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.Comment: 9 pages, 4 figure

Scattering of coherent states on a single artificial atom

In this work we theoretically analyze a circuit QED design where propagating quantum microwaves interact with a single artificial atom, a single Cooper pair box. In particular, we derive a master equation in the so-called transmon regime, including coherent drives. Inspired by recent experiments, we then apply the master equation to describe the dynamics in both a two-level and a three-level approximation of the atom. In the two-level case, we also discuss how to measure photon antibunching in the reflected field and how it is affected by finite temperature and finite detection bandwidth.Comment: 18 pages, 7 figure