Free-Fermionic Topological Quantum Sensors.

Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations.

Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.

We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.