相关论文: Topological quantization by controlled paths: appl…

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…

In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper,…

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a…

We report on the topological pumping of quadratic optical solitons, observed through their quantized transport in a dynamic optical potential. A distinctive feature of this system is that the two fields with different frequencies, which…

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the…

Quantum graphs provide an analytically tractable setting for the study of Chern numbers and band degeneracies in periodic systems. We study the Chern numbers of energy bands in a two-dimensional square lattice quantum graph. We approach the…

Topological quantum pumps are topologically equivalent to the quantum Hall state: In these systems, the charge pumped during each pumping cycle is quantized and coincides with the Chern invariant. However, differently from quantum Hall…

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in $q_3$ ($q_3$ denotes the curvilinear coordinate variable perpendicular to…

In topological field theories determinants of maps with negative as well as positive eigenvalues arise. We give a generalisation of the zeta-regularisation technique to derive expressions for the phase and scaling-dependence of these…

Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in non-Hermitian parity-time symmetric systems, where the topological invariant remains conserved,…

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is…

In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance $\kappa_{xy}=c \frac{\pi^2 k_B^2}{3h}T$, where the dimensionless $c$ is called chiral central charge. If there…

We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum…

Two singularity theorems can be proven if one attempts to let a Lorentzian cobordism interpolate between two topologically distinct manifolds. On the other hand, Cartier and DeWitt-Morette have given a rigorous definition for quantum field…

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

We discuss adiabatic quantum phenomena at a level crossing. Given a path in the parameter space which passes through a degeneracy point, we find a criterion which determines whether the adiabaticity condition can be satisfied. For paths…

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite…

Topological invariants, including the Chern numbers, can topologically classify parameterized Hamiltonians. We find that topological invariants can be properly defined and calculated even if the parameter space is discrete, which is done by…

Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling…