The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.
Topological pumping of edge states in finite crystals or quasicrystals with non-trivial topological phases provides a powerful means for robust excitation transfer. In most schemes of topological pumping, the edge states become delocalized and immersed into the continuum during the adiabatic cycle, requiring extremely slow evolution to avoid nonadiabatic effects. Here a scheme of topological pumping based on adiabatic passage of edge and interface states is proposed, which is more robust against nonadiabatic effects and avoids delocalization of the state over the entire adiabatic cycle. The sc…
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the `shortcut to adiabaticity' (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting …
Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly…
The path dependence of adiabatic evolution in classical harmonic chains with clamps is examined. It is shown that cutting and joining a chain may braid adiabatic normal mode frequencies. Accordingly, different adiabatic paths with the same endpoints may transport a normal mode to a different one, and an adiabatic cycle pumps action variables, i.e., the adiabatic invariants of integrable classical systems. Another adiabatic pump for artificial edge modes induced by clamps is shown as an application. Extensions to completely integrable systems and quantum systems are outlined.
Characterization of equilibrium topological quantum phases by non-equilibrium quench dynamics provides a novel and efficient scheme in detecting topological invariants defined in equilibrium. Nevertheless, most of the previous studies have focused on the ideal sudden quench regime. Here we provide a generic non-adiabatic protocol of slowly quenching the system Hamiltonian, and investigate the non-adiabatic dynamical characterization scheme of topological phase. The {\it slow} quench protocol is realized by introducing a Coulomb-like Landau-Zener problem, and it can describe, in a unified way, …
We present a complete topological characterization of a bilayer composite of two Chern insulators (specifically, Haldane models) and explicitly establish the bulk-boundary correspondences. We show that an appropriately defined Chern number accurately maps out all the possible phases of the system and remains well-defined even in the presence of degeneracies in the occupied bands. Importantly, our result paves the way for realizing adiabatic preparation of monolayer Chern insulators. This has been a major challenge till date, given the impossibility of unitarily connecting inequivalent topologi…
We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits interacting with external magnetic fields, and make use of the analogy between the Berry curvature and magnetic fields in parameter space, with spectrum degeneracies associated to magnetic charges. Symmetry-breaking terms induce sharp topological transitions on these charge distributions, and we show how one can exploit this effect to bypass crossing degeneracies. We …
Global adiabatic criterion for fast topological photon transfer in Fock-state lattices
School of Physics, Zhengzhou University（郑州大学物理学院）；School of Electronics and Information, Zhengzhou University of Light Industry（郑州轻工业大学电子与信息工程学院）；Institute of Quantum Materials and Physics, Henan Academy of Science（河南省科学院量子物质与物理研究所）
Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate the Berry phase and use it to classify the topological order of both single-particle and interacting models, highlighting the differences between the two. This algorithm is immediately extensible to any interacting topological system. Our results evidence the potential of near-term quantum hardware for the topological classification of quantum matter.
We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant exploiting the property of the bulk macroscopic electric polarisation (Resta polarisation) of the CI. This Chern invariant defined from observable correlations is also established to topologically classify many body Chern states in equilibrium. The non-equilibrium behavior of the invariant is probed by ramping the paradigmatic Haldane model of graphene from i…
We investigate both pure and mixed states Floquet dynamical quantum phase transition (DQPT) in the periodically time-dependent extended XY model. We exactly show that the proposed Floquet Hamiltonian of interacting spins can be expressed as a sum of noninteracting quasi-spins imposed by an effective time dependent magnetic field (Schwinger-Rabi model). The calculated Chern number indicates that there is a topological transition from nonadiabatic to adiabatic regime. In the adiabatic regime, the quasi-spins trace the time dependent effective magnetic field and then oscillate between spin up and…
When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow "slowly enough" is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [Phys. Rev. Lett. 119, 200401 (2017)]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless p…
Recent theoretical and experimental work has suggested the tantalizing possibility of opening a topological gap upon driving the surface states of a three-dimensional strong topological insulator (TI) with circularly polarized light. With this motivation, we study the response of TIs to a driving field that couples to states near the surface. We unexpectedly find coherent oscillations between the surface and the bulk and trace their appearance to unavoidable resonances caused by photon absorption from the drive. We show how these resonant oscillations may be captured by the Demkov- Osherov mod…
Minimal action shortcut to adiabaticity in a driven Kitaev chain: competing gaps in a topological transition at finite-time
Instituto de Física Teórica, Universidade Estadual Paulista（圣保罗州立大学理论物理研究所）；Instituto de Física de São Carlos, Universidade de São Paulo（圣保罗大学圣卡洛斯物理研究所）
The recent "honeycomb code" is a fault-tolerant quantum memory defined by a sequence of checks which implements a nontrivial automorphism of the toric code. We argue that a general framework to understand this code is to consider continuous adiabatic paths of gapped Hamiltonians and we give a conjectured description of the fundamental group and second and third homotopy groups of this space in two spatial dimensions. A single cycle of such a path can implement some automorphism of the topological order of that Hamiltonian. We construct such paths for arbitrary automorphisms of two-dimensional …
In quantum mechanics, adiabatic elimination is a standard tool that produces a low-lying reduced Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher energy. Suppose this powerful elimination approach is applied to quasi-energy states in periodically-driven systems, a critical question then arises that the violation of the adiabatic condition caused by driven forces challenges such a presence of spectral reduction in the non-equilibrium driven system. Here, both theoretically and experimentally, we newly reported two kinds of driven-in…
We propose a fast and robust quantum state transfer protocol employing a Su-Schrieffer-Heeger chain, where the interchain couplings vary in time. Based on simple considerations around the terms involved in the definition of the adiabatic invariant, we construct an exponential time-driving function that successfully takes advantage of resonant effects to speed up the transfer process. Using optimal control theory, we confirm that the proposed time-driving function is close to optimal. To unravel the crucial aspects of our construction, we proceed to a comparison with two other protocols. One wh…
An adiabatic time evolution of a closed quantum system connects eigenspaces of initial and final Hermitian Hamiltonians for slowly driven systems, or, unitary Floquet operators for slowly modulated driven systems. We show that the connection of eigenspaces depends on a topological property of the adiabatic paths for given initial and final points. An example in slowly modulated periodically driven systems is shown. These analysis are based on the topological analysis of the exotic quantum holonomy in adiabatic closed paths.
We suggest a method for fast and robust quantum-state transfer in a Su-Schrieffer-Heeger (SSH) chain, which exploits the use of next-to-nearest-neighbour (NNN) interactions. The proposed quantum protocol combines a rapid change in one of the topological edge states, induced by a modulation of nearest-neighbour interactions, with a fine tuning of NNN interactions operating a counter-adiabatic driving. The latter cancels nonadiabatic excitations from the edge state multiplicity to the energy bands. We use this shortcut technique for topological pumping of edge states on a single dimerized chain …
We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on $1+1$ dimensional quantum electrodynamics with the $θ$-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact r…
讨论了粒子数守恒与拓扑相的关系。在四维空间中，我们发现在U（1）电荷守恒的存在下，属于不同拓扑相的系统可以按拓扑关系连接，即，而不闭合间隙，在中间通过超导项破坏该局部对称性。二维和三维的时间反转保持拓扑绝缘体态可以通过降维从四维母态得到，从而通过电荷守恒继承了这种保护。因此，所有的拓扑绝缘体都可以在不破坏时间反演对称性的情况下被绝热地连接到平凡绝缘状态，只要在绝热变形期间允许中间超导项。相反，在一维空间中，非对称保护的拓扑相只出现在破坏U（1）电荷守恒的系统中。这些结果可以直观地理解，通过考虑一个自然的嵌入到相应的Bogoliubov de Gennes类的分类空间的电荷守恒哈密顿。
We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor in order to understand their use as a building block for topological quantum computers. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied, and calculate their dynamical evolution when rotating the magnetic field, with special emphasis on non-adiabatic effects. We characterize the phase transition between high-frequency and near-adiabatic evolution using Floquet analysis. We show that oscillations persist even in the adiabatic phase because…
Motivated by the $Ω$-spectrum proposal of unique gapped ground states by Kitaev, we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvable models in one and two spatial dimensions and discuss how nontrivial adiabatic cycles are detected. For one spatial dimension, we study the adiabatic cycle in detail with the matrix product state and show that the symmetry charge can act on the space of matrices without changing the physical states, which leads to nontrivial loops with symmetry charges. For generic spatial dimensions, based on the Bock…
