Geometry of time-dependent PT-symmetric quantum mechanics

A new type of quantum theory known as time-dependent𝒫PT-symmetric quantum mechanics has received much attention recently.It has a conceptually intriguing feature of equipping the Hilbert space of a𝒫PT-symmetric system with a time-varying inner product.In this work,we explore the geometry of time-dependent𝒫𝒯PT-symmetric quantum mechanics.We find that a geometric phase can emerge naturally from the cyclic evolution of a PT-symmetric system,and further formulate a series of related differential-geometry concepts,including connection,curvature,parallel transport,metric tensor,and quantum geometric tensor.These findings constitute a useful,perhaps indispensible,tool to investigate geometric properties of𝒫PT-symmetric systems with time-varying system’s parameters.To exemplify the application of our findings,we show that the unconventional geometric phase[Phys.Rev.Lett.91187902(2003)],which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase,can be expressed as a single geometric phase unveiled in this work.

Direct dynamical characterization of higher-order topological phases with nested band inversion surfaces

Higher-order topological phases(HOTPs) are systems with topologically protected in-gap boundary states localized at their ed à nT-dimensional boundaries, with d the system dimension and n the order of the topology. This work proposes a dynamics-based characterization of one large class of Z-type HOTPs without specifically relying on any crystalline symmetry considerations. The key element of our innovative approach is to connect quantum quench dynamics with nested configurations of the socalled band inversion surfaces(BISs) of momentum-space Hamiltonians as a sum of operators from the Clifford algebra(a condition that can be partially relaxed), thereby making it possible to dynamically detect each and every order of topology on an equal footing. Given that experiments on synthetic topological matter can directly measure the winding of certain pseudospin texture to determine topological features of BISs, the topological invariants defined through nested BISs are all within reach of ongoing experiments. Further, the necessity of having nested BISs in defining higher-order topology offers a unique perspective to investigate and engineer higher-order topological phase transitions.

Probing higher-order band topology via spin texture measurements:quantum simulation

The long-term goal of quantum simulation is to assemble at will many-body quantum systems of vast complexity,to discover emerging new physics or obtain important results beyond the computational capability of classical supercomputers.Along this ambitious and game-changing journey,one milestone is to achieve flexible and high-fidelity quantum simulations with a few qubits.Indeed,qubits based on superconducting Josephson junction.

Topologicalπmodes and beyond

Topological states of matter,which have seen rapid development since the last few decades,are characterized by the presence of robust boundary modes.In 2001,Kitaev[1]identified a particularly important example of such topological modes at the ends of a one-dimensional(1D)p-wave superconducting chain(now also known as the Kitaev chain).Due to the presence of particle-hole symmetry in the system,the obtained topological edge modes are pinned at zero energy and are related to the sought-after Majorana particles.Such Majorana zero modes are promising for robust quantum information processing due to their ability to encode qubits nonlocally.Since then,studies of Majorana zero modes and their quantum computing applications have developed into an active research area of their own.