Engineering topological state transfer in four-period Su–Schrieffer–Heeger chain

An extended Su–Schrieffer–Heeger(SSH) model containing four periods of the hopping coefficients, called SSH4 model, is constructed to explore robust quantum state transfer. The gap state protected by the energy gap plays the role of the topological channel where the particle initially located at the last lattice site has the probability to arise at the first and all even lattice sites equally. Serving those sites as ports, a multi-port router can be realized naturally, and the fidelity reaches unity in a wide range of parameters under the long chain and random disorder. Further, when we reduce the third intracell hopping to a small value, the occupancy probability of the second lattice site in every unit cell will reduce to zero, by which a new topological router can be induced. In addition, our SSH4 model can work as a 1/3 beam splitter. Namely, the particle initially occupies the first lattice site and finally appears with equal probability at three lattice sites. We can also realize a 1/2 beam splitter. Our four-period SSH model provides a novel way for topological quantum information processing and can engineer two kinds of quantum optical devices.

High-fidelity topological quantum state transfers in a cavity-magnon system

We propose a scheme for realizing high-fidelity topological state transfer via the topological edge states in a onedimensional cavity-magnon system.It is found that the cavity-magnon system can be mapped analytically into the generalized Su-Schrieffer-Heeger model with tunable cavity-magnon coupling.It is shown that the edge state can be served as a quantum channel to realize the photonic and magnonic state transfers by adjusting the coupling strength between adjacent cavity modes.Further,our scheme can realize the quantum state transfer between photonic state and magnonic state by changing the cavity-magnon coupling strength.With the numerical simulation,we quantitatively show that the photonic,magnonic and magnon-to-photon state transfers can be achieved with high fidelity in the cavity-magnon system.Spectacularly,three different types of quantum state transfer schemes can be even transformed into each other in a controllable fashion.The Su-Schrieffer-Heeger model based on the cavity-magnon system provides us a tunable platform to engineer the transport of photon and magnon,which may have potential applications in topological quantum processing.

Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime.We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer Heeger(SSH)model via designing the effective optomechanical coupling.Especially,the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the opto mechanical coupling.We stress that the to pological phase transition is mainly induced by the decay of the cavity field,which is counter-intuitive since the dissipation is usually detrimental to the system.Also,we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice.We find that the quantum st ate transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields.Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.

The value does not exist!A motivation for extremal analysis

Standard mathematical economics studies the production,exchange,and consumption of goods“provided with units of measurement,”as in physics,in order to be enumerated,quantified,added,etc.Therefore,“baskets of goods,”which should describe subsets of goods,are mathematically represented as commodity vectors of a vector space,linear combination of units of goods,evaluated by prices,which are linear numerical functions.Therefore,in this sense,mathematical economics is a branch of physics.However,economics,and many other domains of life sciences,investigate also what will be called entities,defining elements deprived of units of measure,which thus cannot be enumerated.(1)Denoting by X the set of entities x∈X deprived of units of measurement,a“basket of goods”is actually a subset K■X of the set entities,i.e.,an element of the“hyperset”P(X),the family of subsets of X,and no longer a commodity vector of the vector space of commodities;(2)Entities can be“gathered”instead of being“added”;(3)Entities can still be evaluated by a family of functions A:x 2 X 7!A(x)2 Rregarded as a“valuators,”in lieu and place of linear“prices”evaluating the units of economic goods.(4)Subsets of entities can be evaluated by an“interval of values”between two extremal ones,the minimum and the maximum,instead of the sum of values of units of goods weighted by their quantities.Life sciences dealing with intertwined relations among many combinations of entities,hypersets offer metaphors of“Lamarckian complexity”that keeps us away from binary relations,graphs of functions,and set-valued maps,to focus our attention on“multinary relations”between families of hypersets.Even deprived of units of measurement,these“proletarian”entities still enjoy enough properties for this pauperization to be mathematically consistent.This is the object of this extremal manifesto:in economics and other domains of life sciences,vector spaces should yield their imperial status of“state space”to hypersets and linear prices to hypervaluators.We no longer have to add goods which can only be gathered,prices do not have to be linear,although it costs some effort to deprive oneself of the powerful and luxurious charms of convex and linear functional analysis motivated by physics.These sacrifices concern only economics and other fields of life science,since physicists deal with experimental observations of objects endowed with unit of measurement by adequate processes of measurement.They can happily live in vector spaces without any guilt.This is not the case of life scientists,who have mainly history to support and validate their observations,with,sometimes,the privilege to statistically measure the frequency of some of them.