scholarly journals Dynamical signatures of topological order in the driven-dissipative Kitaev chain

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Moos van Caspel ◽  
Sergio Enrique Tapias Arze ◽  
Isaac Pérez Castillo
Keyword(s):  
Steady State ◽  
Closed System ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Topological Phases ◽  
Topological Order ◽  
Superconducting Nanowires ◽  
Boundary Correspondence ◽  
Steady State Current ◽  
Different Types

We investigate the effects of dissipation and driving on topological order in superconducting nanowires. Rather than studying the non-equilibrium steady state, we propose a method to classify and detect dynamical signatures of topological order in open quantum systems. Bulk winding numbers for the Lindblad generator \hat{\mathcal{L}}ℒ̂ of the dissipative Kitaev chain are found to be linked to the presence of Majorana edge master modes – localized eigenmodes of \hat{\mathcal{L}}ℒ̂. Despite decaying in time, these modes provide dynamical fingerprints of the topological phases of the closed system, which are now separated by intermediate regions where winding numbers are ill-defined and the bulk-boundary correspondence breaks down. Combining these techniques with the Floquet formalism reveals higher winding numbers and different types of edge modes under periodic driving. Finally, we link the presence of edge modes to a steady state current.

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

Novel topological end modes and breaking of bulk boundary correspondence in skin-effect absent superconductive chain

2021 ◽  
Author(s):  
Huan-Yu Wang ◽  
Wu-Ming Liu
Keyword(s):  
Skin Effect ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Topological Invariants ◽  
Quantum Matter ◽  
Topological Quantum ◽  
Boundary Correspondence ◽  
Quantum Chain ◽  
New Type ◽  
Majorana Modes

Abstract Topological nontrivial systems feature isolated gapless edge modes, and play a key role in advancing our understanding of quantum matter. A most profound way to characterize edge modes above is through bulk topological invariants, which is known as bulk boundary correspondence. Recent studies on non-Hermitian physics have pronounced the broken bulk-boundary correspondence with the presence of skin effect. Here, we propose a new type of fermionic topological edge modes η, satisfying η+= iη,η2=-i. Remarkably, we demonstrate that for both two cases: superconductive chain with purely η modes and quantum chain with η, Majorana modes γ on different ends, fermion parity can be well defined. Interestingly, for the latter case, broken bulk boundary correspondence is observed despite the absence of skin effects . The phenomenon above is unique to open quantum systems. For the junction with both η,γ modes, the current will not remain sinusoid form but decay exponentially. The exchange of η modes obeys the rules of non-abelian statistics, and can find its applications in topological quantum computing.

scholarly journals Perturbation theory for open quantum systems at the steady state

2018 ◽  
Vol 10 ◽  
pp. 353-355 ◽  
Author(s):  
Edgar A. Gómez ◽  
Jorge David Castaño-Yepes ◽  
Saravana Prakash Thirumuruganandham
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Topological Order, Mixed States and Open Systems

2019 ◽  
Vol 26 (03) ◽  
pp. 1950012 ◽  
Author(s):  
Manuel Asorey ◽  
Paolo Facchi ◽  
Giuseppe Marmo
Keyword(s):  
Open Systems ◽  
Quantum Systems ◽  
Topological Phases ◽  
Topological Order ◽  
Mixed States ◽  
Quantum Matter ◽  
Physical Role ◽  
Topological Quantum ◽  
Pure States

The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.

scholarly journals Bistabilities and domain walls in weakly open quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Florian Lange ◽  
Achim Rosch
Keyword(s):  
Steady State ◽  
Conservation Laws ◽  
Weak Coupling ◽  
Domain Walls ◽  
Hydrodynamic Equation ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Multiple Steady State ◽  
One Dimensional ◽  
Steady State Solutions

Weakly pumped systems with approximate conservation laws can be efficiently described by (generalized) Gibbs ensembles if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the zz-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength \epsilonϵ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as \sim 1/\sqrt{\epsilon}∼1/ϵ while the density of domain walls is exponentially small in 1/\sqrt{\epsilon}1/ϵ. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

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