Physical approach to quantum networks with massive particles

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Physical approach to quantum networks with massive particles. / Andersen, Molte Emil Strange; Zinner, Nikolaj Thomas.

In: Physical Review B, Vol. 97, No. 15, 155407, 2018.

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Andersen, Molte Emil Strange ; Zinner, Nikolaj Thomas. / Physical approach to quantum networks with massive particles. In: Physical Review B. 2018 ; Vol. 97, No. 15.

Bibtex

@article{80c840961cd24e40925519007fe1152d,
title = "Physical approach to quantum networks with massive particles",
abstract = "Assembling large-scale quantum networks is a key goal of modern physics research with applications in quantum information and computation. Quantum wires and waveguides in which massive particles propagate in tailored confinement is one promising platform for realizing a quantum network. In the literature, such networks are often treated as quantum graphs, that is, the wave functions are taken to live on graphs of one-dimensional edges meeting in vertices. Hitherto, it has been unclear what boundary conditions on the vertices produce the physical states one finds in nature. This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by crossing two quantum wires, and we consider a massive particle in such an X well. The system is analyzed using a variational method based on an expansion into modes with fast convergence and it provides a very clear intuition for the physics of the problem. The particle is found to have a ground state that is exponentially localized to the center of the X well, and the other symmetric solutions are formed so to be orthogonal to the ground state. This is in contrast to the predictions of the conventionally used so-called Kirchoff boundary conditions in quantum graph theory that predict a different sequence of symmetric solutions that cannot be physically realized. Numerical methods have previously been the only source of information on the ground-state wave function and our results provide a different perspective with strong analytical insights. The ground-state wave function has a spatial profile that looks very similar to the shape of a solitonic solution to a nonlinear Schrodinger equation, enabling an analytical prediction of the wave number. When combining multiple X wells into a network or grid, each site supports a solitonlike localized state. These localized solutions only couple to each other and are able to jump from one site to another as if they were trapped in a discrete lattice.",
keywords = "ELECTRON GAS-MODEL, BOUND-STATES, WAVE-GUIDE, VARIATIONAL-PROBLEMS, SPECTRAL STATISTICS, ROOM-TEMPERATURE, GRAPHS, SCATTERING, SYSTEMS, CONVERGENCE",
author = "Andersen, {Molte Emil Strange} and Zinner, {Nikolaj Thomas}",
year = "2018",
doi = "10.1103/PhysRevB.97.155407",
language = "English",
volume = "97",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "american physical society",
number = "15",

}

RIS

TY - JOUR

T1 - Physical approach to quantum networks with massive particles

AU - Andersen, Molte Emil Strange

AU - Zinner, Nikolaj Thomas

PY - 2018

Y1 - 2018

N2 - Assembling large-scale quantum networks is a key goal of modern physics research with applications in quantum information and computation. Quantum wires and waveguides in which massive particles propagate in tailored confinement is one promising platform for realizing a quantum network. In the literature, such networks are often treated as quantum graphs, that is, the wave functions are taken to live on graphs of one-dimensional edges meeting in vertices. Hitherto, it has been unclear what boundary conditions on the vertices produce the physical states one finds in nature. This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by crossing two quantum wires, and we consider a massive particle in such an X well. The system is analyzed using a variational method based on an expansion into modes with fast convergence and it provides a very clear intuition for the physics of the problem. The particle is found to have a ground state that is exponentially localized to the center of the X well, and the other symmetric solutions are formed so to be orthogonal to the ground state. This is in contrast to the predictions of the conventionally used so-called Kirchoff boundary conditions in quantum graph theory that predict a different sequence of symmetric solutions that cannot be physically realized. Numerical methods have previously been the only source of information on the ground-state wave function and our results provide a different perspective with strong analytical insights. The ground-state wave function has a spatial profile that looks very similar to the shape of a solitonic solution to a nonlinear Schrodinger equation, enabling an analytical prediction of the wave number. When combining multiple X wells into a network or grid, each site supports a solitonlike localized state. These localized solutions only couple to each other and are able to jump from one site to another as if they were trapped in a discrete lattice.

AB - Assembling large-scale quantum networks is a key goal of modern physics research with applications in quantum information and computation. Quantum wires and waveguides in which massive particles propagate in tailored confinement is one promising platform for realizing a quantum network. In the literature, such networks are often treated as quantum graphs, that is, the wave functions are taken to live on graphs of one-dimensional edges meeting in vertices. Hitherto, it has been unclear what boundary conditions on the vertices produce the physical states one finds in nature. This paper treats a quantum network from a physical approach, explicitly finds the physical eigenstates and compares them to the quantum-graph description. The basic building block of a quantum network is an X-shaped potential well made by crossing two quantum wires, and we consider a massive particle in such an X well. The system is analyzed using a variational method based on an expansion into modes with fast convergence and it provides a very clear intuition for the physics of the problem. The particle is found to have a ground state that is exponentially localized to the center of the X well, and the other symmetric solutions are formed so to be orthogonal to the ground state. This is in contrast to the predictions of the conventionally used so-called Kirchoff boundary conditions in quantum graph theory that predict a different sequence of symmetric solutions that cannot be physically realized. Numerical methods have previously been the only source of information on the ground-state wave function and our results provide a different perspective with strong analytical insights. The ground-state wave function has a spatial profile that looks very similar to the shape of a solitonic solution to a nonlinear Schrodinger equation, enabling an analytical prediction of the wave number. When combining multiple X wells into a network or grid, each site supports a solitonlike localized state. These localized solutions only couple to each other and are able to jump from one site to another as if they were trapped in a discrete lattice.

KW - ELECTRON GAS-MODEL

KW - BOUND-STATES

KW - WAVE-GUIDE

KW - VARIATIONAL-PROBLEMS

KW - SPECTRAL STATISTICS

KW - ROOM-TEMPERATURE

KW - GRAPHS

KW - SCATTERING

KW - SYSTEMS

KW - CONVERGENCE

UR - http://www.scopus.com/inward/record.url?scp=85045151278&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.155407

DO - 10.1103/PhysRevB.97.155407

M3 - Journal article

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 15

M1 - 155407

ER -