scholarly journals Quantum Optimal Control for Bose-Einstein-Condensates at Complex Space

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Complex Space ◽  
Pitaevskii Equation ◽  
Interesting Topic ◽  
Quantum Optimal Control ◽  
Control Target ◽  
Bose Einstein

Quantum control of Bose-Einstein-Condensates is interesting topic in the areas of control and physics. In this work, Gross-Pitaevskii equation expressed Bose-Einstein-Condensates is considered as control target. Full theoretical proof for the existence of quantum optimal control is provided for cubical Schrodinger equation in complex Hilbert spaces.

scholarly journals Quantum Optimal Control for Bose-Einstein-Condensates at Complex Space

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Complex Space ◽  
Pitaevskii Equation ◽  
Interesting Topic ◽  
Quantum Optimal Control ◽  
Control Target ◽  
Bose Einstein

Quantum control of Bose-Einstein-Condensates is interesting topic in the areas of control and physics. In this work, Gross-Pitaevskii equation expressed Bose-Einstein-Condensates is considered as control target. Full theoretical proof for the existence of quantum optimal control is provided for cubical Schrodinger equation in complex Hilbert spaces.

scholarly journals Quantum Surface Control of Trapped Bose-Einstein-Condensates

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Quantum Control ◽  
Three Dimensions ◽  
Pitaevskii Equation ◽  
System Control ◽  
Variational Theory ◽  
Surface Control ◽  
Electro Magnetic ◽  
Bose Einstein

In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.

scholarly journals Quantum Surface Control of Trapped Bose-Einstein-Condensates

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Quantum Control ◽  
Three Dimensions ◽  
Pitaevskii Equation ◽  
System Control ◽  
Variational Theory ◽  
Surface Control ◽  
Electro Magnetic ◽  
Bose Einstein

In this work, quantum control of trapped Bose-Einstein-Condensates (BEC) is considered at matter surface. For particles at BEC status, quantum system is described by Gross-Pitaevskii equation, experimental control of BEC is happened at physics field, and achieved at laboratory. At theoretic aspect, control of trapped condensates is not sufficiently investigated at academic level. What we interest is applying control theory to BEC trapped on the surface (metallic, crystal). At optical lattice, particles are trapping by constrained forces at cooling technique, and temporally take the same quantum states, such kind of condensates phenomena had already been surveyed at a variety of areas. The most works are reported on free BEC particles, quite natural question is arising on the surface science: BEC particles created,detected, and placed on a certain chemical surface, control of trapped particles is difference or not? We are curious about optical and mechanical constraints take action together on particles. In the viewpoint of quantum control realm, our purpose is to apply optimal control theory (OCT) to trapped Bose-Einstein-Condensates as they are occurred at surface. In the framework of variational theory at complex Hilbert spaces, prove the existence of quantum optimal control, and characterize optimal control using optimality (Euler-Lagrange) system. Control variables for trapped BEC contain three functions: one is electro-magnetic force; another is external constraint from optical equipment (optical frequency, lattice number); third is quantum mechanics against gravitational force, which making BEC particles stay at surface stationary. Review the literatures, electro-magnetic-optical controls are extremely considered at last couple of years. Gravitational control is rarely considered. Further extension of the work is to do real-time computer-aided BEC control at matter surface. Computational approach for simulation of BEC control at two and three dimensions would be a promise direction.

scholarly journals Quantum Numerical Control for Particles at Matter Surface

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Control Theory ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Numerical Control ◽  
System Control ◽  
Control Input ◽  
Quantum Control Theory

In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.

scholarly journals Quantum Control for Neutrons in Nuclear Reaction

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Variational Method ◽  
Control Theory ◽  
Nuclear Reaction ◽  
Quantum Control ◽  
Many Body ◽  
Chain Reaction ◽  
Quantum Optimal Control ◽  
Full Proof

Quantum control of neutrons in nuclear reaction in considered in this work. Neutrons fission from uranium <sup>235</sup>U of chain reaction is interested to be controlled as target theoretically. Control theory is applied to interacted many-body neutrons collision in the framework of variational method. Full proof is provided for quantum optimal control of scattered poly-neutrons.

scholarly journals Quantum Numerical Control for Particles at Matter Surface

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Control Theory ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Numerical Control ◽  
System Control ◽  
Control Input ◽  
Quantum Control Theory

In this work, time-depended Schrodinger equation described particles at matter (crystal, catalysis, metal) surface could be considered as propose of numerical control of quantum system. Accessing existing physical experimental results on the motion of particles (molecules, atoms) at surface, based on variational method of quantum control theory in Hilbert space, using density function theory (DFT), time-depended Schrodinger equation to proceed the investigation of computational approach. To do quantum calculation at surface, physically, first needs a concept as control goal: such as breaking a chemical bond as target; reducing energy of high intensity shaped laser pulse. Particles at surface is a kind of constrain control for spatial variable. Optimal control is to find and characterize the quantum optima for minimizing or maximizing the cost functional. Control methods contain selecting chemical reagent, designing chemical reaction, making control scope for a quantized system: time varying Schrodinger equation. Precisely, for general quadratic cost function, in two or three dimensional cases, a semi discrete (time continuous, spatial discrete) algorithm consisting of finite element method and conjugate gradient method, would be utilized for solving a numerical solution of state system, and obtaining quantum optimal control from a initial guess of control input. It is quite curious: what is the difference of control particles occurred at surface than control free particles? whether one can develop a suit of theory or methodology for quantum surface control? It is certainly expected to connect theoretical control, to numerical or computational control, and to experimental control as carrying out quantum system control of particles on the surface. It is desired that quantum control theory (QCT) for quantum dot at surface would be evidenced in visualization method, and attained confidential verification in the guidance of real-time computer-aided experiments in the viewpoint of chemistry and physics.

scholarly journals Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
J. J. W. H. Sørensen ◽  
M. O. Aranburu ◽  
T. Heinzel ◽  
J. F. Sherson
Keyword(s):  
Optimal Control ◽  
Quantum Optimal Control ◽  
Bose Einstein

scholarly journals Krotov: A Python implementation of Krotov's method for quantum optimal control

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Michael Goerz ◽  
Daniel Basilewitsch ◽  
Fernando Gago-Encinas ◽  
Matthias G. Krauss ◽  
Karl P. Horn ◽  
...  
Keyword(s):  
Optimal Control ◽  
Quantum Control ◽  
Control Method ◽  
Optimization Methods ◽  
Continuous Control ◽  
Wide Range ◽  
Quantum Optimal Control ◽  
Monotonic Convergence ◽  
Krotov’S Method ◽  
High Level

We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization.

scholarly journals Quantum Control for Neutrons in Nuclear Reaction

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Variational Method ◽  
Control Theory ◽  
Nuclear Reaction ◽  
Quantum Control ◽  
Many Body ◽  
Chain Reaction ◽  
Quantum Optimal Control ◽  
Full Proof

Quantum control of neutrons in nuclear reaction in considered in this work. Neutrons fission from uranium <sup>235</sup>U of chain reaction is interested to be controlled as target theoretically. Control theory is applied to interacted many-body neutrons collision in the framework of variational method. Full proof is provided for quantum optimal control of scattered poly-neutrons.

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