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Modeling of Quantum Control Systems; Examples

Domenico D’Alessandro

Quantum systems whose dynamics depends on one or more control functions are called quantum control systems. This chapter describes elements of the theory of field-particle interaction. It starts with the classical theory of electrodynamics and shows how to obtain the quantum mechanical description through a process called canonical quantization. The chapter presents physical examples of quantum control systems of interest in applications and highlights the fact that such systems have a common mathematical structure. In the external system, the motion of the charges, are fixed and independent of the field. Canonical quantization is the process which associates quantities in classical mechanics with operators in quantum mechanics.Quantum systems whose dynamics depends on one or more control functions are called quantum control systems. This chapter describes elements of the theory of field-particle interaction. It starts with the classical theory of electrodynamics and shows how to obtain the quantum mechanical description through a process called canonical quantization. The chapter presents physical examples of quantum control systems of interest in applications and highlights the fact that such systems have a common mathematical structure. In the external system, the motion of the charges, are fixed and independent of the field. Canonical quantization is the process which associates quantities in classical mechanics with operators in quantum mechanics.

Chapman & Hall/CRC eBooksJul 13, 20210 citations

Optimization And Control Of Quantum-Mechanical Processes

Pãnos M. Pardalos, Vitaliy A. Yatsenko

Springer optimization and its applicationsJan 1, 20080 citations

CONTROL OF QUANTUM SYSTEMS

J. W. Clark, Dennis G. Lucarelli, Tzyh‐Jong Tarn

Recent Progress in Many-Body TheoriesDec 1, 20023 citations

Quantization of optimal control system & Synthesis of optimal controls of quantum diffusion process

B. C. Roy

When applied quantization to classical control system, quantum mechanics opens completely new perspectives; by exploiting quantum mechanical features, such as, time evolution of quantum state and costate (generalized momenta) of the Hamiltonian of the system, one can formulate and solve the optimal control problems of the quantum mechanical system more efficiently than the classical system. The physical perspective of quantization of the optimal feedback system is outlined by exploiting the formulation of the optimization problem of the system within the context of Hamilton-Jacobi theory and Pontryagin maximum/minimum principle in abstract Hubert space. One of the most striking example is the optimal control problem of synthesizing the feedback law of quantum diffusion process. The optimal diffusion process is shown to satisfy the Schrödinger wave equation of energy with the feedback law as potential function.When applied quantization to classical control system, quantum mechanics opens completely new perspectives; by exploiting quantum mechanical features, such as, time evolution of quantum state and costate (generalized momenta) of the Hamiltonian of the system, one can formulate and solve the optimal control problems of the quantum mechanical system more efficiently than the classical system. The physical perspective of quantization of the optimal feedback system is outlined by exploiting the formulation of the optimization problem of the system within the context of Hamilton-Jacobi theory and Pontryagin maximum/minimum principle in abstract Hubert space. One of the most striking example is the optimal control problem of synthesizing the feedback law of quantum diffusion process. The optimal diffusion process is shown to satisfy the Schrödinger wave equation of energy with the feedback law as potential function.

International Conference on Control, Automation, Robotics and Vision (ICARCV)Dec 1, 20101 citation

Control of quantum systems

G. Huang

Mar 1, 198013 citations

Controlling the dynamics of quantum mechanical systems using meta-atoms

Carsten Rockstuhl, Robert Filter, Toni Eichelkraut +3 more

We provide an overview of our latest activities on using optical meta-atoms to mediate the interaction of light with molecular systems. The first subject concerns the control of the dynamics of quantum mechanical systems featuring dipole-forbidden transitions. There, the meta-atoms provide local fields that exhibit a large electric quadrupole moment. The second issue is related to the enhancement of the upconversion process in erbium-doped glasses. There, the optical meta-atom has to show a resonance at multiple frequencies which matches the term schema of erbium. It will be concluded that optical meta-atoms are promising to enable inaccessible processes in a quantum mechanical system which will allow groundbreaking applications.We provide an overview of our latest activities on using optical meta-atoms to mediate the interaction of light with molecular systems. The first subject concerns the control of the dynamics of quantum mechanical systems featuring dipole-forbidden transitions. There, the meta-atoms provide local fields that exhibit a large electric quadrupole moment. The second issue is related to the enhancement of the upconversion process in erbium-doped glasses. There, the optical meta-atom has to show a resonance at multiple frequencies which matches the term schema of erbium. It will be concluded that optical meta-atoms are promising to enable inaccessible processes in a quantum mechanical system which will allow groundbreaking applications.

Jan 1, 20120 citations

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