This paper presents a novel approach to modeling dynamic quantum control scenarios involving nonlinear quantum systems. The core claim is the establishment of a model capable of accurately describing the behavior of such systems under dynamic control. This model is built upon the introduction of a nonlinear Schrödinger equation, coupled with principles from dynamic control theory. The methodology allows for detailed analysis and manipulation of nonlinear quantum systems, expanding the theoretical foundation for quantum control and manipulation research. We explore the challenges and potential solutions in designing control strategies for systems exhibiting complex, nonlinear interactions. The presented framework offers a foundation for further research into advanced quantum control techniques. The key mathematical components are detailed within the subsequent sections, including the nonlinear Schrödinger equation, control vector formulation, and analysis of system dynamics. The focus is on providing a rigorous mathematical framework rather than a specific experimental implementation.This paper presents a novel approach to modeling dynamic quantum control scenarios involving nonlinear quantum systems. The core claim is the establishment of a model capable of accurately describing the behavior of such systems under dynamic control. This model is built upon the introduction of a nonlinear Schrödinger equation, coupled with principles from dynamic control theory. The methodology allows for detailed analysis and manipulation of nonlinear quantum systems, expanding the theoretical foundation for quantum control and manipulation research. We explore the challenges and potential solutions in designing control strategies for systems exhibiting complex, nonlinear interactions. The presented framework offers a foundation for further research into advanced quantum control techniques. The key mathematical components are detailed within the subsequent sections, including the nonlinear Schrödinger equation, control vector formulation, and analysis of system dynamics. The focus is on providing a rigorous mathematical framework rather than a specific experimental implementation.

Aug 28, 20260 citations

Nonlinear Quantum Systems: Adaptive Dynamics Through Quantum Entanglement and Nonlinear Effects

Jincheng Zhang

This paper explores the application of adaptive dynamics within nonlinear quantum systems to achieve complex and realistic quantum system behavior. Traditional analytical approaches often struggle to capture the intricate dynamics of these systems, particularly when dealing with non-linear interactions. We propose a novel framework leveraging quantum entanglement and nonlinear effects to simulate and model such systems more effectively. The core of this approach lies in mimicking the behavior of quantum systems through dynamically adjusted parameters, allowing for a more nuanced and robust representation of quantum phenomena. This research aims to provide a new method for quantum system modeling, offering a departure from conventional approaches and potentially unlocking novel functionalities in quantum technologies.This paper explores the application of adaptive dynamics within nonlinear quantum systems to achieve complex and realistic quantum system behavior. Traditional analytical approaches often struggle to capture the intricate dynamics of these systems, particularly when dealing with non-linear interactions. We propose a novel framework leveraging quantum entanglement and nonlinear effects to simulate and model such systems more effectively. The core of this approach lies in mimicking the behavior of quantum systems through dynamically adjusted parameters, allowing for a more nuanced and robust representation of quantum phenomena. This research aims to provide a new method for quantum system modeling, offering a departure from conventional approaches and potentially unlocking novel functionalities in quantum technologies.

Aug 31, 20260 citations

Nonlinear dynamics from linear quantum evolutions

F.M. Ciaglia, F. Di Cosmo, A. Figueroa +5 more

arXiv:1908.03699Annals of PhysicsSep 24, 20198 citations

Advances in Dynamical Systems and Quantum Physics

Sergio A Albeverio, Rodolfo Figari, Enza Orlandi +1 more

Feb 1, 199530 citations

Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides

Bing He, Shubin Yan, Jing Wang +1 more

It is generally difficult to study the dynamical properties of a quantum system with both inherent quantum noises and nonperturbative nonlinearity. Due to the possibly drastic intensity increase of an input coherent light in gain-loss waveguide couplers with parity-time $(\mathcal{PT})$ symmetry, the Kerr effect from a nonlinearity added into the system can be greatly enhanced and is expected to create macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, quantum noises also coexist with the amplification and dissipation of the light fields. Under the interplay between the quantum noises and nonlinearity, the quantum dynamical behaviors of the systems become rather complicated. However, the important quantum noise effects have been mostly neglected in previous studies about nonlinear $\mathcal{PT}$ -symmetric systems. Here we present a solution to this nonperturbative quantum nonlinear problem, showing the real-time evolution of the system observables. The enhanced Kerr nonlinearity is found to give rise to a previously unknown decoherence effect that is irrelevant to the quantum noises and imposes a limit on the emergence of macroscopic nonclassicality. In contrast to what happens in linear systems, the quantum noises exert significant impact on the system dynamics and can create nonclassical light field states in conjunction with the enhanced Kerr nonlinearity. This study on the noise involved in quantum nonlinear dynamics of coupled gain-loss waveguides can help to better understand the quantum noise effects in many nonlinear systems.It is generally difficult to study the dynamical properties of a quantum system with both inherent quantum noises and nonperturbative nonlinearity. Due to the possibly drastic intensity increase of an input coherent light in gain-loss waveguide couplers with parity-time $(\mathcal{PT})$ symmetry, the Kerr effect from a nonlinearity added into the system can be greatly enhanced and is expected to create macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, quantum noises also coexist with the amplification and dissipation of the light fields. Under the interplay between the quantum noises and nonlinearity, the quantum dynamical behaviors of the systems become rather complicated. However, the important quantum noise effects have been mostly neglected in previous studies about nonlinear $\mathcal{PT}$-symmetric systems. Here we present a solution to this nonperturbative quantum nonlinear problem, showing the real-time evolution of the system observables. The enhanced Kerr nonlinearity is found to give rise to a previously unknown decoherence effect that is irrelevant to the quantum noises and imposes a limit on the emergence of macroscopic nonclassicality. In contrast to what happens in linear systems, the quantum noises exert significant impact on the system dynamics and can create nonclassical light field states in conjunction with the enhanced Kerr nonlinearity. This study on the noise involved in quantum nonlinear dynamics of coupled gain-loss waveguides can help to better understand the quantum noise effects in many nonlinear systems.

arXiv:1408.0565Physical Review AMay 18, 201559 citations

(\mathcal{PT})

symmetry, the Kerr effect from a nonlinearity added into the system can be greatly enhanced and is expected to create macroscopic entangled states of the output light fields with huge photon numbers. Meanwhile, quantum noises also coexist with the amplification and dissipation of the light fields. Under the interplay between the quantum noises and nonlinearity, the quantum dynamical behaviors of the systems become rather complicated. However, the important quantum noise effects have been mostly neglected in previous studies about nonlinear

\mathcal{PT}

-symmetric systems. Here we present a solution to this nonperturbative quantum nonlinear problem, showing the real-time evolution of the system observables. The enhanced Kerr nonlinearity is found to give rise to a previously unknown decoherence effect that is irrelevant to the quantum noises and imposes a limit on the emergence of macroscopic nonclassicality. In contrast to what happens in linear systems, the quantum noises exert significant impact on the system dynamics and can create nonclassical light field states in conjunction with the enhanced Kerr nonlinearity. This study on the noise involved in quantum nonlinear dynamics of coupled gain-loss waveguides can help to better understand the quantum noise effects in many nonlinear systems.