We demonstrate the existence of bright solitons in a repulsively interacting, harmonically trapped quasi-one-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Using a neural-network quantum state (NNQS) approach, we parametrize the initial wavefunction and optimize it to find solutions that recur after one trap period, effectively balancing repulsion with trap-induced attraction. Aside from the bright solitonic solution, we also report double bright and dark soliton states. Perturbing the initial state with multiplicative phase and amplitude noise confirms that these periodic orbits are orbitally stable. Our results indicate that NNQS provides a powerful framework for uncovering coherent structures in nonlinear wave systems.We demonstrate the existence of bright solitons in a repulsively interacting, harmonically trapped quasi-one-dimensional Bose-Einstein condensate described by the Gross-Pitaevskii equation. Using a neural-network quantum state (NNQS) approach, we parametrize the initial wavefunction and optimize it to find solutions that recur after one trap period, effectively balancing repulsion with trap-induced attraction. Aside from the bright solitonic solution, we also report double bright and dark soliton states. Perturbing the initial state with multiplicative phase and amplitude noise confirms that these periodic orbits are orbitally stable. Our results indicate that NNQS provides a powerful framework for uncovering coherent structures in nonlinear wave systems.

arXiv:2604.14529Apr 16, 20260 citations

Quantum noise of the fundamental soliton

Franz X. Kärtner, Luc Boivin

We investigate the noise in a fundamental soliton state constructed from the exact energy eigenstates of the quantized nonlinear Schr\"odinger equation. It is shown that such a state has statistical properties that are substantially different from those of a coherent state with the same mean field. We can construct, for example, a fundamental soliton state that has initially minimum fluctuations for the four linearized soliton operators (particle number, phase, momentum, and position). We also show that the linearized noise analysis is not valid for nonlinear phase shifts larger than ${\mathit{n}}_{0}^{1/4}$ , where ${\mathit{n}}_{0}$ is the average number of particles in the fundamental soliton. \textcopyright{} 1996 The American Physical Society.We investigate the noise in a fundamental soliton state constructed from the exact energy eigenstates of the quantized nonlinear Schr\"odinger equation. It is shown that such a state has statistical properties that are substantially different from those of a coherent state with the same mean field. We can construct, for example, a fundamental soliton state that has initially minimum fluctuations for the four linearized soliton operators (particle number, phase, momentum, and position). We also show that the linearized noise analysis is not valid for nonlinear phase shifts larger than ${\mathit{n}}_{0}^{1/4}$, where ${\mathit{n}}_{0}$ is the average number of particles in the fundamental soliton. \textcopyright{} 1996 The American Physical Society.

Physical Review AJan 1, 199625 citations

Quantum noise of damped N-solitons

Eduard Schmidt, L. Knöll, Dirk‐Gunnar Welsch

Optics CommunicationsMay 1, 20006 citations

Quantum Fluctuations in Cavity Solitons

Gian‐Luca Oppo, John Jeffers

Springer eBooksNov 2, 20076 citations

Quasi-Bell entangled coherent states and its quantum discrimination problem in the presence of thermal noise

Kentaro Kato

The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set of the quasi-Bell entangled coherent states with thermal noise is considered, and the error probabilities of the minimax discrimination for the two cases are computed with the help of Helstrom's algorithm for finding the Bayes optimal error probability of binary states.

arXiv:1508.01597Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIESep 1, 20152 citations

{\mathit{n}}_{0}^{1/4}

, where

{\mathit{n}}_{0}

is the average number of particles in the fundamental soliton. \textcopyright{} 1996 The American Physical Society.