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-mechanical stability of solitons and the correspondence principle

Franz X. Kärtner, H. A. Haus

A Hanbury Brown--Twiss experiment is described that is capable of demonstrating, in principle, the solitary behavior of a quantum soliton in an arbitrary fundamental soliton state. The relevant correlation functions are evaluated and show that the quantum noise does not cause a breakup of the solitons of the quantized nonlinear Schr\"odinger equation. For large photon numbers, the intensity autocorrelation function of the fundamental soliton becomes independent of certain momentum and photon-number distributions, which gives us a correspondence principle for the fundamental soliton. Whereas intensity-correlation measurements based on direct detection show essentially classical behavior for large photon numbers, homodyne-detection experiments can uncover quantum effects such as the generation of Schr\"odinger-cat solitons.A Hanbury Brown--Twiss experiment is described that is capable of demonstrating, in principle, the solitary behavior of a quantum soliton in an arbitrary fundamental soliton state. The relevant correlation functions are evaluated and show that the quantum noise does not cause a breakup of the solitons of the quantized nonlinear Schr\"odinger equation. For large photon numbers, the intensity autocorrelation function of the fundamental soliton becomes independent of certain momentum and photon-number distributions, which gives us a correspondence principle for the fundamental soliton. Whereas intensity-correlation measurements based on direct detection show essentially classical behavior for large photon numbers, homodyne-detection experiments can uncover quantum effects such as the generation of Schr\"odinger-cat solitons.

Physical Review ASep 1, 199321 citations

Quantum solitons in a linear chain

Banasri Basu, P. Bandyopadhyay

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoMay 1, 19850 citations

Localized gap-soliton trains of Bose-Einstein condensates in an optical lattice

D. L. Wang, X. H. Yan, Weixi Liu

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu's functions ce_{n-1} and se_{n} ; and the Bloch wave in the nth band gap is a linear superposition of ce_{n} and se_{n} . For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons-fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann, Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu's functions ce_{n-1} and se_{n} ; and the Bloch wave in the nth band gap is a linear superposition of ce_{n} and se_{n} . For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons-fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann, Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.

arXiv:0807.3989Physical Review EAug 14, 200843 citations

Quantum expansion of soliton solutions

N. H. Christ, T. D. Lee

Birkhäuser Boston eBooksJan 1, 19860 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.