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Modulational instability and discrete quantum droplets in a deep quasi-one-dimensional optical lattice
Sherzod R Otajonov1,2, Bakhram A Umarov1, Fatkhulla Kh Abdullaev1,2
1Physical-Technical Institute of the Uzbek Academy of Sciences, Chingiz Aytmatov Str. 2-B, Tashkent 100084, Uzbekistan.
Physical Review. E
|June 19, 2025
Summary
This study explores modulational instability and discrete breathers in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections, identifying quantum droplet solutions and confirming their stability.
Area of Science:
- Nonlinear physics
- Quantum mechanics
- Condensed matter physics
Background:
- The Gross-Pitaevskii equation describes Bose-Einstein condensates.
- Lee-Huang-Yang corrections account for interactions in dilute quantum gases.
- Modulational instability and discrete breathers are key nonlinear phenomena.
Purpose of the Study:
- Investigate modulational instability and discrete breathers in a quasi-one-dimensional discrete Gross-Pitaevskii equation with Lee-Huang-Yang corrections.
- Determine conditions for modulation instability and instability regions of nonlinear plane waves.
- Analytically and numerically study quantum droplet solutions and their stability.
Main Methods:
- Page method and variational approach for analytical solutions.
- Linear stability analyses.
- Numerical simulations for stability verification.
Main Results:
- Conditions for modulation instability and instability regions were determined.
- Existence of various quantum droplet solutions (intersite, onsite, front-like, flat-top, dark localized modes) was analytically shown.
- Analytical predictions were corroborated by numerical simulations, confirming solution stability.
Conclusions:
- The study successfully characterized modulational instability and discrete breathers in the studied system.
- Various quantum droplet solutions were identified and their stability confirmed.
- The findings provide insights into nonlinear dynamics in quasi-one-dimensional quantum systems.
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