Unveiling solitonic structures of ultradilute quantum liquid and Er-doped optical fiber

Singh, Dheerendra (2025) Unveiling solitonic structures of ultradilute quantum liquid and Er-doped optical fiber. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

This thesis unveils the solitonic structures of two different dynamical systems. The first system, an ultradilute quantum liquid (UQL), is governed by the amended Gross-Pitaevskii (GP) equation, which involves both cubic and quadratic nonlinearities. The second system, an Erdoped bimodal optical fiber, is dynamically characterized by the coupled Bloch-NLSE, which incorporates Kerr (cubic) nonlinearity and a three-level Λ-type atomic configuration. First, we investigate modulation instability of the 1D dynamical system of UQL, considering both the presence and absence of spin-orbit and Rabi couplings, and delineate the parameter domains for the formation of periodic matter-wave soliton trains. We observe that the MI occurs below the spinodal point of 1D UQL system, i.e. P < 9/16n₀, where P is the background of continuous wave and n0 is the equilibrium density of UQL. Further, we calculate the energy dispersion relations of phonons and free-particle regimes using the Bogoliubov theory. The branches of free particles exhibit a positive energy band gap above the spinodal point, i.e. P > 9/16n₀, which shifts to a negative energy band gap within the instability domain, means when P < 9/16n₀. Next, we investigate an exact solution in the form of Jacobi elliptic function for the UQL system. The exact solution resembles an array of small droplets embedded in a residual superfluid background for small values of the modulus parameter (MP). In contrast, for larger values of MP (approaching 1), the solution represents an array of large, flat-top droplets with a significantly reduced superfluid background, presenting a physical explanation of the supersolid phase. This periodic class of solutions has a kink-like solitonic structure for the unit value of MP. Additionally, we demonstrate the exact solitonic structures of quantum droplet (QD) and bubble (QB) as a bound pair of kink-like solutions. The governing parameters of both solitonic solutions can be efficiently regulated by the distance between the constituents of a bound pair. The numerical analysis indicates that the small-sized QB exhibits instability and collapses into the bound pair of kink and antikink during spacetime development, but the large-sized bubble demonstrates stability throughout the space-time evolution.

Item Type: Thesis (PhD)
Additional Information: Supervisor: Prof. Prasanta K. Panigrahi ; Co-Supervisor: Dr. Kamaraju Natarajan
Uncontrolled Keywords: Dynamical Systems; Erdoped Bimodal Optical Fiber; Solitonic Structures; UQL; ultradilute Quantum Liquid
Subjects: Q Science > QC Physics
Divisions: Department of Physical Sciences
Depositing User: IISER Kolkata Librarian
Date Deposited: 21 May 2025 06:57
Last Modified: 21 May 2025 07:03
URI: http://eprints.iiserkol.ac.in/id/eprint/1707

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