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.

Text (PhD thesis of Dheerendra Singh (17IP010)) 17IP010.pdf - Submitted Version Restricted to Repository staff only Download (8MB)

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.

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