arXiv subjects

Ayan Khan

Publications and source records attributed to Ayan Khan.

At least 19 recordsLinked to original sources

arXiv2026

Exact Analytical Vortex Solution for a Two-Dimensional Quantum Gas with LHY Correction

In this investigation, we provide an exact analytical vortex solution for a Bose liquid in two dimensions with beyond mean-field correction (BMF). Analytical solutions in two-dimensional systems with BMF corrections are rarely found in the literature. The present result provides a clear framework for understanding vortex structures in low-dimensional quantum fluids and serves as a reliable benchmark for future theoretical and experimental studies.

cond-mat.quant-gas↗

arXiv2026

Josephson Oscillation and Nonlinear Self-Trapping in Quasi-one-dimensional Quantum Liquid

In this article, we study the two-mode method to analyze the Josephson oscillation for a trapped binary Bose-Einstein condensate while taking into account the beyond mean-field and three body interactions. For this purpose, we use the archetypal model of double well potential and study the Josephson oscillation and self-trapping phases in quasi-one dimension. Additionally, our analysis provides quantitative discussion on the effect of asymmetry and dimension. We further corroborate our findings with Bogoliubov quasi-particle method and notice regions of instabilities and roton like mode.

cond-mat.quant-gas↗

arXiv2025

Improving Cooperation in Collaborative Embodied AI

The integration of Large Language Models (LLMs) into multiagent systems has opened new possibilities for collaborative reasoning and cooperation with AI agents. This paper explores different prompting methods and evaluates their effectiveness in enhancing agent collaborative behaviour and decision-making. We enhance CoELA, a framework designed for building Collaborative Embodied Agents that leverage LLMs for multi-agent communication, reasoning, and task coordination in shared virtual spaces. Through systematic experimentation, we examine different LLMs and prompt engineering strategies to identify optimised combinations that maximise collaboration performance. Furthermore, we extend our research by integrating speech capabilities, enabling seamless collaborative voice-based interactions. Our findings highlight the effectiveness of prompt optimisation in enhancing collaborative agent performance; for example, our best combination improved the efficiency of the system running with Gemma3 by 22% compared to the original CoELA system. In addition, the speech integration provides a more engaging user interface for iterative system development and demonstrations.

cs.AI↗

arXiv2025

Dynamics of Quantum Droplets in a Quasi-one-dimensional Framework: An Analytical Approach

Quantum droplets have been recently observed in dipolar Bose-Einstein condensates (BECs) and in BEC mixtures. This forms the motivation for us to explore the dynamics of these droplets. We make use of the Extended Gross-Pitaevski equation which apart from the effective mean field (MF) interaction, also includes a beyond mean field interaction. The competition of these two interactions in the context of droplet formation is explored. Further, the conditions for droplet formation are studied.

cond-mat.quant-gas↗

arXiv2024

Quantum Liquid in Lower Dimensions: From the perspective of Surface Tension

We analyze the surface tension in ultra-cold atomic gases in a quasi one-dimensional and one-dimensional geometry. In recent years, experimental observations have confirmed the ``clustering of atoms" to form droplets in ultra-cold atomic gases and the emergence of this new phase is attributed to the beyond mean-field interaction. However, two decades earlier, liquid formation was predicted due to the competition of two-body and three-body interactions. Here, we review both propositions and comment on the role of beyond mean-field and three-body interaction in liquid formation by calculating the surface tension.

cond-mat.quant-gas↗

arXiv2023

Dynamics of Bright Soliton Under Cubic-Quartic Interactions in Quasi One-Dimensional Geometry

Recent inspection of liquid-like state in ultracold atomic gases due to the stabilization mechanism through the delicate balance between effective mean-field and beyond mean-field (BMF) interactions, has motivated us to study the modified/extended Gross-Pitaevskii (eGP) equation which includes the BMF contribution. In this article, we focus on variational analysis of solitonic regime with eGP equation while the soliton is subjected to an obstacle. This reveals different scattering scenarios of the soliton with explicit dependence of the BMF interaction. The results show the existence of tunneling, partial and complete trappings, in different parameter domains. These observations are further corroborated by the fast-Fourier transform method. In the later part we also extend our analysis to trapped systems. The controlled trapping in defect potential and its release can be potentially useful for quantum information storage.

cond-mat.quant-gas↗

arXiv2023

Interaction of One-Dimensional Quantum Droplets with Potential Wells and Barriers

We address static and dynamical properties of one-dimensional (1D) quantum droplets (QDs) under the action of local potentials in the form of narrow wells and barriers. The QDs are governed by the 1D Gross-Pitaevskii equation including the mean-field cubic repulsive term and the beyond-mean-field attractive quadratic one. In the case of the well represented by the delta-functional potential, three exact stable solutions are found for localized states pinned to the well. The Thomas-Fermi approximation for the well and the adiabatic approximation for the collision of the QD with the barrier are developed too. Collisions of incident QDs with the wells and barriers are analyzed in detail by means of systematic simulations. Outcomes, such as fission of the moving QD into transmitted, reflected, and trapped fragments, are identified in relevant parameter planes. In particular, a counter-intuitive effect of partial or full rebound of the incident QD from the potential well is studied in detail and qualitatively explained.

cond-mat.quant-gas↗

arXiv2022

Dropleton-Soliton Crossover mediated via Trap Modulation

We report a droplet to a soliton crossover by tuning the external confinement potential in a dilute Bose-Eienstein condensate by numerically solving the modified Gross-Pitaevskii equation. The testimony of such a crossover is presented via studying the fractional density of the condensate which smoothly migrates from being a flat-head curve at weak confinement to a bright soliton at strong confinement. Such a transition occurs across a region of the potential whose strength varies over an order of magnitude and thus should be fit to be termed as a crossover. We supplement our studies via exploring the size of the bound pairs and the ramifications of the particle density therein. Eventually, all of these aid us in arriving at a phase diagram in a space defined by the trap strength and the particle number that shows the formation of two phases consisting of droplets and solitons, along with a regime of coexistence of these two.

cond-mat.quant-gas↗

arXiv2022

Signature of Supersolidity in a Driven Cubic-Quartic Nonlinear Schrödinger Equation

We present analytical solution, which is periodic in nature, for a driven cubic-quartic nonlinear Schrödinger equation (DCQNLSE) placed in a bi-chromatic optical lattice. The solution indicates the creation of density wave. Since, beyond mean-field contribution in quasi one dimensional and one-dimensional geometry differs on the even exponents of the nonlinearity thus we extend our analysis towards quadratic-cubic-quartic and quadratic-cubic nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study indicates the existence of stripe phase along with considerable phase coherence. These findings allow us to comment on the possible emergence of supersolid phase in a condensate.

cond-mat.quant-gas↗

arXiv2021

Investigation of Quantum Droplet: An Analytical Approach

Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in detail. Precisely, we are interested in investigating the possibility of droplet formation in a quasi-one-dimensional geometry. The recent observations have concluded that the droplets are stabilized by the competition between effective mean-field and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schrödinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and verified them numerically. Based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self-bound droplet formations.

cond-mat.quant-gas↗

arXiv2020

Formation of Solitonic Bound State via Light-Matter Interaction

Exchange of energy by means of light-matter interaction provides a new dimension to various nonlinear dynamical systems. Here, the effects of light-matter interaction are investigated for a situation, where two counter-propagating, orthogonally polarized laser pulses are incident on the atomic condensate. It's observed that a localized laser pulse profile can induce localized modes in Bose-Einstein condensate. A stability analysis performed using Vakhitov-Kolokolov-like criterion has established that these localized modes are stable, when the atom-atom interaction is repulsive. The cooperative effects of light-matter interactions and atom-atom interactions on the Lieb-mode have been studied in the stable region through atomic dispersion, revealing the signature of bound state formation when the optical potential is Pöschl-Teller type. The energy diagram also indicates a continuous transfer of energy from the laser pulses to the atoms as the light-matter interaction changes its sign.

cond-mat.quant-gas↗

arXiv2020

On Solving Cubic-Quartic Nonlinear Schrödinger Equation in a Cnoidal Trap

The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues of fundamental research. The competition between mean-field and beyond mean-field interactions, in ultra-cold dilute alkali gases, are believed to be instrumental in stabilizing the droplets. These new understanding has motivated us to investigate the analytical solutions of a trapped cubic-quartic nonlinear Schrödinger equation (CQNLSE). The quartic contribution in the NLSE is derived from the beyond mean-field formalism of Bose-Einstein condensate (BEC). To the best of our knowledge, a comprehensive analytical description of CQNLSE is non-existent. Here, we study the existence of the analytical solutions which are of the cnoidal type for CQNLSE. The external trapping plays a significant role in the stabilization of the system. In the limiting case, the cnoidal wave solutions lead to the localized solution of bright solution and delocalized kink-antikink pair. The nonexistence of the sinusoidal mode in the current scheme is also revealed in our analysis.

cond-mat.quant-gas↗

arXiv2016

Effect of Weak Disorder on the BCS-BEC crossover in a two-dimensional Fermi Gas

In this article we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that, at the crossover the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect.

cond-mat.quant-gas↗

arXiv2015

Topology of Quantum Grey Soliton in Multi-Component Inhomogeneous Bose-Einstein Condensates

We study the dispersion mechanism of Lieb mode excitations of both single and multi component ultra-cold atomic Bose gas, subject to a harmonic confinement through chirp management. It is shown that in some parameter domain, the hole-like excitations lead to the soliton's negative mass regime, arising due to the coupling between chirp momentum and Kohn mode. In low momenta region the trap considerably affects the dispersion of the grey soliton, which opens a new window to observe Lieb-mode excitations. Further, we extend our analysis to binary condensate, which yields usual shape compatible grey-bright soliton pairs. The inter-species interaction induces a shift in the Lieb-mode excitations, where the pair can form a bound state. We emphasize that the present model provides an opportunity to study such excitations in the low momenta regime, as well as the formation of bound state in binary condensate.

cond-mat.quant-gas↗

arXiv2015

Tunneling dynamics of correlated bosons in a double well potential

The quantum dynamics of a few bosons in a double well potential is studied using a Bose Hubbard model. We consider both signs for the on-site interparticle interaction and also investigated the situations where they are large and small. Interesting distinctive features are noted for the tunneling oscillations of these bosons corresponding to the above scenarios. Further, the sensitivity of the particle dynamics to the initial conditions has been studied. It is found that corresponding to an odd number of particles, such as three (or five), an initial condition of having unequal number of particles in the wells has interesting consequences, which is most discernible when the population difference between the wells is unity.

cond-mat.quant-gas↗

arXiv2014

Investigating Dirty Crossover through Fidelity Susceptibility and Density of States

We investigate the BCS-BEC crossover in an ultracold atomic gas in the presence of disorder. The disorder is incorporated in the mean-field formalism through Gaussian fluctuations. We observe evolution to an asymmetric line-shape of fidelity susceptibility as a function of interaction coupling with increasing disorder strength which may point to an impending quantum phase transition. The asymmetric line-shape is further analyzed using the statistical tools of skewness and kurtosis. We extend our analysis to density of states (DOS) for a better understanding of the crossover in the disordered environment.

cond-mat.quant-gas↗

arXiv2013

Bell Soliton in Ultra-cold Atomic Fermi Gas

We demonstrate the existence of supersonic bell soliton in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover regime. Starting from the extended Thomas-Fermi density functional theory of superfluid order parameter, a density transformation is used to map the hydrodynamic mean field equation to a Lienard type equation. As a result, bell solitons are obtained as exact solutions, which is further verified by the numerical solution of the dynamical equation. The stability of the soliton is established and its behaviour in the entire crossover domain is obtained. It is found that, akin to the case of vortices, the bell solitons yield highest contrast in the BEC regime.

cond-mat.quant-gas↗

arXiv2013

Electron pairing and evidence of a BCS-BEC crossover in d-wave superconductors

We have demonstrated that it is possible to access a crossover scenario starting with a weak coupling (BCS) d-wave superconductor to a strongly coupled Bose-Einstein condensate (BEC) phase as the exchange interaction is tuned in a two dimensional system described by a t-J-U model via numerically solving the Bogoliubov-de Gennes (BdG) equations. While in the extreme dilute limit, the electronic pairing phenomena is independent of the Coulomb repulsion, U, the superconductivity depends on U, and so does the crossover. Further, the effect of variation in the carrier density on the BCS-BEC crossover has also been investigated. The crossover picture is illustrated by computing the chemical potential, which when falls below the noninteracting band minimum, signals the onset of a phase with tightly bound, shorter pairs. As an evidence of the above feature, the Cooper pair radius is calculated which shows a significant shortening at the emergence of a BEC-like phase. Besides, in contrast to the previous work where a crossover was claimed only in the dilute limit, we have demonstrated it at large densities near half filling.

cond-mat.str-el↗