arXiv subjects

Argha Debnath

Publications and source records attributed to Argha Debnath.

9 recordsLinked to original sources

arXiv2026

Dynamical Signatures and Kibble-Zurek Scaling of Localization in Tilted Bose-Einstein Condensates

We study nonequilibrium signatures of tilt-induced localization in a one-dimensional Bose-Einstein condensate loaded in a shallow optical lattice. The tilt strength acts as a control parameter for the localization-delocalization crossover. We also consider the effects of repulsive interactions, which tend to delocalize the condensate. We first characterize localized and delocalized regimes through sudden quenches of the interaction strength and the external tilt. The resulting dynamics is analyzed using the survival probability and its power spectral density. Localized condensates exhibit strong memory retention, pronounced revivals, regular dynamics and a narrow spectral response, whereas delocalized condensates show suppressed recurrences, irregular dynamics and a broader distribution of spectral weight over many frequencies. We then investigate finite-rate ramps of the tilt strength across the localization threshold. Using the localization length and the Bogoliubov excitation gap, we extract the relevant critical exponents and perform Kibble-Zurek scaling analysis in the driven dynamics. Our results establish quench response and finite-rate scaling as complementary dynamical probes of localization in interacting Bose gases, with direct relevance to cold-atom experiments in tilted optical lattices.

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arXiv2026

Tilt-Induced Localization in Interacting Bose-Einstein Condensates for Quantum Sensing

We investigate localization transitions in interacting Bose-Einstein condensates (BECs) confined in tilted optical lattices, focusing on both the continuum limit accessed via shallow lattice depths and the tight-binding limit realized in the deep lattice regime. Utilizing the Gross-Pitaevskii equation (GPE) and the many-body Bose-Hubbard model, we analyze the scaling behavior of localization indicators, such as the root mean square width and fidelity susceptibility, as a function of the applied tilt. Our results reveal clear signatures of a localization-delocalization transition driven by the linear potential, with scaling properties that characterize criticality even in the presence of interactions within the GPE description. Despite the single-mode nature of the condensate wavefunction, we demonstrate that it can effectively probe quantum criticality. Building on this, we propose the use of interacting BECs in tilted lattices as a platform for quantum critical sensing, where the condensate wavefunction serves both as a sensitive probe of localization and a practical resource for quantum-enhanced metrology. This approach opens new avenues for precision gradient sensing based on localization phenomena in bosonic systems.

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arXiv2025

Localization from Infinitesimal Kinetic Grading: Finite-size Scaling, Kibble-Zurek Dynamics and Applications in Sensing

We study a one-dimensional lattice model with site-dependent nearest-neighbor hopping amplitudes that follow a power-law profile. The hopping variation is controlled by a grading exponent, $|alpha|$, which serves as the tuning parameter of the system. In the thermodynamic limit, the ground state becomes localized in the limit $|alpha| \to 0$, signaling the presence of a critical point characterized by a diverging localization length. Using exact diagonalization methods, we perform finite-size scaling analysis, and extract the associated critical exponent governing the near-critical behavior. To further characterize the criticality, we analyze inverse participation ratio (IPR), energy gap between the ground and first excited state, and fidelity-susceptibility. We also investigate the nonequilibrium dynamics by linearly ramping the hopping profile at various rates and tracking the evolution of the localization length and the IPR. The Kibble-Zurek mechanism successfully explains the resulting dynamics of the system via the critical exponents obtained from static scaling analysis. Beyond its fundamental significance, the kinetic-grading-induced localization transition provides a natural platform for quantum sensing. Using the critical enhancement of the quantum Fisher information (QFI), we demonstrate that the system enables quantum-enhanced parameter estimation of the grading exponent. We propose both adiabatic and dynamical quantum critical sensors and demonstrate that they exhibit enhanced scaling of the QFI. Our results therefore establish graded kinetic systems not only as a new setting for localization physics, but also as a potential resource for designing quantum-enhanced sensing devices.

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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.

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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.

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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.

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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

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.

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