arXiv subjects

Thudiyangal Mithun

Publications and source records attributed to Thudiyangal Mithun.

12 recordsLinked to original sources

arXiv2023

Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, $Ω_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the $Ω_{\text{cr}}$ values for vortex nucleation. The critical frequencies and thereby, the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional $\textit{s}$-wave scattering lengths through the strength of nonlinear rotation, $\mathit{C}$, such that $Ω_{\text{cr}}(\mathit{C}>0) < Ω_{\text{cr}}(\mathit{C}=0) < Ω_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity ($ε_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($ε$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.

cond-mat.quant-gas↗

arXiv2022

How close Are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model

In the present work we revisit the Salerno model as a prototypical system that interpolates between a well-known integrable system (the Ablowitz-Ladik lattice) and an experimentally tractable non-integrable one (the discrete nonlinear Schrödinger model). The question we ask is: for "generic" initial data, how close are the integrable to the non-integrable models? Our more precise formulation of this question is: how well is the constancy of formerly conserved quantities preserved in the non-integrable case? Upon examining this, we find that even slight deviations from integrability can be sensitively felt by measuring these formerly conserved quantities in the case of the Salerno model. However, given that the knowledge of these quantities requires a deep physical and mathematical analysis of the system, we seek a more "generic" diagnostic towards a manifestation of integrability breaking. We argue, based on our Salerno model computations, that the full spectrum of Lyapunov exponents could be a sensitive diagnostic to that effect.

nlin.PS↗

arXiv2022

Dragging A Defect in a Droplet Bose-Einstein Condensate

In the present work we consider models of quantum droplets in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations and dynamics in 1D, 2D and 3D settings. In the absence of an analytical solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically, and the unstable states, as well as the dynamics past the existence of stable states is monitored. The connection of the resulting states with dark solitonic patterns in 1D, vortical states in 2D and vortex rings in 3D is accordingly elucidated.

nlin.PS↗

arXiv2021

Existence, Stability and Dynamics of Monopole and Alice Ring Solutions in Anti-Ferromagnetic Spinor Condensates

In this work we study the existence, stability, and dynamics of select topological point and line defects in anti-ferromagnetic, polar phase, $F=1$ $^{23}$Na spinor condensates. Specifically, we leverage fixed-point and numerical continuation techniques in three spatial dimensions to identify solution families of monopole and Alice rings as the chemical potential (number of atoms) and trapping strengths are varied within intervals of realizable experimental parameters. We are able to follow the monopole from the linear limit of small atom number all the way to the Thomas-Fermi regime of large atom number. Additionally, and importantly, our studies reveal the existence of {\em two} Alice ring solution branches, corresponding to, relatively, smaller and larger ring radii, that bifurcate from each other in a saddle-center bifurcation as the chemical potential is varied. We find that the monopole solution is always dynamically unstable in the regimes considered. In contrast, we find that the larger Alice ring is indeed stable close to the bifurcation point until it destabilizes from an oscillatory instability bubble for a larger value of the chemical potential. We also report on the possibility of dramatically reducing, yet not completely eliminating, the instability rates for the smaller Alice ring by varying the trapping strengths. The dynamical evolution of the different unstable waveforms is also probed via direct numerical simulations.

cond-mat.quant-gas↗

arXiv2020

Nonlinear caging in All-Bands-Flat Lattices

We study the impact of classical short-range nonlinear interactions on transport in lattices with no dispersion. The single particle band structure of these lattices contains flat bands only, and cages non-interacting particles into compact localized eigenstates. We demonstrate that there always exist local unitary transformations that detangle such lattices into decoupled sites in dimension one. Starting from a detangled representation, inverting the detangling into entangling unitary transformations and extending to higher lattice dimensions, we arrive at an All-Bands-Flat generator for single particle states in any lattice dimension. The entangling unitary transformations are parametrized by sets of angles. For a given member of the set of all-bands-flat, additional short-range nonlinear interactions destroy caging in general, and induce transport. However, fine-tuned subsets of the unitary transformations allow to completely restore caging. We derive the necessary and sufficient fine-tuning conditions for nonlinear caging, and provide computational evidence of our conclusions for one-dimensional systems.

cond-mat.quant-gas↗

arXiv2020

Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices

We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves nonlinear caging, i.e. keeps compact excitations compact in the presence of Kerr-like local nonlinearities. Here we replace nonlinear terms by Bose-Hubbard interactions and study quantum caging. We prove the existence of degenerate energy renormalized compact states for two and three particles, and use an inductive conjecture to generalize to any finite number M of participating particles in one dimension. Our results explain and generalize previous observations for two particles on a diamond chain [Vidal et.al. Phys. Rev. Lett. 85, 3906 (2000)]. We further prove that quantum caging conditions guarantee the existence of extensive sets of conserved quantities in any lattice dimension, as first revealed in [Tovmasyan et al Phys. Rev. B 98, 134513 (2018)] for a set of specific networks. Consequently transport is realized through moving pairs of interacting particles which break the single particle caging.

cond-mat.quant-gas↗

arXiv2020

Fragile Many Body Ergodicity

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales. Short range networks instead yield a dramatic slowing down of ergodization in action space, and lead to rare resonance diffusion. We use Josephson junction chains as a paradigmatic study case. We exploit finite time average distributions to characterize the thermalizing dynamics of actions. We identify a novel action resonance diffusion regime responsible for the slowing down. We extract the diffusion coefficient of that slow process and measure its dependence on the proximity to the integrable limit. Independent measures of correlation functions confirm our findings. The observed fragile diffusion is relying on weakly chaotic dynamics in spatially isolated action resonances. It can be suppressed, and ergodization delayed, by adding weak action noise, as a proof of concept.

nlin.CD↗

arXiv2020

Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices

We numerically investigate the quench expansion dynamics of an initially confined state in a two-dimensional Gross-Pitaevskii lattice in the presence of external disorder. The expansion dynamics is conveniently described in the control parameter space of the energy and norm densities. The expansion can slow down substantially if the expected final state is a non-ergodic non-Gibbs one, regardless of the disorder strength. Likewise stronger disorder delays expansion. We compare our results with recent studies for quantum many body quench experiments.

cond-mat.quant-gas↗

arXiv2020

Modulational instability, inter-component asymmetry and formation of quantum droplets in one-dimensional binary Bose gases

Quantum droplets are ultradilute liquid states which emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of droplets in symmetric and asymmetric two-component one-dimensional boson systems to the modulational instability of a spatially uniform state driven by the beyond-mean-field term. Asymmetry between the components may be caused by their unequal populations or unequal intra-component interaction strengths. Stability of both symmetric and asymmetric droplets is investigated. Robustness of the symmetric solutions against symmetry-breaking perturbations is confirmed.

cond-mat.quant-gas↗

arXiv2019

Dynamical glass in weakly non-integrable Klein-Gordon chains

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a {\it nonintegrable} perturbation creates a coupling network in action space which can be short- or long-ranged. We analyze the dynamics of observables which turn into the conserved actions in the integrable limit. We compute distributions of their finite-time averages and obtain the ergodization time scale $T_E$ on which these distributions converge to $δ$-distributions. We relate $T_E \sim (σ_τ^+)^2/μ_τ^+$ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations $σ_τ^+$ dominating the means $μ_τ^+$. The Lyapunov time $T_Λ$ (the inverse of the largest Lyapunov exponent) is then compared to the above time scales. We use a simple Klein-Gordon chain to emulate long- and short-range coupling networks by tuning its energy density. For long-range coupling networks $T_Λ\approx σ_τ^+$, which indicates that the Lyapunov time sets the ergodization time, with chaos quickly diffusing through the coupling network. For short-range coupling networks we observe a {\it dynamical glass}, where $T_E$ grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which $T_Λ \lesssim μ_τ^+$. This is due to the formation of a highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of non-chaotic regions. These structures persist up to the ergodization time $T_E$.

nlin.CD↗

arXiv2018

Modulation instability associated nonlinear dynamics of spin-orbit coupled Bose-Einstein condensates

We study pattern-forming nonlinear dynamics starting from a continuous wave state of quasi-one-dimensional two-component Bose-Einstein condensates with synthetic spin-orbit coupling induced by Raman lasers. Modulation instability can occur even when the miscibility condition due to the interatomic interactions is satisfied. We find that the initial stage of the nonlinear development is consistent with the prediction of modulation instability, where the two primary and secondary instability bands lead to the spontaneous growth of the modulation and the subsequent complicated dynamics of pattern formation. At later stages of the evolution, the wave functions undergo clear separation in the momentum space, reflected in the dispersion of the single particle Hamiltonian.

cond-mat.quant-gas↗

arXiv2018

Continuous-wave solutions and modulational instability in spinor condensates of positronium

We obtain general continuous-wave (CW)\ solutions in the model of a spinor positronium condensate in the absence of magnetic field. The CW solutions with both in-phase ($n=0$) and out-of-phase ($n=1$) spin components exist, with their ranges limited by the total particle density, $ρ$. In the limit of negligible population exchange between the spin components, the CW solutions are found to be stable or unstable, depending on the particle density of the para positronium. Ortho positronium, in the $F=1$ spinor state, forms a ferromagnetic condensate with stable in-phase CW solutions only. Subsequent examination of the modulational instability (MI) is carried out both in the limit case of identical wavenumbers in the spin components, $% Δk\equiv k_{1}-k_{-1}=0$, and in the more general case of $Δk\neq 0$ too. The CW solutions with $n=0$ and $1$ solutions, which are stable in the case of $Δk=0$, are unstable for $Δk\neq 0$, for the natural repulsive sign of the nonlinearities. The total particle density, $ρ$, in the limit of $Δk=0$ is found to have a significant role for the stability of the condensate, which is determined by the sign of the self-interaction nonlinearity.

cond-mat.quant-gas↗