arXiv subjects

R. Kishor Kumar

Publications and source records attributed to R. Kishor Kumar.

15 recordsLinked to original sources

arXiv2025

Rayleigh-Taylor, Kelvin-Helmholtz and immiscible to miscible quenching instabilities in binary Bose-Einstein condensates

We investigate three kinds of instabilities in binary immiscible homogeneous Bose-Einstein condensate, considering rubidium isotopes $^{85}$Rb and $^{87}$Rb confined in two-dimensional circular box. Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) instability types are studied under strong perturbations. Without external perturbation, instabilities are also probed by immiscible to miscible quenching transition (IMQT), under two different initial configurations. Our numerical simulations show that all such instability dynamics are dominated by large vortex productions and sound-wave (phonon) propagations. For long-term propagation, vortex dynamics become dominant over sound waves in the KH instability, while sound wave excitations predominate in the other cases. For all the dynamical simulations, the emergence of possible scaling laws are investigated for the compressible and incompressible parts of the kinetic energy spectra, in terms of the wave number $k$. The corresponding results are compared with the classical Kolmogorov scalings, $k^{-5/3}$ and $k^{-3}$, for turbulence, which are observed in the kinetic energy spectra at some specific time intervals. Deviating from the classical scaling, a kind of ``Bottleneck effect" is noticed in the IMQT spectra.

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arXiv2024

Dynamical vortex production and quantum turbulence in perturbed Bose-Einstein condensates

Dynamical vortex production and quantum turbulence emerging in periodic perturbed quasi-two-dimensional (q2D) Bose-Einstein condensates are reported by considering two distinct time-dependent approaches. In both cases, dynamical simulations were performed by solving the corresponding 2D mean-field Gross-Pitaevskii formalism. (i) In the first model, a binary mass-imbalanced system is slightly perturbed by a stirring time-dependent elliptic external potential. (ii) In the second model, for single dipolar species confined in q2D geometry, a circularly moving external Gaussian-shaped obstacle is applied in the condensate, at a fixed radial position and constant rotational speed, enough for the production of vortex-antivortex pairs. Within the first case, vortex patterns are crystalized after enough longer period, whereas in the second case, the vortex pairs remains interacting dynamically inside the fluid. In both cases, the characteristic Kolmogorov spectral scaling law for turbulence can be observed at some short time interval.

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arXiv2024

Vortex dynamics and turbulence in dipolar Bose-Einstein condensates

Quantum turbulence indicators in dipolar Bose-Einstein condensed fluids, following emissions of vortex-antivortex pairs generated by a circularly moving detuned laser, are being provided by numerical simulations of the corresponding quasi-two-dimensional Gross-Pitaevskii formalism with repulsive contact interactions combined with tunable dipole-dipole strength. The critical velocities of two variants of a circularly moving obstacle are determined and analyzed for vortex-antivortex nucleation in the form of regular and cluster emissions. The turbulent dynamical behavior is predicted to follow closely the initial emission of vortex-antivortex pairs, relying on the expected Kolmogorov's classical scaling law, which is verified by the spectral analysis of the incompressible part of the kinetic energy. Within our aim to provide further support in the up-to-now investigations of quantum turbulence, which have been focused on non-dipolar Bose-Einstein condensates, we emphasize the role of dipole-dipole interactions in the fluid dynamics.

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arXiv2022

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit- and coherently-coupled spin-1 Bose-Einstein condensates trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, spin-orbit and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, under specific coupling and rotation strengths, we illustrate that a boson in these rotating spin-orbit- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials. In the presence of mean-field interactions, using the coupled Gross-Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin expectation per particle of an antiferromagnetic spin-1 Bose-Einstein condensate approaches unity indicating a similarity in the response with ferromagnetic spin-orbit-coupled condensates.

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arXiv2022

Spectral analysis for compressible quantum fluids

Turbulent fluid dynamics typically involves excitations on many different length scales. Classical incompressible fluids can be cleanly represented in Fourier space enabling spectral analysis of energy cascades and other turbulence phenomena. In quantum fluids, additional phase information and singular behaviour near vortex cores thwarts the direct extension of standard spectral techniques. We develop a formal and numerical spectral analysis for $U(1)$ symmetry-breaking quantum fluids suitable for analyzing turbulent flows, with specific application to the Gross-Pitaevskii fluid. Our analysis builds naturally on the canonical approach to spectral analysis of velocity fields in compressible quantum fluids, and establishes a clear correspondence between energy spectral densities, power spectral densities, and autocorrelation functions, applicable to energy residing in velocity, quantum pressure, interaction, and potential energy of the fluid. Our formulation includes all quantum phase information and also enables arbitrary resolution spectral analysis, a valuable feature for numerical analysis. A central vortex in a trapped planar Bose-Einstein condensate provides an analytically tractable example with spectral features of interest in both the infrared and ultraviolet regimes. Sampled distributions modelling the dipole gas, plasma, and clustered regimes exhibit velocity correlation length increasing with vortex energy, consistent with known qualitative behaviour across the vortex clustering transition. The spectral analysis of compressible quantum fluids presented here offers a rigorous tool for analysing quantum features of superfluid turbulence in atomic or polariton condensates.

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arXiv2022

Stability Window of Trapless Polariton Bose-Einstein condensates

We theoretically explore the possibility of stabilizing the trapless polariton Bose-Einstein condensates (pBECs). Exploiting the variational method, we solve the associated nonlinear, complex Gross-Pitaevskii (cGP) equation and derive the equation of motion for the amplitude and width of the condensate. These variational results described by ordinary differential equations are rewritten to perform a linear stability analysis to generate a stability window in the repulsive domain. A set of coupled nonlinear ordinary differential equations obtained through variational approach are then solved by numerical simulations through the fourth order Runge-Kutta method, which are further supported by split-step Crank-Nicholson method, thereby setting the platform for stable pBECs. In particular, we generate a window containing system parameters in the $g_1-γ_{eff}$ space within which the system can admit stable condensates. The highlight of the results is that one observes beating effects in the real time evolution of the condensates with attractive interactions much similar to multicomponent BECs, and their periodicity can be varied by manipulating linear and nonlinear loss/gain terms. For repulsive condensates, one notices the stretching of the density.

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arXiv2022

Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

Many of the static and dynamic properties of an atomic Bose-Einstein condensate (BEC) are usually studied by solving the mean-field Gross-Pitaevskii (GP) equation, which is a nonlinear partial differential equation for short-range atomic interaction. More recently, BEC of atoms with long-range dipolar atomic interaction are used in theoretical and experimental studies. For dipolar atomic interaction, the GP equation is a partial integro-differential equation, requiring complex algorithm for its numerical solution. Here we present numerical algorithms for both stationary and non-stationary solutions of the full three-dimensional (3D) GP equation for a dipolar BEC, including the contact interaction. We also consider the simplified one- (1D) and two-dimensional (2D) GP equations satisfied by cigar- and disk-shaped dipolar BECs. We employ the split-step Crank-Nicolson method with real- and imaginary-time propagations, respectively, for the numerical solution of the GP equation for dynamic and static properties of a dipolar BEC. The atoms are considered to be polarized along the z axis and we consider ten different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar BEC in 1D (along x and z axes), 2D (in x-y and x-z planes), and 3D, and we provide working codes in Fortran 90/95 and C for these ten cases (twenty programs in all). We present numerical results for energy, chemical potential, root-mean-square sizes and density of the dipolar BECs and, where available, compare them with results of other authors and of variational and Thomas-Fermi approximations.

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arXiv2022

Vortex generation in stirred binary Bose-Einstein condensates

The dynamical vortex production, with a trap-confining time-dependent stirred potential, is studied by using mass-imbalanced cold-atom coupled Bose-Einstein condensates (BEC). The vortex formation is explored by considering that both coupled species are confined by a pancake-like harmonic trap, slightly modified elliptically by a time-dependent periodic potential, with the characteristic frequency enough larger than the transversal trap frequency. The approach is applied to the experimentally accessible binary mixtures $^{85}$Rb-$^{133}$Cs and $^{85}$Rb-$^{87}$Rb, which allow us to verify the effect of mass differences in the dynamics. For both species, the time evolutions of the respective energy contributions, together with associated velocities, are studied in order to distinguish turbulent from non-turbulent flows. By using the angular momentum and moment of inertia mean values, effective classical rotation frequencies are suggested, which are further considered within simulations in the rotating frame without the stirring potential. Spectral analysis is also provided for both species, with the main focus being the incompressible kinetic energies. In the transient turbulent regime, before stable vortex patterns are produced, the characteristic $k^{-5/3}$ Kolmogorov behavior is clearly identified for both species at intermediate momenta $k$ above the inverse Thomas-Fermi radial positions, further modified by the universal $k^{-3}$ scaling at momenta higher than the inverse of the respective healing lengths. Emerging from the mass-imbalanced comparison, relevant is to observe that, as larger is the mass difference, much faster is the dynamical production of stable vortices.

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arXiv2020

Mass-imbalanced Bose-Einstein condensed mixtures in rotating perturbed trap

We consider the mass-imbalanced sensibility for the emergence of vortex patterns in the Bose-Einstein condensed binary mixture of rubidium-cesium ($^{85}$Rb-$^{133}$Cs), confined in quasi-two-dimensional harmonic traps, with one species linearly perturbed in one direction. Non-dipolar coupled species are chosen to highlight mass symmetry effects. We first analyze the condensed mixture in the unperturbed non-rotating regime, where radial phase separation is verified in the immiscible regime, which occurs for large ratio between inter- and intra-species repulsive interactions. By going to the linear perturbed regime, the radial phase separation that occurs in the immiscible condition splits up with the two densities having their maxima at distinct positions. In the rotating regime of both unperturbed and perturbed cases, the minimum rotation is determined in terms of the inter-species interaction to observe vortex structures. In the immiscible regime a dramatic spatial interchange between the species is verified by increasing the rotation.

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arXiv2018

Effect of an oscillating Gaussian obstacle in a Dipolar Bose-Einstein condensate

We study the dynamics of vortex dipoles in erbium ($^{168}$Er) and dysprosium ($^{164}$Dy) dipolar Bose-Einstein condensates (BECs) by applying an oscillating blue-detuned laser (Gaussian obstacle). For observing vortex dipoles, we solve a nonlocal Gross-Pitaevskii (GP) equation in quasi two-dimensions in real-time. We calculate the critical velocity for the nucleation of vortex dipoles in dipolar BECs with respect to dipolar interaction strengths. We also show the dynamics of the group of vortex dipoles and rarefaction pulses in dipolar BECs. In the dipolar BECs with Gaussian obstacle, we observe rarefaction pulses due to the interaction of dynamically migrating vortex dipoles.

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arXiv2018

Information entropy for a two-dimensional rotating Bose-Einstein condensate

We study the information entropy, order, disorder, and complexity for the two-dimensional (2D) rotating and nonrotating Bose-Einstein condensates. The choice of our system is a complete theoretical laboratory where the complexity is controlled by the two-body contact interaction strength and the rotation frequency ($Ω$) of the harmonic trap. The 2D nonrotating condensate shows the complexity of the category I where the disorder-order transition is triggered by the interaction strength. In the rotating condensates, $Ω$ is chosen as the disorder parameter when the interaction strength is fixed. With respect to $Ω$, the complexity shifts between the maximum and minimum confirm the existence of category II complexity in the rotating condensate. Also, We consider the interaction strength as the disorder parameter when $Ω$ is unchanged and complexity as a function of interaction strength exhibits category III complexity. The present work also includes the calculation of upper bound and lower bound of entropy for 2D quantum systems.

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arXiv2014

Effect of optical lattice potentials on the vortices in rotating dipolar Bose-Einstein condensates

We study the interplay of dipole-dipole interaction and optical lattice (OL) potential of varying depths on the formation and dynamics of vortices in rotating dipolar Bose-Einstein condensates. By numerically solving the time-dependent quasi-two dimensional Gross-Pitaevskii equation, we analyse the consequence of dipole-dipole interaction on vortex nucleation, vortex structure, critical rotation frequency and number of vortices for a range of OL depths. Rapid creation of vortices has been observed due to supplementary symmetry breaking provided by the OL in addition to the dipolar interaction. Also the critical rotation frequency decreases with an increase in the depth of the OL. Further, at lower rotation frequencies the number of vortices increases on increasing the depth of OL while it decreases at higher rotation frequencies. This variation in the number of vortices has been confirmed by calculating the rms radius, which shrinks in deep optical lattice at higher rotation frequencies.

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arXiv2013

Vortical and fundamental solitons in dipolar Bose-Einstein condensates trapped in isotropic and anisotropic nonlinear potentials

We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $\sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities $\ell =0$ (fundamental solitons), $\ell =1$, and $\ell =2$. The fundamental solitons and vortices with $\ell =1$ exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with $\ell =2$ are stable solely in the isotropic model.

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arXiv2012

Vortex dynamics of rotating dipolar Bose-Einstein condensates

We study the influence of dipole-dipole interaction on the formation of vortices in a rotating dipolar Bose-Einstein condensate (BEC) of $^{52}$Cr and $^{164}$Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross-Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices while a repulsive contact interaction increases the stability of the vortices. Further, an ordered vortex lattice of relatively large number of vortices is found in a strongly dipolar BEC.

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arXiv2010

Localization of a dipolar Bose-Einstein condensate in a bichromatic optical lattice

By numerical simulation and variational analysis of the Gross-Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose-Einstein condensate (DBEC) of $^{52}$Cr atoms in a three-dimensional bichromatic optical-lattice (OL) generated by two monochromatic OL of incommensurate wavelengths along three orthogonal directions. For a fixed dipole-dipole interaction, a localized state of a small number of atoms ($\sim 1000$) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with short-range interaction and dipole-dipole interaction is given.

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