arXiv subjects

Golam Ali Sekh

Publications and source records attributed to Golam Ali Sekh.

At least 19 recordsLinked to original sources

arXiv2026

Loss induced dynamics of optical pulses in saturable nonlinear media

We consider pulse propagation in a saturable nonlinear coupler whose other arm is dissipative and other is transparent. A flow of energy from transparent to dissipative arm takes place for weak value of dissipation and the coupler losses its energy. The energy loss of the coupler reduces for strong dissipation. This energy loss depends on the saturable nonlinearity. We find that the flow of relative energy at the output of a finite-sized coupler has a peak at a particular value of nonlinear strength. The peak value decreases with the increase of dissipation and it vanishes for stronger dissipation due to Zeno effect.

physics.atom-ph↗

arXiv2026

Quantum droplets in dipolar quasi-one-dimensional Bose-Einstein condensates in optical lattices

We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.

cond-mat.quant-gas↗

arXiv2026

Simulation of single-qubit gates in spin-orbit coupled Bose-Einstein condensate with cubic-quintic nonlinearity by nonlinear perturbations

We consider spin-orbit coupled Bose-Einstein condensates with cubic-quintic nonlinear interaction within the framework of second quantization formulation and find eigen states using numerical simulation and mean-field approximation. We show that two low-lying Schrodinger cat states remain degenerate up to a certain value of Raman coupling strength and these states can serve as qubit basis. We take three different nonlinear perturbations and find that the perturbations can result in different rotations of qubit state on Bloch sphere. We calculate the unitary operator corresponding to each perturbation and suggest the possibilities for obtaining various gates in ultra-cold atomic system.

cond-mat.quant-gas↗

arXiv2026

Bloch oscillations of helicoidal spin-orbit coupled Bose-Einstein condensates in deep optical lattices

We consider helicoidal spin-orbit coupled Bose-Einstein condensates in deep optical lattice and study the dynamics of Bloch oscillation. We show that the variation of helicoidal gauge potential with spin-orbit coupling is different in zero-momentum and plane-wave phases. The characteristics of Bloch oscillation are different in the two phases. In the zero-momentum phase, the Bloch oscillation is harmonic while it is anharmonic in the plane-wave phase. The amplitude of Bloch oscillation is found to be affected by the helicoidal gauge potential and spin-orbit coupling. We examine that the decay of Bloch oscillation caused by mean-field interaction can be managed by helicoidal spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2025

Dynamics of bright solitons in spin-orbit coupled Bose-Einstein condensates under the influence of optical and Rabi-coupling lattices

We consider coupled matter-wave bright solitons in spatial coherence spin-orbit coupled Bose-Einstein condensates in optical and Rabi-coupling lattice potentials and find an effective potential for separation of coupled matter-wave solitons. We show that the Rabi lattice significantly affects the potential near the region of overlap between the solitons. We study the effects of Rabi lattice on the dynamics of solitons for different initial overlap and that the dynamics is controlled by the interplay between the Rabi lattice and inter-component interaction. We investigate that, by tuning the Rabi lattice strength, one can realize localize, periodic and splitting dynamics of the total density profile of the coupled solitons.

cond-mat.quant-gas↗

arXiv2025

Josephson effect and self-trapping in helicoidal spin-orbit coupled Bose-Einstein condensates with optical lattices

We consider matter-wave bright solitons in helicoidal spin-orbit coupled Bose-Einstein condensates in optical lattices with a view to study Josephson-type oscillation and self-trapping of population imbalance between two pseudo-spin states. For fixed values of nonlinear interaction and lattice parameters, the population imbalance executes Josephson-type oscillation and the frequency of oscillation decreases with the increase of helicoidal gauge potential. The frequency of oscillation, however, increases in presence of nonlinear optical lattices. We find that the population imbalance can oscillate about a non-zero value and result self-trapping for proper choices of parameters of the system. The self-trapping can be enhanced by the increase of helicoidal gauge potential and by properly tuning the lattice parameters.

cond-mat.quant-gas↗

arXiv2024

Information theoretic measures on quantum droplets in ultracold atomic systems

We consider Shannon entropy, Fisher information, Rényi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang correction gives a family of quantum droplets with different chemical potentials. At a larger value of chemical potential, quantum droplet with sharp-top probability density distribution starts to form while it becomes flat top for a smaller value of chemical potential. We show that entropic measures can distinguish the shape change of the probability density distributions and thus can identify the onset of the droplet phase. During the onset of droplet phase, the Shannon entropy decreases gradually with the decrease of chemical potential and attains a minimum in the vicinity where a smooth transition from flat-top to sharp-top QDs occurs. At this stage, the Shannon entropy increases abruptly with the lowering of chemical potential. We observe an opposite trend in the case of Fisher information. These results are found to be consistent with the Rényi and Tsallis entropic measures.

cond-mat.quant-gas↗

arXiv2024

Effective spin dynamics of spin-orbit coupled matter-wave solitons in optical lattices

We consider matter-wave solitons in spin-orbit coupled Bose-Einstein condensates embedded in optical lattice and study dynamics of soliton within the framework of Gross-Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equation and investigate effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by the optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.

cond-mat.quant-gas↗

arXiv2023

Josephson-type oscillations in spin-orbit coupled Bose-Einstein condensates with nonlinear optical lattices

We consider spin-orbit coupled Bose Einstein Condensate in presence of linear and nonlinear optical lattices within the framework of quasi-one-dimensional Gross-Pitaevskii equation. The population imbalance between the states changes periodically with time and the oscillation amplitude depends sensitively on the initial phase. The optical lattice is found to change phase velocity of the oscillation of population imbalance. This oscillation can also be arrested beyond critical values of parameters. We find that the optical lattice can efficiently be used to control the critical point.

cond-mat.quant-gas↗

arXiv2023

Fisher information on the phase transition from regular to flat top optical pulse in cubic-quintic nonlinear media

We study the properties of optical pulse in cubic-quintic nonlinear media using information theoretic approach. The system can support regular (sharp top) and flat top pulse depending on the type of quintic interaction and the frequency of the pulse. For defocusing quintic nonlinearity, it holds both regular and flat top soliton. We find that Fisher information suddenly drops near the transition from sharp to flat top pulse. This is also reflected in the linear stability curve where power of the pulse suddenly grows near the point of transition. However, the solution is linearly stable according to Vakhitov-Kolokolov criterion. We examine that, in the case of focusing nonlinearity, the change from linearly stable and unstable solitons becomes imperceptible through Fisher information.

nlin.PS↗

arXiv2023

Compressing the atomic cloud in a matter-wave stripe soliton

We consider an attractive quasi-one dimensional spin-orbit coupled Bose-Einstein condensate (SOC BEC) confined in a periodic potential produced by the combination of linear and nonlinear optical lattices, and study the effects of squeezing a stripe soliton by varying the inter-atomic interaction in the nonlinear lattice. It is observed that the nodes on the soliton arising entirely due to the effect of spin-orbit coupling tend to disappear as we increase the squeezing effect to finally get a stable fundamental soliton. This leads us to conclude that external pressure can reduce the effect of spin-orbit coupling in the SOC BEC and even convert the system to a traditional BEC without spin-orbit coupling. We make use of an information theoretic measure to visualize how does the atomic density distribution in the condensate respond to continual reduction in the spin-orbit coupling effect.

cond-mat.quant-gas↗

arXiv2022

Satyendra Nath Bose: Quantum statistics to Bose-Einstein condensation

Satyendra Nath Bose is one of the great Indian scientists. His remarkable work on the black body radiation or derivation of Planck's law led to quantum statistics, in particular, the statistics of photon. Albert Einstein applied Bose's idea to a gas made of atoms and predicted a new state of matter now called Bose-Einstein condensate. It took 70 years to observe the predicted condensation phenomenon in the laboratory. With a brief introduction to the formative period of Professor Bose, this research survey begins with the founding works on quantum statistics and, subsequently, provides a brief account of the series of events terminating in the experimental realization of Bose-Einstein condensation. We also provide two simple examples to visualize the role of synthetic spin-orbit coupling in a quasi-one-dimensional condensate with attractive atom-atom interaction.

physics.hist-ph↗

arXiv2022

Schwarzian derivative in higher-order Riccati equations

The Sturm-Liouville equation represents the linearized form of the first-order Riccati equation. This provides an evidence for the connection between Schwarzian derivative and this first-order nonlinear differential equation. Similar connection is not obvious for higher-order equations in the Riccati chain because the corresponding linear equations are of order greater than two. With special attention to the second- and third-order Riccati equations we demonstrate that Schwarzian derivative has a natural space in higher Riccati equations. There exist higher-order analogues of the Schwarztan derivative. We demonstrate that equations in the Riccati hierarchy are embedded in these higher-order derivatives.

math-ph↗

arXiv2021

Information theoretic approach to effects of spin-orbit coupling in Bose-Einstein condensates

We make use of Shannon entropy ($S$) and Fisher information ($I$) to study the response of atomic density profiles of a spin-orbit coupled Bose-Einstein condensate to changes in the wave number ($κ_L$) of the Raman laser that couples two hyperfine states of atoms in the condensate. The choice for values of $κ_L$, the so-called spin-orbit parameter, and Rabi frequency ($Ω$) leads to two distinct regions in the system's energy spectrum with different order parameters and/or probability densities. In addition, we can have a spatially modulated density profile, reminiscent of the so called stripe phase. Our numbers for $S$ and $I$ demonstrate that for $κ_L^2<Ω$ (region 1) the density profile becomes localized as $κ_L$ increases while we observe delocalization in the density distribution for $κ_L^2>Ω$ (region 2) for increasing values of $κ_L$. In the stripe phase the nature of $S$ and $I$ to changes in $κ_L$ is similar to that found for the condensate in region 2. The results for information theoretic quantities in the stripe phase are, in general, augmented compared to those of region 2. In particular, the highly enhanced values of position-space Fisher information imply an extremely concentrated atomic density distribution to provide an evidence for supersolid properties of Bose-Einstein condensates in the presence of spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2021

Effects of optical lattices on bright solitons in spin-orbit coupled Bose-Einstein condensates

The stationary bright solitons that appear in the ground state of the spin-orbit coupled Bose-Einstein condensate (SOC-BEC) exhibit nodes. We consider SOC-BEC in combined linear and nonlinear optical lattices and study their effects on the matter-wave bright soliton and find that the parameters of the nonlinear lattice or atomic scattering length can be judiciously manipulated to have useful control over the nodes of the soliton. It is seen that the soliton with large number of nodes is less stable compared to one having fewer number of nodes. We infer that that the synthetic spin-orbit coupling induces instability in the ordinary matter-wave soliton.

physics.atom-ph↗

arXiv2021

Optical solitons in saturable cubic-quintic nonlinear media with nonlinear dispersion

We study an intense-short pulse propagation in a saturable cubic-quintic nonlinear media in the presence of nonlinear dispersion within the framework of an extended variational approach. We derive an effective equation for the pulse width and demonstrate how the saturation due to nonlinearity is achieved in presence of nonlinear dispersion. We find that the nonlinear dispersion can change the pulse width and induce motion in the system. The direction of induced motion depends on the sign of nonlinear dispersion. The pulse is energetically stable at an equilibrium width. A disturbance can, however, induce oscillation in pulse width, the frequency of which is always smaller due to nonlinear dispersion. We check dynamical stability by a direct numerical simulation.

physics.atom-ph↗

arXiv2020

Integrable systems: From the inverse spectral transform to zero curvature condition

This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to \textquoteleft inverse spectral transform', \textquoteleft Lax pair representation', and \textquoteleft zero-curvature condition' as applied to these equations. We provide a number of interesting examples to gain some physico-mathematical feeling for the methods presented.

nlin.SI↗

arXiv2020

Inverse variational problem for nonlinear dynamical systems

In this paper we have chosen to work with two different approaches to solving the inverse problem of the calculus of variation. The first approach is based on an integral representation of the Lagrangian function that uses the first integral of the equation of motion while the second one relies on a generalization of the well known Noether's theorem and constructs the Lagrangian directly from the equation of motion. As an application of the integral representation of the Lagrangian function we first provide some useful remarks for the Lagrangian of the modified Emden-type equation and then obtain results for Lagrangian functions of (i) cubic-quintic Duffing oscillator, (ii) Liénard-type oscillator and (iii) Mathews-Lakshmanan oscillator. As with the modified Emden-type equation these oscillators were found to be characterized by nonstandard Lagrangians except that one could also assign a standard Lagrangian to the Duffing oscillator. We used the second approach to find indirect analytic (Lagrangian) representation for three velocity-dependent equations for (iv) Abraham-Lorentz oscillator, (v) Lorentz oscillator and (vi) Van der Pol oscillator. For each of the dynamical systems from (i)-(vi) we calculated the result for Jacobi integral and thereby provided a method to obtain the Hamiltonian function without taking recourse to the use of the so-called Legendre transformation.

physics.class-ph↗