Cold Bosonic Atoms Research Articles

Forecasting the dynamics of the model of cold bosonic atoms in a zig-zag optical lattice by symbolic computation

The work aims to explore the exponential rational function technique and the generalized Kudryashov procedure to investigate one of the most important equations which is the equation of cold bosonic atoms in a zig-zag optical lattice. The considered equation is reduced to a supreme equation by using the continuum approximation which describes the soliton’s dynamics with the implication pulse variables. The adopted techniques are accurate, simple, straightforward, and succinct to compute.

Homoclinic breather, periodic wave, lump solution, and M-shaped rational solutions for cold bosonic atoms in a zig-zag optical lattice

Abstract In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross-rational propagation, and interaction between lump periodic and kink wave was examined. Some M-shaped solution, M-shaped interaction with periodic and kink, M-shaped interaction with rogue and kink, M-shaped rational solution, M-shaped rational solution with one kink, M-shaped rational solution with two kink, solutions for lump soliton waves, lump one kink waves, lump two kink waves, periodic-cross lump wave propagation, periodic wave propagation, rogue wave propagation, and multiwave propagation were also acquired. Likewise, our solution was also graphically presented, and also their stability was checked.

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques.

The wave propagation has the significant role in the field of coastal engineering and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on floating structure. This study aims to investigate the system of cold bosonic atoms in zig-zag optics lattices. The solitonic patterns of the considered model successfully surveyed by using two integrated analytical techniques new extended direct algebraic and frac{G'}{G^{2}} expansion method. The exact solutions are presented by rational, trigonometric, hyperbolic and exponential functions. On the basis of solitons, we need to show that which one is more integrated and robust scheme. These solutions will help to understood the dynamics of cold bosonic atoms in zig-zag optical lattices and the several other systems. Three dimensional as well as two dimensional comparison presented for a cold bosonic atoms model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. This study will help physicists to predict some new hypothesis and theories in the field of mathematical physics.

Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes

In this present paper, we obtain hyperbolic, exponential, trigonometric function, other soliton solutions, and their combinations for the cold bosonic atoms in a zig-zag optical lattice model based on two efficient methods, such as the generalized Riccati equation mapping (GREM) method and generalized Kudryashov (GK) method. The used techniques are very reliable and effective tools and provide numerous exact soliton solutions of the nonlinear PDE. The zig-zag optical lattice model, widely used to represent the nonlinear wave and the soliton dynamics in fluid dynamics and plasma physics, is examined in this article to obtain exact optical soliton solutions and study their physical properties. For this, we first convert a partial differential equation (PDE) into an ordinary differential equation (ODE) by employing wave transformation and then split the equation into imaginary and real parts. The derived optical soliton solutions are illustrated graphically using Mathematica software to distinguish constant parameter values. Consequently, bell-shape, anti-bell-shape, traveling wave, periodic, mix periodic, singular soliton, and some new types of solitons demonstrate to validate these acquired outcomes with physical phenomena and make the results worthy. Furthermore, the 3D, 2D, and contour graphs are sketched to assign suitable constant parameters to illustrate the physical phenomena of the obtained solutions. The accomplished soliton solutions indicate that the applied computational system is a direct, reliable, productive, and more complex physical phenomenon. Symbolic computation is used in the software package Mathematica to obtain the various soliton solutions and different dynamical behavior of the newly formed solutions

New Optical Solitons with Variational Principle and Collective Variable Strategy for Cold Bosons in Zig-Zag Optical Lattices

The theme of this piece of research is to investigate the collective variable (CV) as well as semi-inverse techniques to explore a significant model of cold bosonic atoms in a zig-zag optical lattice. The system is reduced to an important equation by utilizing the continuum approximation and explains the soliton’s dynamics in sense of pulse variables. These parameters are amplitude, temporal position, chirp, width, frequency, and phase which are termed as collective variables (CVs). The proposed methods are more straightforward, succinct, accurate, and simple to calculate. Furthermore, to employ the computational counterfeit on the system of six ordinary differential equations that denote all the CVs incorporated in the supposed ansatz, a well-established computational method which is the Runge–Kutta scheme of order four is applied. The CV method is exerted to resolve the evolution of pulse parameters with the propagation distance and graphical illustrations which are also given. Moreover, figures reveal the fascinating periodic oscillations of frequency, width, amplitude, and chirp of soliton. Solitons and their numerical behavior to interpret fluctuations in CVs are presented for several values of super-Gaussian pulse parameters. Also, the results for the semi-inverse method which are bright solitons are provided in the form of 2D, 3D, and density plots for the distinct values of the fractal parameter to understand their physical significance. This scheme is effective in finding variational principles of various nonlinear evolution equations. Some compelling characteristics pertaining to the current scrutiny are also deduced.

Analytical soliton solutions for cold bosonic atoms (CBA) in a zigzag optical lattice model employing efficient methods

This research finds an equation in a continuous domain and a discrete equation governing the system of cold bosonic atoms (CBA) in a zigzag optical lattice using a continuum approximation. Many solutions to the equation were obtained using two distinct methods: the three-wave approach (multi-wave interaction, rational solutions, and rational solution interaction) and the extended sub-equation method. These analytical approaches are more effective, consistent, and comprehensive mathematical tools for obtaining various exact closed-form solutions for a wide range of fractional space-time nonlinear evolution equations encountered in optical physics, condensed matter physics, and plasma physics. The solutions generated are in the form of hyperbolic and trigonometric solutions, and other-form solutions are obtained. Three-dimensional graphics and contour plots are often used to depict the graphical representations of the combined soliton solutions. These findings will aid our understanding of the dynamics of the zigzag optical grids and many other structures formed by colder bosonic atoms. The applied approaches are more simple, efficient, and straightforward to obtain the closed-form solutions for various nonlinear evolution equations in the fields of nonlinear sciences and physical engineering.

Influence of the next-nearest neighbor and the boson–boson interactions on U-shaped, W-shaped profile and modulation instability gain spectra in a zig–zag optical lattice

In this paper, we employ the auxiliary equation method (AEM) to show the leverage of the nearest neighbors hopping and the boson–boson interaction in a zig zag optical lattice on the stressed optical solitons (os) and the Modulation Instability (MI) gain of cold bosonic atoms. The pedestal of the work is set on the continuum approximation of a cold bosonic atoms in a zig zag optical lattice which has demonstrated in detailed in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589]. The results collected have enclosed bright, dark optical solitons and the combined bright-dark and bright-bright optical solitons. Compared the acquired results with Tala-Tebue et al. [Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44], further the os including U-shaped and W-shaped profile have been drop in and the powerful of the nearest neighbors hopping and the boson–boson interaction has been exposed across the spatiotemporal and plot evolution of the bright and dark os. Therewith, the MI bands have been stressed and it is observed some new attitude of the MI gain spectra under the induction of the model parameters. The collected results are new in literature in our knowledge and will improve the previous results acquired in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589; Zhao XH, Tian B, Liu DY, et al. Dark solitons interaction for a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Superlattices Microstruct 100(2016):587–595; Uddin MF, Hafez MG, Hammouch Z, et al. Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness. Waves Random Complex Media 2020. https://doi.org/10.1080/17455030.2020.1722331; Inc M, Aliyu AI, Yusuf A. Optical solitons to the nonlinear Shrdingers equation with spatio-temporal dispersion using complex amplitude ansatz. J Mod Opt 2017;64(21):2273–2280].

Optical solutions of cold bosonic atoms in a zig-zag optical lattice

In this paper, using the continuum approximation and from a discrete equation governing a system of cold bosonic atoms in zig-zag optical lattices derived an equation in a continuum domain. With two different methods, namely the $$exp_a$$ function method and the Hyperbolic function method, found many solutions of the equation considered. These solutions are Hyperbolic solutions and trigonometric solutions. Discrete representations have been done to observe their behaviors. These results will help to understand the dynamics of cold bosonic atoms in zig-zag optical lattices and several other systems. More importantly, in this article derived the Lagrangian and the stability condition of the model studied. The methods employed here are very simple and concise.

Collective dynamics of Fermi-Bose mixtures with an oscillating scattering length

Collective oscillations of superfluid mixtures of ultra cold fermionic and bosonic atoms are investigated while varying the fermion-boson scattering length. We study the dynamics with respect to excited center of mass modes and breathing modes in the mixture. Parametric resonances are also analyzed when the scattering length varies periodically in time, by comparing partial differential equation (PDE) models and ordinary differential equation (ODE) models for the dynamics. An application to the recent experiment with fermionic $^{6}$Li and bosonic $^{7}$Li atoms, which approximately have the same masses, is discussed.

Entanglement-like properties in spin–orbit coupled ultra cold atom and violation of Bell-like inequality

We show that the general quantum state of synthetically spin–orbit coupled ultra cold bosonic atoms, whose condensate was experimentally created recently by Lin et al (2011 Nature 471, 83), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provide a unique opportunity to verify fundamental principles like quantum contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such an atom-laser system and how this influences quantities like entanglement entropy, the violation of Bell-like inequality, etc. We also discuss the implications of our result in testing quantum contextuality and Bell’s Inequality violation by macroscopic quantum object like Bose–Einstein condensate of ultra cold atoms.

Probing Quantum Turbulence in ^{4}He by Quantum Evaporation Measurements.

Theory of superfluid ^{4}He shows that, due to strong correlations and backflow effects, the density profile of a vortex line has the character of a density modulation and it is not a simple rarefaction region as found in clouds of cold bosonic atoms. We find that the basic features of this density modulation are represented by a wave packet of cylindrical symmetry in which rotons with a positive group velocity have a dominant role: The vortex density modulation can be viewed as a cloud of virtual excitations, mainly rotons, sustained by the phase of the vortex wave function. This suggests that in a vortex reconnection some of these rotons become real so that a vortex tangle is predicted to be a source of nonthermal rotons. The presence of such vorticity induced rotons can be verified by measurements at low temperature of quantum evaporation of ^{4}He atoms. We estimate the rate of evaporation and this turns out to be detectable by current instrumentation. Additional information on the microscopic processes in the decay of quantum turbulence will be obtained if quantum evaporation by high energy phonons should be detected.

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.

Mixture of two ultra cold bosonic atoms confined in a ring: stability and persistent currents

In this article we investigate the stability of quantized yrast states in a mixture of two distinguishable equal mass bosonic atoms confined in a ring. We focus in the study of energetic stability since the Bloch analysis and the Bogoliubov theory establishes that only energetically stable quantized yrast states are capable of sustain a persistent current. In the framework of the Bogoliubov theory we study the stability in two different cases chosen by physical considerations. In one case we analyze how the inter and intraspecies interaction strengths affect the stability of a selected quantized yrast state specified by the angular momentum per particle and the population imbalance. In the other case, for a fixed dynamics specified by given values of interaction strengths, we determine the stability of quantized yrast states as function of the angular momentum per particle and the population imbalance. We also examined the stability of the mixture in the rarefied limit and we found a critical value of the population imbalance which gives the size of the window of energetic stability and a critical value of angular momentum per particle which is an upper bound of the possible values of angular momentum per particle carried by energetically stable quantized yrast states.

Probing the conformal Calabrese-Cardy scaling with cold atoms

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c=1. This can be accomplished with a very small hoping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S_2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)\ln(N_s), for N_s sites with open boundary conditions, provided that the large subleading corrections are taken into account.

Quantum Phases of Cold Bosonic Atoms in an Optical Lattice with Inhomogeneous Atomic Interactions and Coexistence of Multi Phases**Supported by the National Natural Science Foundation of China under Grant No. 11274061

We study cold bosonic atoms on a two-dimensional inhomogeneous optical lattice with site-dependent atomic interactions. With the tight-binding approximation, we derive the extended Bose–Hubbard model. Base on the mean-field approximation, the ground states are solved by the exact diagonalization method. We calculate the mean-field order parameter and particle number density for the ground states. We find the coexistence of superfluid phase and Mott-insulator phase on the two-dimensional inhomogeneous optical lattice in appropriate parameter ranges.

Quantized conductance through the quantum evaporation of bosonic atoms

We analyze theoretically the quantization of conductance occurring with cold bosonic atoms trapped in two reservoirs connected by a constriction with an attractive gate potential. We focus on temperatures slightly above the condensation threshold in the reservoirs. We show that a conductance step occurs, coinciding with the appearance of a condensate in the constriction. Conductance relies on a collective process involving the quantum condensation of an atom into an elementary excitation and the subsequent quantum evaporation of an atom, in contrast with ballistic fermion transport. The value of the bosonic conductance plateau is strongly enhanced compared to fermions and explicitly depends on temperature. We highlight the role of weak repulsive interactions between the bosons in preventing them from collapsing into the constriction.

Hubbard Model for Atomic Impurities Bound by the Vortex Lattice of a Rotating Bose-Einstein Condensate.

We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the Bose-Einstein condensate. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes.

Watching fermions transition on site

Quantum Simulation Optical lattices are a promising platform for simulating the many-body physics that occurs in solids. In lattices filled with cold bosonic atoms, “quantum microscopy” makes it possible to watch quantum phase transitions as they unravel. Greif et al. bring a similar capability

Site-resolved imaging of a fermionic Mott insulator.

The complexity of quantum many-body systems originates from the interplay of strong interactions, quantum statistics, and the large number of quantum-mechanical degrees of freedom. Probing these systems on a microscopic level with single-site resolution offers important insights. Here we report site-resolved imaging of two-component fermionic Mott insulators, metals, and band insulators, using ultracold atoms in a square lattice. For strong repulsive interactions, we observed two-dimensional Mott insulators containing over 400 atoms. For intermediate interactions, we observed a coexistence of phases. From comparison to theory, we find trap-averaged entropies per particle of 1.0 times the Boltzmann constant (k(B)). In the band insulator, we find local entropies as low as 0.5 k(B). Access to local observables will aid the understanding of fermionic many-body systems in regimes inaccessible by modern theoretical methods.

Proposal to directly observe the Kondo effect through enhanced photoinduced scattering of cold fermionic and bosonic atoms

We propose an experimental protocol to directly observe the Kondo effect by scattering ultracold atoms with spin-dependent interactions. We propose using an optical Feshbach resonance to engineer Kondo-type spin-dependent interactions in a system with ultracold $^6$Li and $^{87}$Rb gases. We calculate the momentum transferred from the $^{87}$Rb gas to the $^6$Li gas in a scattering experiment and show that it has a logarithmically enhanced temperature dependence, characteristic of the Kondo effect and analogous to the resistivity of alloys with magnetic impurities. Experimentally detecting this enhancement will give a different perspective on the Kondo effect, and allow us to explore a rich variety of problems such as the Kondo lattice problem and heavy-fermion systems.