Bose-Einstein Condensate Research Articles

On the mass of the charge carrier in LSCO cuprate: Bose–Einstein condensation of preformed pairs point of view

In this paper, the dependence of the charge carrier mass in the LSCO cuprate on the doping level (x) has been theoretically studied. Our theoretical consideration is based on the bipolaron theory of high-Tc superconductivity, which implies superfluidity of a gas (liquid) of bipolarons (pre-formed pairs). The theoretical explanation of the dependency is achieved by associating the superconducting critical temperature of the LSCO cuprate, Tc, with the temperature of Bose–Einstein condensation of the ideal gas of the intersite bipolarons, TBEC, and calculating the value of (bi)polaron mass at different doping levels. Meanwhile, the anisotropy of the LSCO cuprate crystal lattice is also taken into account to obtain precise results. Our results practically reproduce the known experimental dependencies of the charge carrier mass on the doping level. Besides, they clearly demonstrate the potential of using the pre-formed pair concept in studying the high-Tc superconductivity of the LSCO cuprate.

One-dimensional magnetic excitonic insulators

Abstract Dimensionality significantly affects exciton production and condensation. Despite the report of excitonic instability in one-dimensional materials, it remains unclear whether these spontaneously produced excitons can form Bose–Einstein condensates. In this work, we first prove statistically that one-dimensional condensation exists when the spontaneously generated excitons are thought of as an ideal neutral Bose gas, which is quite different from the inability of free bosons to condense. We then derive a general expression for the critical temperature in different dimensions and find that the critical temperature increases with decreasing dimension. We finally predict by first-principles GW-Bethe–Salpeter equation calculations that experimentally accessible single-chain staircase Scandocene and Chromocene wires are an antiferromagnetic spin-triplet excitonic insulator and a ferromagnetic half-excitonic insulator, respectively.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principle of the SSB theory, the solitons with broken inter-component symmetry prevail with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Mass concentration near the boundary for attractive Bose–Einstein condensates in bounded domains

We are devoted to studying the ground states of trapped attractive Bose–Einstein condensates in a bounded domain Ω⊂R2, which can be described by minimizers of L2-critical constraint Gross–Pitaevskii energy functional. It has been shown that there is a threshold a∗>0 such that minimizers exist if and only if the interaction strength a satisfies a<a∗. In present paper, we prove that when the trapping potential V(x) attains its flattest global minimum only at the boundary of Ω, the mass of minimizers must concentrate near the boundary of Ω as a↗a∗. This result extends the work of Luo and Zhu (2019).

A numerical study of vortex nucleation in 2D rotating Bose–Einstein condensates

This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose–Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.

Role of Higher-Order Scattering Coefficient and Residual Nonlinearities on Instability Criteria in Three-Body Bose-Einstein Condensates

We examine the instability characteristics in a three-body condensate and the effect of higher-order nonlinear effects caused by shape-dependent imprisonment and higher-order scattering coefficients such as S-wave scattering length and effective range for collisions. Using the linear stability technique, we study the spreading relations and gain profile of the adapted Gross Pitaevski equation with higher-order scattering coefficients and enduring nonlinearity. The role of higher-order interactions S-wave scattering length, residual nonlinearity, and effective range for collisions over the modulational instability in immiscible and miscible three-body Bose-Einstein condensates has been discussed in detail. MI can be excited in miscible condensates and changed in immiscible condensates because of residual nonlinearity, without taking into account higher-order nonlinearity and three-body condensates. However, the results of this work demonstrate that the influence of higher-order residual nonlinearity can cause the MI to change in both immiscible and immiscible condensates. The discovered MI spectrum reveals a new soliton production regime in three-body condensates. The results exhibit that higher-order scattering coefficient and remaining nonlinearity interplay can successfully switch the instability gain profile in miscible and immiscible condensates. This makes it possible to regulate the dynamics by varying the MI in a ternary combination of Bose-Einstein condensates.

Novel soliton solutions and phase plane analysis in nonlinear Schrödinger equations with logarithmic nonlinearities

This paper investigates a generalized form of the nonlinear Schrödinger equation characterized by a logarithmic nonlinearity. The nonlinear Schrödinger equation, a fundamental equation in nonlinear wave theory, is applied across various physical systems including nonlinear optics, Bose–Einstein condensates, and fluid dynamics. We specifically explore a logarithmic variant of the nonlinear Schrödinger equation to model complex wave phenomena that conventional polynomial nonlinearities fail to capture. We derive four distinct forms of the nonlinear Schrödinger equation with logarithmic nonlinearity and provide exact solutions for each, encompassing bright, dark, and kink-type solitons, as well as a range of periodic solitary waves. Analytical techniques are employed to construct bounded and unbounded traveling wave solutions, and the dynamics of these solutions are analyzed through phase portraits of the associated dynamical systems. These findings extend the scope of the nonlinear Schrödinger equation to more accurately describe wave behaviors in complex media and open avenues for future research into non-standard nonlinear wave equations.

Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group

Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group

Surface excitation of Rydberg dressed quantum droplet of Bose–Einstein Condensates

We have considered a quantum droplet of two components of Bose–Einstein condensate (BEC) inside the electron of a Rydberg atom to study the surface mode of collective excitation using the Bogoliubov theory of excitation. We have calculated the surface excitation spectrum for various Rydberg electron-atom interaction strengths. From the energy spectrum, we calculated the surface tension of the droplet as a function of Rydberg electron-atom interaction strength. Our study shows that the electron-atom interaction enhances the surface energy; hence, the droplet will be more stable inside the electron of a Rydberg atom.

Collision Dynamics of One-Dimensional Bose–Einstein Condensates

Collision Dynamics of One-Dimensional Bose–Einstein Condensates

Phase separation and metastability in a mixture of spin-1 and spin-2 Bose-Einstein condensates

Phase separation and metastability in a mixture of spin-1 and spin-2 Bose-Einstein condensates

Detecting axion dark matter with black hole polarimetry

The axion, as a leading dark matter candidate, is the target of many ongoing and proposed experimental searches based on its coupling to photons. Ultralight axions that couple to photons can also cause polarization rotation of light which can be probed by the cosmic microwave background. In this work, we show that a large axion field is inevitably developed around black holes due to the Bose-Einstein condensation of axions, enhancing the induced birefringence effects. Therefore, measuring the modulation of supermassive black hole imaging polarization angles is a strong probe to the axion-photon coupling due to the formation of the axion condensation (axion star) which enhances the axion field. The oscillating axion field around black holes induces polarization rotation on the black hole image, which is detectable and distinguishable from astrophysical effects on the polarization angle, as it exhibits distinctive temporal variability and frequency invariability. In this work, we perform the theoretical calculation on the axion star formation rate and correspondingly the enhanced axion field value near supermassive black holes. Then, we present the range of axion-photon couplings within the axion mass range 10−21–10−16 eV that can be probed by the Event Horizon Telescope. The axion parameter space probed by black hole polarimetry will expand with the improvement in sensitivity on the polarization measurement and more black hole polarimetry targets with determined black hole masses. Published by the American Physical Society 2024

Bose–Einstein Condensation dark matter models generated by gravitational decoupling

A study on massive compact objects influenced by Bose–Einstein condensation (BEC) dark matter (DM) with a gravitational decoupling approach is presented within the context of f(Q) gravity, assuming a linear form of f(Q). In order to obtain physically valid solutions to the basic field equations of the decoupled systems, we take the Tolman IV potential ansatz for the seed system and the BEC-DM density profile for the new source into consideration. After that, we apply the boundary conditions on the decoupled system with Schwarzschild-de Sitter spacetime as the exterior metric. Eventually, we obtain a complete non-singular solution to the decoupled system, consisting of a strange stellar configuration with a BEC-DM density profile. All the physical properties, such as the effective energy density, pressure along the radial as well as the tangential direction, and anisotropy in the system, are rigorously investigated. Analyzing the stability conditions of the decoupled stellar configuration, we study mass–radius (M−R) relations with observational constraints related to the supermassive compact stars, such as PSR J0740+6620, PSR J2215+5135, GW190814, and GW200210, with observed masses larger than or equal to 2 M⊙. Notably, we examine the influence of DM on constraining the M−R measurements of the observed stars, which satisfy the MIT bag model equation of state as well as the condition of mimicking, i.e., ρθ=ρDM, in the background of f(Q) gravity. Interestingly, any possible conversion of massive compact stars to smaller black holes can be restrained, as the presence of a DM halo in the strange stellar system reduces the maximum mass effectively, as indicated by the M−R curves. This result regarding the maximum mass of the compact star can be associated with the astrophysical data concerning the mass gap of the events GW190814 and GW200210. Specifically, the present model predicts the radius for PSR J0740+6620 as 13.69−0.10+0.09 km, which nearly matches the NICER and XMM-Newton data.

Magnon tunnelling between two magnon Bose–Einstein condensates

Magnon tunnelling between two magnon Bose–Einstein condensates

Induced supersolidity and hypersonic flow of a dipolar Bose-Einstein condensate in a rotating bubble trap

Induced supersolidity and hypersonic flow of a dipolar Bose-Einstein condensate in a rotating bubble trap

Circumventing the polariton bottleneck via dark excitons in 2D semiconductors

Efficient scattering into the exciton polariton ground state is a key prerequisite for generating Bose–Einstein condensates and low-threshold polariton lasing. However, this can be challenging to achieve at low densities due to the polariton bottleneck effect that impedes phonon-driven scattering into low-momentum polariton states. The rich exciton landscape of transition metal dichalcogenides (TMDs) provides potential intervalley scattering pathways via dark excitons to rapidly populate these polaritons. Here, we present a theoretical and fully microscopic study exploring the time- and momentum-resolved relaxation of exciton polaritons supported by a MoSe2 monolayer integrated within a Fabry–Perot cavity. By exploiting phonon-assisted transitions between momentum-dark excitons and the lower polariton branch, we demonstrate that it is possible to circumvent the bottleneck region and efficiently populate the polariton ground state. Furthermore, this intervalley pathway is predicted to give rise to, yet unobserved, angle-resolved phonon sidebands in low-temperature photoluminescence spectra that are associated with momentum-dark excitons. This represents a distinct signature for efficient phonon-mediated polariton-dark-exciton interactions.

Modular properties of massive scalar partition functions

We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form ℝd−q × \U0001d54bq+1 and show that they possess an SL(q + 1, ℤ) symmetry. Non-trivial relations between equivalent expressions for the result are obtained by doing the computation using functional, canonical and worldline methods. For q = 1, the results exhibit modular symmetry and may be expressed in terms of massive Maass-Jacobi forms. In the complex case with chemical potential for U(1) charge turned on, the usual discussion of relativistic Bose-Einstein condensation is modified by the presence of the small dimensions.

Phase Diagrams of a Relativistic Self-Interacting Boson System

Within the Canonical Ensemble, we investigate a system of interacting relativistic bosons at finite temperatures and finite isospin densities in a mean-field approach. The mean field contains both attractive and repulsive terms. Temperature and isospin density dependences of thermodynamic quantities are obtained. It is shown that, in the case of attraction between particles in a bosonic system, a liquid-gas phase transition develops against the background of the Bose–Einstein condensate. The corresponding phase diagrams are given. We explain the reasons for why the presence of a Bose condensate significantly increases the critical temperature of the liquid-gas phase transition compared to that obtained for the same system within the framework of Boltzmann statistics. Our results may have implications for the interpretation of experimental data, in particular, how sensitive the critical point of the mixed phase is to the presence of the Bose–Einstein condensate.

Parallel finite-element codes for the Bogoliubov-de Gennes stability analysis of Bose-Einstein condensates

We present and distribute a parallel finite-element toolbox written in the free software FreeFEM for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to one- and two-component Gross-Pitaevskii (GP) equations, in two or three spatial dimensions. The parallelization of the toolbox relies exclusively upon the recent interfacing of FreeFEM with the PETSc library. The latter contains itself a wide palette of state-of-the-art linear algebra libraries, graph partitioners, mesh generation and domain decomposition tools, as well as a suite of eigenvalue solvers that are embodied in the SLEPc library. Within the present toolbox, stationary states of the GP equations are computed by a Newton method. Branches of solutions are constructed using an adaptive step-size continuation algorithm. The combination of mesh adaptivity tools from FreeFEM with the parallelization features from PETSc makes the toolbox efficient and reliable for the computation of stationary states. Their BdG spectrum is computed using the SLEPc eigenvalue solver. We perform extensive tests and validate our programs by comparing the toolbox's results with known theoretical and numerical findings that have been reported in the literature. Program summaryProgram Title: FFEM_BdG_ddm_toolbox.zipCPC Library link to program files:https://doi.org/10.17632/w9hg964wpb.1Licensing provisions: GPLv3Programming language:FreeFEM (v 4.12) free software (www.freefem.org)Nature of problem: Among the plethora of configurations that may exist in Gross-Pitaevskii (GP) equations modeling one or two-component Bose-Einstein condensates, only the ones that are deemed spectrally stable (or even, in some cases, weakly unstable) have high probability to be observed in realistic ultracold atoms experiments. To investigate the spectral stability of solutions requires the numerical study of the linearization of GP equations, the latter commonly known as the Bogoliubov-de Gennes (BdG) spectral problem. The present software offers an efficient and reliable tool for the computation of eigenvalues (or modes) of the BdG problem for a given two- or three-dimensional GP configuration. Then, the spectral stability (or instability) can be inferred from its spectrum, thus predicting (or not) its observability in experiments.Solution method: The present toolbox in FreeFEM consists of the following steps. At first, the GP equations in two (2D) and three (3D) spatial dimensions are discretized by using P2 (piece-wise quadratic) Galerkin triangular (in 2D) or tetrahedral (in 3D) finite elements. For a given configuration of interest, mesh adaptivity in FreeFEM is deployed in order to reduce the size of the problem, thus reducing the toolbox's execution time. Then, stationary states of the GP equations are obtained by a Newton method whose backbone involves the use of a reliable and efficient linear solver judiciously selected from the PETSc1 library. Upon identifying stationary configurations, to trace branches of such solutions a parameter continuation method over the chemical potential in the GP equations (effectively controlling the number of atoms in a BEC) is employed with step-size adaptivity of the continuation parameter. Finally, the computation of the stability of branches of solutions (i.e. the BdG spectrum), is carried out by accurately solving, at each point in the parameter space, the underlying eigenvalue problem by using the SLEPc2 library. Three-dimensional computations are made affordable in the present toolbox by using the domain decomposition method (DDM). In the course of the computation, the toolbox stores not only the solutions but also the eigenvalues and respective eigenvectors emanating from the solution to the BdG problem. We offer examples for computing stationary configurations and their BdG spectrum in one- and two-component GP equations.Running time: From minutes to hours depending on the mesh resolution and space dimension.

Three-dimensional vortex and multipole quantum droplets in a toroidal potential

We investigate the existence, stability, and evolution dynamics of three-dimensional quantum droplets (QDs) in binary Bose–Einstein condensates trapped in a toroidal potential. The interplay of competing mean-field (MF) and beyond-MF nonlinear terms (attractive and repulsive ones) with the potential enables the formation of a variety of stable QDs with complex structures, from higher-order vortices and multipoles to necklace complexes. There are two branches of the vortex and multipole QDs with opposite slopes of the norm-vs.-chemical-potential curves. The upper-branch vortex QDs are completely stable, regardless of the value of their topological charge (winding number), m. On the other hand, multipole QDs are stable only near the turning point of the curves. Although the stability region shrinks with the growth of the number of poles, necklace-shaped QDs remain stable for the number up to 16. Applying a torque perpendicular to the original QD’s angular momentum, we observe stable precession of vortex QDs. Periodic rotation is also observed when multipole QDs are set in motion by a planar phase torque.