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Ring polymer self-consistent field theory is used to calculate the critical temperatures and heat capacities of an ideal Bose gas for an order of magnitude more particles than previously reported. A λ -transition indicative of Bose-Einstein condensation is observed as expected. Using a known proof of spatial mode entanglement in Bose-Einstein condensates, a relationship between boson exchange and quantum entanglement is established. This is done without the use of state vectors, since ring polymer quantum theory uses instead a thermal degree of freedom, sometimes called the “imaginary time”, to map classical statistical mechanics onto non-relativistic quantum mechanics through the theorems of density functional theory. It is shown that quantum phenomena, such as Bose-Einstein condensation, boson exchange, entanglement and contextuality, can be visualized in terms of merging and separating ring polymer threads in thermal-space. A possible extension to fermions is mentioned. [ABSTRACT FROM AUTHOR]

In this study, the effects of q-deformed Rosen–Morse potential, particle number and interaction types (two-body, three-body and higher-order (HO) interactions) on Bose–Einstein condensate (BEC) were investigated. The wave functions, which are the solutions of the Gross–Pitaevskii (GP) equation for different conditions, and energies with Shannon information entropies of the BEC systems were calculated, considering attractive interactions between particles. It is found that q-deformed potential values, particle number and interaction types have significant effects on the main dynamics of the systems, while it is found that the high number of particles in the system is more effective than the interactions between the particles, especially, HO interaction is the dominant factor rather than the q deformation value. Also, the change in the entire dynamics of the systems starts around q = 0.1 because the trap potential becomes anti-symmetric at this value. [ABSTRACT FROM AUTHOR]

Based on the dissipative Gross–Pitaevskii equation, effects of dissipation strength and interaction strength on the linear instability and the splitting processes of quadruply quantized vortices are studied. Using the linear perturbation theory to calculate out the elementary excitation modes of the quadruply quantized vortices, we reveal a novel and very important dynamical transition of the most unstable mode. It is found that the most unstable mode is the twofold rotational symmetry mode at a small dissipation strength, while it is the fourfold rotational symmetry mode at a larger dissipation strength. What's more, the transition dissipation strength decreases with the increase in the interaction strength. The full nonlinear numerical simulations further demonstrate the process of such a dynamical transition. Our work has shed light on the long-standing puzzle in Bose–Einstein condensate, why the fourfold rotational symmetry splitting pattern of quadruply quantized vortex has not yet been observed in the laboratory. We propose a promising direction to solve this problem by increasing the dissipation strength or the interaction strength. Our predictions are likely to be tested in the laboratory in the near future. [ABSTRACT FROM AUTHOR]

In this work, we consider the numerical computation of ground states and dynamics of single-component Bose–Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as Localized Orthogonal Decomposition (LOD). Despite the outstanding approximation properties of such a discretization in the context of BECs, taking full advantage of it without creating severe computational bottlenecks can be tricky. In this paper, we therefore present two fully-discrete numerical approaches that are formulated in such a way that they take special account of the structure of the LOD spaces. One approach is devoted to the computation of ground states and another one for the computation of dynamics. A central focus of this paper is also the discussion of implementation aspects that are very important for the practical realization of the methods. In particular, we discuss the use of suitable data structures that keep the memory costs economical. The paper concludes with various numerical experiments in 1d, 2d and 3d that investigate convergence rates and approximation properties of the methods and which demonstrate their performance and computational efficiency, also in comparison to spectral and standard finite element approaches. [ABSTRACT FROM AUTHOR]

The vortex distribution in rotating Bose-Einstein condensates (BEC) trapped in a potential composed of two-dimensional optical lattice and harmonic potential is studied by using the multigrid preconditioned conjugate gradient method, and the effects of the depth of the optical lattice, the lattice constant and the rotation frequency of the condensates on the vortex distribution in rotating condensates are discussed. The results show that due to the introduction of the optical lattices, vortices are generated in the condensates, and the vortices are located with the minimum value of the external potential. As the depth of the optical lattice increases, the condensates gather at the bottom of the optical lattice, forming a lattice-like distribution, in which the vortices form vortex pairs and merge to form larger vortices. When the lattice constant is small, the vortex distribution in BEC is similar to the Abrikosov vortex lattice. With the increase of the lattice constant, the distribution of vortices in the condensate becomes diversified, and a three-layer structure appears. When the rotation frequency of the condensates increases, the number of vortices in BEC increases, and the vortex distribution becomes more complex and varied. The density distribution range of the condensate also expands with the increase of the rotation frequency. When the rotation frequency of the condensate is close to the frequency of the harmonic potential, that is, when the condensate is at the lowest Landau level approximation, the number of vortices in the condensate increases dramatically, and the phenomenon of vortex combination and fusion appear, then a vortex pattern will be formed. [ABSTRACT FROM AUTHOR]

We investigate the properties of a double-path Josephson junction connected to Bose-Einstein condensate reservoirs. By comparing the current in the proposed setup with that in a similar system connected to superconductors, we elucidate the key differences between the two systems. The systems are influenced by the Aharonov-Bohm effect, Rashba spin-orbit interaction, and phase difference of order parameters between left and right leads. Utilizing the Keldysh formalism, it turns out that, in the system connected to Bose-Einstein condensate reservoirs, the Josephson current includes higher frequency components of the phase difference between left and right reservoirs. Additionally, the dependence of critical current on energy level does not show the complete symmetric resonance but the Fano-type resonance with single or double peaks. These differences result from the bosonic statistics of reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, we consider an energy-conserving continuous Galerkin discretization of the Gross–Pitaevskii equation with a magnetic trapping potential and a stirring potential for angular momentum rotation. The discretization is based on finite elements in space and time and allows for arbitrary polynomial orders. It was first analyzed by O. Karakashian and C. Makridakis (SIAM J. Numer. Anal. , 36(6) ,1779–1807, 1999) in the absence of potential terms and corresponding a priori error estimates were derived in |$2D$|⁠. In this work we revisit the approach in the generalized setting of the Gross–Pitaevskii equation with rotation and we prove uniform |$L^{\infty }$| -bounds for the corresponding numerical approximations in |$2D$| and |$3D$| without coupling conditions between the spatial mesh size and the time step size. With this result at hand, we are particularly able to extend the previous error estimates to the |$3D$| setting while avoiding artificial CFL conditions. [ABSTRACT FROM AUTHOR]

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Nonlinear feedback between the gauge field and the material field can yield novel quantum phenomena. Here, the interplay between a density-dependent artificial gauge field and Bose–Einstein condensates (BECs) trapped in an optical lattice is studied. The energy spectrum and superfluidity represented by energetic and dynamical stabilities of the system are systematically discussed. A density-dependent artificial gauge field with a back-action between the BECs dynamics and the gauge field induces an effective atomic interaction that depends on the quasi-momentum and density of the condensates, resulting in a symmetry-broken energy spectrum and exotic stability phase diagram, that is, the system is only stable in a certain range of atoms density and under a limited lattice strength. The density-dependent artificial gauge field changes the sequence for the emergence of energetic and dynamical instability and the regimes of the energetic and dynamical instabilities are significantly separated, offering an efficient way to examine the energetic and dynamical instabilities of superfluids separately. In particular, the density-dependent artificial gauge field, as a mechanism for transferring momentum to the fluid, results in dynamic instability of the condensates even in free space. Our results provide deep insights into the dynamical response of superfluid systems to gauge fields and have potential applications for the coherent control of exotic superfluid states. [ABSTRACT FROM AUTHOR]

We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross–Pitaevskii theory. Our primary focus is on a two-dimensional Bose–Einstein condensate with a non-local soft-core interaction, where the superfluid fraction is described by a rank-2 tensor. We then calculate the superfluid fraction tensor for crystalline states exhibiting triangular, square, and stripe geometries across a broad range of interaction parameters. Factors leading to an anisotropic superfluid fraction tensor are also considered. We also refine the Leggett bounds for the superfluid fraction of the 2D system. We systematically compare these bounds to our full numerical results, and other results in the literature. This work is of direct relevance to other supersolid systems of current interest, such as supersolids produced using dipolar Bose–Einstein condensates. [ABSTRACT FROM AUTHOR]

In this paper, we study-induced spin–orbit coupling (SOC) in one-dimensional ultracold quantum gases composed of atoms of different species. One species is subjected to an equal combination of Rashba and Dresselhaus SOC generated by Raman transition. The two species interact with each other through spin-independent and spin-exchange contact interactions. The spin-exchange interaction introduces a locking pattern of the momentum and spin degrees of freedom for the species without direct SOC. For small spin-independent interactions, the two species overlap and the induced SOC is effective. For large spin-independent interactions, however, the two species keep separate from each other and the induced SOC is negligible. We propose to generate inhomogeneous SOC by exploiting density engineering technique applied to the directly spin–orbit coupled Bose–Einstein condensate. When the effective potential is of Gaussian type, the single-particle eigenenergies and eigenstates are calculated by exact diagonalization method. For general cases, mean-field ground states are obtained by numerically searching for the minimum of energy functional. With the density engineering technique, it is possible to produce hybrid structures of plane wave, stripe and/or zero-momentum phases. [ABSTRACT FROM AUTHOR]

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while 'the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system. [ABSTRACT FROM AUTHOR]

The dynamics of an exciton–polariton Bose–Einstein condensate in an optical microcavity was considered. A novel version of the stochastic Gross–Pitaevskii equation was proposed to describe the condensate evolution under the non-Markovian interaction with the environment. The proposed version was used to analyze the condensate dynamics at various temperatures. The phase transition from the homogeneous to the fragmented state of the condensate near a temperature of 15 K was detected. This phase transition is accompanied by a sharp drop in the condensate density and a decrease in the correlation length. It was found that, at a temperature of 10 K, the correlation length oscillates with time. The results obtained indicated the necessity to take into account the non-Markovianity of the condensate interaction with the excitonic reservoir. [ABSTRACT FROM AUTHOR]

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by W ± or Z 0 gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. [ABSTRACT FROM AUTHOR]

In this article, we attempt to explore the dark sector of the universe i.e. dark matter and dark energy, where the dark energy components are related to the modified f(Q) Lagrangian, particularly a power law function f (Q) = γ Q Q 0 n , while the dark matter component is described by the Extended Bose–Einstein Condensate (EBEC) equation of state for dark matter, specifically, p = α ρ + β ρ 2 . We find the corresponding Friedmann-like equations and the continuity equation for both dark components along with an interacting term, specifically Q = 3 b 2 H ρ , which signifies the energy exchange between the dark sector of the universe. Further, we derive the analytical expression of the Hubble function, and then we find the best-fit values of free parameters utilizing the Bayesian analysis to estimate the posterior probability and the Markov Chain Monte Carlo (MCMC) sampling technique corresponding to CC+Pantheon+SH0ES samples. In addition, to examine the robustness of our MCMC analysis, we perform a statistical assessment using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Further from the evolutionary profile of the deceleration parameter and the energy density, we obtain a transition from the decelerated epoch to the accelerated expansion phase, with the present deceleration parameter value as q (z = 0) = q 0 = - 0. 56 - 0.03 + 0.04 ( 68 % confidence limit), that is quite consistent with cosmological observations. In addition, we find the expected positive behavior of the effective energy density. Finally, by examining the sound speed parameter, we find that the assumed theoretical f(Q) model is thermodynamically stable. [ABSTRACT FROM AUTHOR]

Palatini-like theories of gravity have a remarkable connection to models incorporating linear generalized uncertainty principles. Considering this, we delve into the thermodynamics of systems comprising both Bose and Fermi gases. Our analysis encompasses the equations of state for various systems, including general Fermi gases, degenerate Fermi gases, Boltzmann gases, and Bose gases such as phonons and photons, as well as Bose–Einstein condensates and liquid helium. [ABSTRACT FROM AUTHOR]

In this work we analyze the effective evolution of a one dimensional Bose-Einstein Condensate (BEC) within a semiclassical description of quantum systems based on expectation values of quantum dispersions and physical observables, known as momentous quantum mechanics. We show that the most prominent features and physical parameters of the system can be determined from the dynamics of the corresponding semiclassical system, consisting of an extended phase space including original classical observables and quantum dispersions, and we also show that particle trajectories for expectation values of observables are a particular characteristic in this framework. We also demonstrate that interactions with several potentials can be implemented in an intuitive way.

The dynamics of bosons in Josephson junctions have drawn much attention where the bosons are initially condensed. When interacting bosons tunnel back and forth along the junction, depletion and, eventually, fragmentation develop. Here, we pose the question how do fragmented bosons tunnel in a bosonic Josephson junction? To this end, we exploit the transverse degree-of-freedom of the junction to encode initial fragmentation to the bosonic cloud. We find rich many-body dynamics, which includes the speed up of the collapse of density oscillations and slow down of the revival process, by analyzing the survival probability along the junction, fluctuations of particle positions across the junction, and the occupancy of the lowest single-particle states. It is found that a fully fragmented state significantly accelerates the revival process compared to the conventional Bose–Einstein condensate. To explain the underlying many-body mechanism, we show that the initial fragmentation in the transverse direction interferes with the development of fragmentation in time along the junction. The magnitude of this interference is quantified by the transition from a decrease of occupation to build up of occupation in the first excited single-particle state. The interference mechanism is a purely many-body effect that does not occur in the mean-field dynamics. All in all, we show that the interference of longitudinal and transversal fragmentations leads to new rules for macroscopic tunneling phenomena of interacting bosons in traps.

Particle emission from a Bose‐Einstein condensate with periodically modulated interactions is investigated in a 1D lattice. Within perturbative analysis, which leads to instabilities for discrete modes, the main regimes are obtained where the system can emit a large particle jet, and the distinctly intermittent rather than continuous emission is found. The time evolution of the trapped particles exhibits a stair‐like decay, and a larger drive induces a more significant intermittency. This study further sheds light on the dynamics of the stimulating process, and demonstrates that instead of a real suspension, the intermittency represents a build‐up stage of the system. The theoretical framework might be generalized to the explorations on multiple‐site systems with analogous configurations and couplings, and offer new insights into other fundamental nonequilibrium problems. [ABSTRACT FROM AUTHOR]

In this work, we investigated a Bose–Einstein condensate (BEC) inside a Rydberg atom. We first observed the system's density profile using the Gross–Pitaevskii equation, and then we used the Bogoliubov theory to examine the collective excitation spectra. We have also extended our study by taking into account a hybrid of two BEC species. Again, for this new system, the density profile and the collective excitation are investigated in a similar manner. The results of the BEC for one species reveal that the Rydberg atom can trap the BEC and that the excitation curve moves upward with increasing Rydberg atom interaction. We have seen roton minima for two species of BEC, and the depth of the minima shifts with the Rydberg interaction. [ABSTRACT FROM AUTHOR]

The distribution of dark matter in four low surface brightness spiral galaxies is studied using two models within the scalar field theory of dark matter, an alternative to the cold dark matter paradigm. The first model is a Bose-Einstein condensate, in which bosons occupy the ground state at zero temperature. The second model includes finite temperature corrections to the scalar field potential, which allows the introduction of excited states. A nonlinear least squares approximation method is used to determine the free parameters of the models, including scale radius, characteristic (central) density and total mass, based on observational data of rotation curves. Quantitative analysis shows the importance of considering finite temperatures at the galactic level. In addition, the two models are compared with results from widely used and accepted phenomenological dark matter profiles such as the isothermal sphere, Navarro-Frank-White and Burkert profiles. The reliability of each model was assessed based on the Bayesian information criterion of completeness. Statistical analysis provides meaningful interpretation of the choice of a particular profile. Ultimately, this study contributes to a better understanding of the distribution of dark matter in low surface brightness spiral galaxies by shedding light on the performance of scalar field models compared to traditional phenomenological profiles. [ABSTRACT FROM AUTHOR]

In this paper, we consider the formation of vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles by numerical simulations of the Gross–Pitaevskii equation. Different dependencies of critical rotation frequency (CRF) and optical lattice height, vortex number, and rotation frequency are studied, depending on the direction of the dipole axis and dipole strength. Our results show that the CRF in z = 0 is minimum. When the optical lattice height is gradually increased, the CRF decreases gradually. Reducing of dipole strength in anisotropic dipole–dipole interaction (DDI) favours the formation of vortices, and such decline in isotropic DDI hinders the creation of vortices. The reason for this difference is that the repulsive interaction is favorable and the attractive interaction is disadvantageous for the vortex formation. In addition, we study the first-order correlation function and focus on variation of coherence. For small rotation frequency, the break of coherence occurs earlier in the case of purely repulsive interaction. With an increase in rotation frequency, the coherence concurrently disappears in layer z = 2. Moreover, we also investigate the quenched dynamics, showing that the increase of angular momentum is induced by changing the direction of dipoles and in this process the vortex number remains unchanged. [ABSTRACT FROM AUTHOR]

The production of quantised vortices having diverse structures is the remarkable effect of rotating Bose–Einstein condensates (BEC). Vortex formation described by the mean-field theory is valid only in the regime of weak interactions. The exploration of the rich and diverse physics of strongly interacting BEC requires a more general approach. This study explores the vortex states of strongly interacting and rapidly rotating BEC from a general ab-initio many-body perspective. We demonstrate that the quantised vortices form various structures that emerge from an intricate interplay between the angular momentum and many-body interaction. We examine the distinct impact of the angular velocity and interaction energy on the vortex formation. Our analysis shows that, while the angular rotation generally augments the vortex formation, the interactions can enhance as well as impede the vortex production. [ABSTRACT FROM AUTHOR]

Theories on the bosonic nature of dark matter are a promising alternative to the cold dark matter model. Here we consider a dark matter halo in the state of a Bose–Einstein condensate (BEC), subject to the gravitation of a black hole. In the low energy limit, we bring together the general relativity in the Schwarzschild metric and the quantum description of the BEC. The model is solvable in the Fermi normal coordinates with the so called highly nonlocal approximation and describes tidal deformations in the condensate wave function. The black hole deforms the localized condensate until the attraction of the compact object overcomes the self-gravitation and destabilizes the solitonic dark matter. Moreover, the model can be implemented as a gravitational analog in the laboratory; the time-dependent potential generated by the galactic black hole can be mimicked by an optical trap acting on a conventional condensate. The results open the way to new laboratory simulators for quantum gravitational effects. [ABSTRACT FROM AUTHOR]

We report on a numerical study of the critical velocity for creation of quantized vortices by a moving Gaussian obstacle in a trapped Bose–Einstein condensate, modeled by the Gross–Pitaevskii equation. We pay attention to impact of density inhomogeneity associated with the global inverted parabolic profile by a trapping potential as well as the local density suppression around the Gaussian obstacle. When the width of the Gaussian potential is large, the wake dynamics is significantly influenced by the nonuniformity around the obstacle potential. The critical velocity, estimated through the time interval between the first and second vortex emission, can be explained by the local sound velocity by taking into account the above two contributions. We find that the ratio of the critical velocity for vortex creation to the sound velocity at the center of the system is minimally influenced by the nonlinear coefficient in the Gross–Pitaevskii equation. This result implies that the analysis in the homogeneous system is directly applicable to the inhomogeneous trapped condensates under the local density approximation. [ABSTRACT FROM AUTHOR]

We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.

By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices. [ABSTRACT FROM AUTHOR]

In this work we analyze the effective evolution of a one dimensional Bose-Einstein Condensate (BEC) within a semi-classical description of quantum systems based on expectation values of quantum dispersions and physical observables, known as momentous quantum mechanics. We show that the most prominent features and physical parameters of the system can be determined from the dynamics of the corresponding semiclassical system, consisting of an extended phase space including original classical observables and quantum dispersions, and we also show that particle trajectories for expectation values of observables are a particular characteristic in this framework. We also demonstrate that interactions with several potentials can be implemented in an intuitive way. [ABSTRACT FROM AUTHOR]

In the last decade, different theoretical methods for entanglement generation between distant BEC qubits (macroscopic cold atomic ensembles) were proposed. However, experimental realization of such states is still challenging beside some special cases. The most theoretically investigated entangled states between macroscopic BECs are nonmaximally entangled states obtained with entangling Hamiltonian. With the use of such states, the protocols for quantum teleportation, remote state preporation and many others were developed for macroscopic qubits on the basis of BECs. Here we show that it is possible to obtain such states with the use of the bosonic analog of Hamiltonian and the methods of quantum optimal control. We compare performance of this scheme in the meaning of fidelity and entanglement for different drift and control Hamiltonians. We use the well-established QuTip open python library for all calculations. [ABSTRACT FROM AUTHOR]

We investigate the steady-state multi-stability in a cavity system containing spin–orbit coupled Bose–Einstein condensate and driven by a strong pump laser. The applied magnetic field splits the Bose–Einstein condensate into pseudo-spin states, which then become momentum sensitive with two counter propagating Raman lasers directly interacting with ultra-cold atoms. After governing the steady-state dynamics for all associated subsystems, we show the emergence of multi-stable behavior of cavity photon number, which is unlike previous investigation on cavity-atom systems. However, this multi-stability can be tuned with associated system parameters. Furthermore, we illustrate the occurrence of mixed-stability behavior for atomic population of the pseudo-spin- ↑ and spin- ↓ states, which appear in so-called bi-unstable form. The collective behavior of these atomic number states interestingly possesses a population transitional phase (or population equilibrium intersection) among both of the spin states, which can be enhanced and controlled by spin–orbit coupling and Zeeman field effects. Additionally, we illustrate the emergence of another equilibrium intersection mediated by the increase in mechanical dissipation rate of the pseudo-spin states. These equilibrium intersections or population transitional phase could be caused by the non-trivial behavior of synthetic spin state mediated by cavity. Our findings are not only crucial for the subject of optical switching but also could provide a foundation for future studies on mechanical aspect of synthetic atomic states with cavity quantum electrodynamics. [ABSTRACT FROM AUTHOR]

Split-step quintic B-spline collocation (SS5BC) methods are constructed for nonlinear Schrödinger equations in one, two and three dimensions in this paper. For high dimensions, new notations are introduced, which make the schemes more concise and achievable. The solvability, conservation and linear stability are discussed for the proposed methods. Numerical tests are carried out, and the present schemes are numerically verified to be convergent with second-order in time and fourth-order in space. The conserved quantity is also computed which agrees with the exact one. And solitary waves in one, two and three dimensions are simulated numerically which coincide with the exact ones. The SS5BC scheme is compared with the split-step cubic B-spline collocation (SS3BC) method in the numerical tests, and the former scheme is more efficient than the later one. Finally, the SS5BC scheme is also applied to compute Bose-Einstein condensates.

Palatini-like theories of gravity have a remarkable connection to models incorporating linear generalized uncertainty principles. Considering this, we delve into the thermodynamics of systems comprising both Bose and Fermi gases. Our analysis encompasses the equations of state for various systems, including general Fermi gases, degenerate Fermi gases, Boltzmann gases, and Bose gases such as phonons and photons, as well as Bose–Einstein condensates and liquid helium.

The spin degrees of freedom in multicomponent Bose–Einstein condensates allow for various types of topological excitations, such as skyrmions and knots. Systems with high spins offer a broader range of internal symmetries. For instance, in spin-1 Bose–Einstein condensates, one can observe not only the two-dimensional (2D) skyrmion spin texture but also the bimeron spin texture. However, it remains challenging to experimentally create or stabilize a bimeron and identify the conditions that facilitate its formation. In this context, our research predicts a novel form of topological structure known as the domain wall bimeron in ferromagnetic spin-1 Bose–Einstein condensates by manipulating the magnetic field. Unlike conventional 2D skyrmions, this unique bimeron exhibits a non-axisymmetric spin texture and features complex off-axis vortices whose cores are connected by domain walls. This work significantly contributes to the study of 2D topological excitations in quantum matter with high spins.

We report on the design and the construction of a sounding rocket payload capable of performing atom interferometry with Bose-Einstein condensates of 41 K and 87 Rb. The apparatus is designed to be launched in two consecutive missions with a VSB-30 sounding rocket and is qualified to withstand the expected vibrational loads of 1.8 g root-mean-square in a frequency range between 20–2000 Hz and the expected static loads during ascent and re-entry of 25 g. We present a modular design of the scientific payload comprising a physics package, a laser system, an electronics system and a battery module. A dedicated on-board software provides a largely automated process of predefined experiments. To operate the payload safely in laboratory and flight mode, a thermal control system and ground support equipment has been implemented and will be presented. The payload presented here represents a cornerstone for future applications of matter wave interferometry with ultracold atoms on satellites. [ABSTRACT FROM AUTHOR]

The Kompaneets equation governs dynamics of the photon energy spectrum in certain high temperature (or low density) plasmas. We prove several results concerning the long time convergence of solutions to Bose--Einstein equilibria and the failure of photon conservation. In particular, we show the total photon number can decrease with time via an outflux of photons at the zero-energy boundary. The ensuing accumulation of photons at zero energy is analogous to Bose-Einstein condensation. We provide two conditions that guarantee that photon loss occurs, and show that once loss is initiated then it persists forever. We prove that as t → ∞, solutions necessarily converge to equilibrium and we characterize the limit in terms of the total photon loss. Additionally, we provide a few results concerning the behavior of the solution near the zero-energy boundary, an Oleinik inequality, a comparison principle, and show that the solution operator is a contraction in L¹. None of these results impose a boundary condition at the zero-energy boundary. [ABSTRACT FROM AUTHOR]

This paper will focus on theoretical treatment of the dynamic of the Bose-Einstein Condensate (BEC) systems contained different external trapping potentials. We construct the phase space diagrams and Lyapunov Characteristic Exponents (LCEs) for master and slave systems depended on the system parameters and propose a nonlinear control for the synchronization of systems in their chaotic states. The synchronization is obtained in master-slave scheme for different initial values. Numerical results are also given to show the efficiency of the used control technique. [ABSTRACT FROM AUTHOR]

Mutual friction caused by scattering of thermal excitations by quantized vortices is a phenomenon of key importance for the understanding of vortex dynamics and quantum turbulence in finite-temperature superfluids. The article reviews theoretical, numerical, and experimental results obtained during the last 40 years in the study of mutual friction in bosonic superfluids such as 4 He and Bose–Einstein condensates. Among several research topics reviewed in this article particular attention is paid to the development of theory and numerical analysis of roton-vortex interactions and mutual friction in superfluid helium; an application of the two-fluid model for the analysis of the flow in the vicinity of the vortex core and the calculation of the longitudinal and transverse forces exerted on a vortex; vortex diffusivity in 4 He films; and theoretical, numerical, and experimental studies of thermal dissipation and mutual friction in finite-temperature Bose–Einstein condensates. [ABSTRACT FROM AUTHOR]

The use of Rydberg dressing technology to achieve long-range soft-core interaction in Bose–Einstein condensates (BECs) opens up new avenues for exploration of supersolid and its related phenomenon. We investigate the ground state of a two-component spin–orbit-coupled BECs with both long-range soft-core and contact interactions in radially periodic potentials. Our results show that the ground-state structures of the system are strongly influenced by spin–orbit coupling, contact interactions, long-range soft-core interactions, and the amplitude of the external potential. We find that such parameters can been used to induce desired ground-states structures, such as necklace structure of lump, striped standing wave, and especially ring dark soliton. Furthermore, we observe that the long-range soft-core interactions are used to manipulate the transition between miscible-immiscible phases like contact interactions. Our research provides another degree of freedom for manipulating supersolids in spin–orbit-coupled BECs. [ABSTRACT FROM AUTHOR]

The modulation instabilities of continuous-wave states in spin-1 Bose-Einstein condensates under spin tensor-momentum couplings are investigated. With the help of the dispersion relation between perturbation frequency and wavenumber, we find that the modulation instability of the system can be adequately described by six unequal branches. Further analysis shows that, for a given Raman coupling strength and atom-atom interaction strength, the modulation instability growth rate distribution in momentum space is symmetric about k=0 and can be characterized by several different instability bands. We also calculate the growth rate of modulation instability in spin-orbit coupled spin-1 Bose-Einstein condensates under the same parameter conditions and compare with the former results. Besides the different number of bands and band intensities, the modulation instability of Bose-Einstein condensates with spin-orbit coupling is actually only related to three unequal branches, which stem from its different symmetries of the single-particle Hamiltonian of a spin-tensor-momentum coupled BEC system. These results not only contribute to the understanding of the nonlinear dynamic properties of the ground state, but also to the analysis of possible nonlinear excitations in the system. [ABSTRACT FROM AUTHOR]

Split-step quintic B-spline collocation (SS5BC) methods are constructed for nonlinear Schrödinger equations in one, two and three dimensions in this paper. For high dimensions, new notations are introduced, which make the schemes more concise and achievable. The solvability, conservation and linear stability are discussed for the proposed methods. Numerical tests are carried out, and the present schemes are numerically verified to be convergent with second-order in time and fourth-order in space. The conserved quantity is also computed which agrees with the exact one. And solitary waves in one, two and three dimensions are simulated numerically which coincide with the exact ones. The SS5BC scheme is compared with the split-step cubic B-spline collocation (SS3BC) method in the numerical tests, and the former scheme is more efficient than the later one. Finally, the SS5BC scheme is also applied to compute Bose-Einstein condensates. [ABSTRACT FROM AUTHOR]

Abstract The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.

Schrödinger cat states, consisting of superpositions of macroscopically distinct states, provide key resources for a large number of emerging quantum technologies in quantum information processing. Here we propose how to generate and manipulate mechanical and optical Schrödinger cat states with distinguishable superposition components by exploiting the unique properties of cavity optomechanical systems based on Bose-Einstein condensate. Specifically, we show that in comparison with its solid-state counterparts, almost a 3 order of magnitude enhancement in the size of the mechanical Schrödinger cat state could be achieved, characterizing a much smaller overlap between its two superposed coherent-state components. By exploiting this generated cat state, we further show how to engineer the quadrature squeezing of the mechanical mode. Besides, we also provide an efficient method to create multicomponent optical Schrödinger cat states in our proposed scheme. Our work opens up a new way to achieve nonclassical states of massive objects, facilitating the development of fault-tolerant quantum processors and sensors.