Bose-Einstein Condensate Research Articles

New Approach to the Formation of a Bose–Einstein Condensate

New Approach to the Formation of a Bose–Einstein Condensate

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 an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by 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 the 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.

Bayesian optimization for state engineering of quantum gases

Abstract State engineering of quantum objects is a central requirement for precision sensing and quantum computing implementations. When the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have been theoretically proposed and experimentally realized. For more complex systems such as interacting quantum gases, simplifying assumptions do not apply anymore and the optimization techniques become computationally impractical. Here, we propose Bayesian optimization based on multi-output Gaussian processes to learn the physical properties of a Bose-Einstein condensate within few simulations only. We evaluate its performance on an optimization study case of diabatically transporting the quantum gas while keeping it in its ground state. Within a few hundred executions, we reach a competitive performance to other protocols. While restricting this benchmark to the well known Thomas-Fermi approximation for straightforward comparisons, we expect a similar performance when employing more complex theoretical models, which would be computationally more challenging, rendering standard optimal control theory protocols impractical. This paves the way for efficient state engineering of complex quantum systems including mixtures of interacting gases or cold molecules.

Extracting work from coherence in a two-mode Bose-Einstein condensate

Extracting work from coherence in a two-mode Bose-Einstein condensate

Relativistic BEC extracted from a complex FRG flow equation

Abstract Based on the functional renormalization group (FRG) under the local potential approximation, we analyze the Bose-Einstein condensation (BEC) in the relativistic complex scalar theory. This framework leads to a complex flow equation of the effective potential, even with the well-known Litim regulator. In order to evaluate the condensate from such a complex effective potential, we impose a condition between chemical potential and mass, analogously to those in the free theory or the mean field theory. We elucidate that for the strongly (weakly) coupled theory, the phase diagrams computed from the FRG are more (less) deviated from that under the mean field approximation. This result implies that quantum fluctuations strongly affect the nonperturbative formation of the BEC.

Modulational instability for a cubic-quintic model of coupled Gross-Pitaevskii equations with residual nonlinearities

Abstract We demonstrate the existence of modulational instability (MI) in both trapped miscible and immiscible two component Bose-Einstein condensates. The study is addressed theoretically and numerically in the framework of one-dimensional coupled Gross-Pitaevskii equations incorporating intra- and interspecies cubic-quintic nonlinearities with higher order ones. Using the time-dependent variational approach, we derive the new Euler-Langrange equations for the time evolution of the phase and amplitude of the modulational perturbation as well as the effective potential and the instability criteria of the system. We examine the effects of higher-order nonlinearities on the instability dynamics of the condensates. We show that the modulational properties of the chosen wave numbers are significantly modified. Direct numerical simulations run by the split step Fourier method confirm the analytical predictions.

Transfer of solitons and half-vortex solitons via adiabatic passage

We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024

Analogous Hawking Radiation in Dispersive Media

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.

The fate for the interior content of a Black Hole from one-quarter entropy area-law

In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature Ti, proportional to the Bekenstein-Hawking one, is such that Ti→0. As a consequence, according to other similar proposals in the literature, only a kind of Bose Einstein condensate (BEC) can exactly support the black hole entropy.

Ground States of Two-Component Bose–Einstein Condensates with Josephson Junction: The Endpoint Cases

Ground States of Two-Component Bose–Einstein Condensates with Josephson Junction: The Endpoint Cases

Abundant vortex dynamics in spin-1 Bose–Einstein condensates induced by Rashba spin–orbit coupling

The paper studies the dynamics of vortices evolved from the ring dark solitons (RDSs) in spin-1 Bose–Einstein condensates with Rashba spin–orbit coupling (SOC). We find that the SOC induces abundant vortex dynamic phenomena, and the numbers of vortex dipoles and lump-like solitons are all determined by the initial depths’ weighted average of the three components of RDSs. For a shallow RDS, the ring first expands and then contracts into a mini RDS, eventually evolving into late vortex dipoles. For the RDS with a moderate initial depth, during the contraction of the ring, it evolves into early vortex dipoles or lump-like solitons, and they evolve back into the mini RDS, which then evolves into late vortex dipoles during the expansion process. For the deep and black RDSs, the early vortex dipoles continue to transform between vortex dipoles and lump-like solitons without forming mini RDS. The motions of vortices mentioned above have a higher disorder degree than that in the system without SOC, because the SOC breaks the mirror symmetry of the condensate. Finally, we reveal that the SOC strength only influences the number of late vortex dipoles, while it does not affect the number of early vortex dipoles and lump-like solitons. Stronger SOC intensity results in a shallower critical depth, and vortices form only at or beyond this depth.

Dynamic instabilities and turbulence of merged rotating Bose–Einstein condensates

We present the simulation results of merging harmonically confined rotating Bose–Einstein condensates in two dimensions. Merging of the condensate is triggered by positioning the rotation axis at the trap minima and moving both condensates toward each other while slowly ramping their rotation frequency. We analyze the dynamics of the merged condensate by letting them evolve under a single harmonic trap. We systematically investigate the formation of solitonic and vortex structures in the final, unified condensate, considering both nonrotating and rotating initial states. In both cases, merging leads to the formation of solitons that decay into vortex pairs through snake instability, and subsequently, these pairs annihilate. Soliton formation and decay-induced phase excitations generate sound waves, more pronounced when the merging time is short. We witness no sound wave generation at sufficiently longer merging times that finally leads to the condensate reaching its ground state. With rotation, we notice off-axis merging (where the rotation axes are not aligned), leading to the distortion and weakening of soliton formation. The incompressible kinetic energy spectrum exhibits a Kolmogorov-like cascade [E(k)∼k−5/3] in the initial stage for merging condensates rotating above a critical frequency and a Vinen-like cascade [E(k)∼k−1] at a later time for all cases. Our findings hold potential significance for atomic interferometry, continuous atomic lasers, and quantum sensing applications.

Optically Tuned Soliton Dynamics in Bose-Einstein Condensates within Dark Traps

Abstract This study investigates the formation and dynamics of solitons in Bose-Einstein condensates (BECs) within dark traps generated by two crossed Laguerre-Gaussian (LG) beams with varying azimuthal indices $\ell$. As the index $\ell$ increases, the potential transitions from a harmonic trap when $\ell = 1$ a square-well potential for larger values of $\ell$. This transition allows us to study a range of soliton dynamics under different confinement conditions while maintaining the same BEC volume.
Through the derivation of the Gross-Pitaevskii equation (GPE) and under these specific conditions in both one-dimensional (1D) and two-dimensional (2D) configurations, we explore the dynamics of solitons across multiple scenarios. The study examines two primary methods for solitons generation: the temporal modulation of the scattering length and the implementation of an initial potential barrier that is subsequently removed. The results indicate that the trap shape plays a critical role in the generation and interaction dynamics of solitons. In harmonic traps, solitons exhibit a behavior different from those observed in anharmonic traps, where the dynamics is significantly influenced by the azimuthal index of the trap. The ability to control soliton dynamics in BECs holds significant promise for applications in quantum technologies, precision sensing, and the exploration of fundamental quantum phenomena.

Neutrinoless double beta decay without vacuum Majorana neutrino mass

We present a proof-of-concept extension to the Standard Model that can generate a non-vanishing neutrinoless double beta decay (0νββ) signal without the existence of Majorana neutrinos or lepton number violation in the zero-density vacuum-ground-state Lagrangian. We propose that the 0νββ can be induced by the capture of an ultralight scalar field, a potential dark matter candidate, that carries two units of lepton number. This makes the observable 0νββ spectrum indistinguishable from the usual 0νββ mechanisms by any practical means. We find that a non-zero 0νββ rate does not require neutrinos to be fundamentally Majorana particles. However, for sizeable decay rates within the range of next-generation experiments, the neutrino will, generally, acquire an (effective) Majorana mass as the scalar field undergoes a transition to the Bose-Einstein condensate phase. We also discuss the distinction between the aforementioned scenario and the case in which the emission of a lepton-number-two scalar leads to 0νββ, exhibiting discernible qualitative features that make it experimentally distinguishable from the conventional scenario.

Quantum effect in a hybrid bose-einstein condensate opto-magnomechanical system

Abstract We present a hybrid opto-magno-mechanical cavity system consisting of an optical cavity that creates an opto-mechanical cavity with a fixed mirror, a magnon mode in a ferrimagnetic crystal linked to the movable mirror and an intracavity Bose–Einstein condensate. The mechanical displacement is coupled to the magnon by the magnetostriction force and to the optical cavity by the radiation pressure, and the latter is also weakly coupled to a Bose–Einstein condensate. We provide a strategy to measure and quantify entanglement using logarithmic negativity. In addition, we study the quantum or EPR steering in order to present the stationary quantum steering. We consider that all composite modes in our model are given in a Gaussian state described by a covariance matrix. In these studies, we focus on the interaction between the Bose–Einstein condensate and the magnonic modes in a ferrimagnetic crystal. It is important to note that we use experimentally controllable realizable parameters to observe the interaction of modes at temperatures in the microkelvin range.

Three-component soliton states in spinor F = 1 Bose-Einstein condensates with PT-symmetric generalized Scarf-II potentials

Abstract Introducing PT-symmetric generalized Scarf-II potentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seeking stable soliton states in quasi-one-dimensional spin-1 Bose-Einstein condensates. In scenarios where the spin-independent parameter c_0 and the spin-dependent parameter c_2 vary, we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-II potentials. We obtain analytical soliton states and find that simply modulating c_2 may change the analytical soliton states from unstable to stable. Additionally, we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations, exhibiting distinct behavior in energy exchange. For further investigation, we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components. These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.

Mirror symmetry breaking of superradiance in a dipolar Bose-Einstein condensate

Dicke superradiance occurs when two or more emitters cooperatively interact via the electromagnetic field. This collective light-scattering process has been extensively studied across various platforms, from atoms to quantum dots and organic molecules. Despite extensive research, the precise role of direct interactions between emitters in superradiance remains elusive, particularly in many-body systems where the complexity of interactions poses significant challenges. In this study, we investigate the effect of dipole-dipole interaction between 18 000 atoms in dipolar Bose-Einstein condensates (BECs) on the superradiance process. In dipolar BECs, we simplify the complex effect of anisotropic magnetic dipole-dipole interaction with Bogoliubov transformation. We observe that anisotropic Bogoliubov excitation breaks the mirror symmetry in decay modes of superradiance. Published by the American Physical Society 2024

Dynamic of bifurcation, chaotic structure and multi soliton of fractional nonlinear Schrödinger equation arise in plasma physics

In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such systems, the researched model captures the physical and mathematical properties of nonlinear dispersive waves, with applications in plasma physics and optics. With the aid of above mentioned approach, we rigorously assess the novel optical soliton solutions in the form of dark, bright–dark, dark–bright, periodic, singular, rational, mixed trigonometric and hyperbolic forms. Additionally, stability assessments using conserved quantities, such as Hamiltonian property, and consistency checks were used to validate the solutions. The dynamic structure of the governing model is further examined using chaos, bifurcation, and sensitivity analysis. With the appropriate parameter values, 2D, 3D, and contour plots can all be utilized to graphically show the data. This work advances our knowledge of nonlinear wave propagation in Bose–Einstein condensates, ultrafast fibre optics, and plasma physics, among other areas with higher-order chromatic effects.

Stability and sensitivity of interacting fermionic superfluids to quenched disorder

The microscopic pair structure of superfluids has profound consequences on their properties. Delocalized pairs are predicted to be less affected by static disorder than localized pairs. Ultracold gases allow tuning the pair size via interactions, where for resonant interaction superfluids show largest critical velocity, i.e., stability against perturbations. The sensitivity of such fluids to strong, time-dependent disorder is less explored. Here, we investigate ultracold, interacting Fermi gases across various interaction regimes after rapid switching optical disorder potentials. We record the ability for quantum hydrodynamic expansion of the gas to quantify its long-range phase coherence. Contrary to static expectations, the Bose-Einstein condensate (BEC) exhibits significant resilience against disorder quenches, while the resonantly interacting Fermi gas permanently loses quantum hydrodynamics. Our findings suggest an additional absorption channel perturbing the resonantly interacting gas as pairs can be directly affected by the disorder quench.

Fractional-order effects on the dynamics and lifetime of ring dark solitons in spin–orbit coupled spin-1 Bose–Einstein condensate

Fractional-order effects on the dynamics and lifetime of ring dark solitons in spin–orbit coupled spin-1 Bose–Einstein condensate