Bose-Einstein Condensate Research Articles

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

Understanding dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses

Abstract Phase transitions in nonequilibrium dynamics of many body quantum systems, 
known as dynamical phase transitions (DPTs), play an important role for understanding
various dynamical phenomena observed in different branches of physics.
In general, there are two types of DPTs, the first one is characterized by 
distinct evolutionary behaviors of a physical observable, while the second one is marked by 
the vanishing overlap between the time-evolved and initial states. 
Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives 
in a spinor Bose-Einstein condensate (BEC), an ideal platform for
investigating nonequilibrium dynamics.
Utilizing the sudden quench process, we demonstrate that the system exhibits 
both types of DPTs as the control parameter is quenched through
the critical value, referring to as the critical quenching. 
We show analytically how to determine the critical quenching via
the semiclassical approach and carry out a detailed examination of both semiclassical 
and quantum signatures of DPTs. 
In particular, we reveal that the occurrence of DPTs is triggered by
the separatrix in the underlying semiclassical system.
Our findings offer deeper insights into the properties of DPTs and verify the usefulness 
of semiclassical analysis for studying DPTs in quantum systems 
with well-defined semiclassical limit. 

Composite cores of monopoles and Alice rings in spin-2 Bose-Einstein condensates

We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration. Published by the American Physical Society 2024

Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

Two-dimensional quantum droplets in binary quadrupolar condensates

Abstract We study the stability and characteristics of two-dimensional (2D) quasi-isotropic quantum droplets (QDs) of fundamental and vortex types, formed by binary Bose-Einstein condensate with magnetic quadrupole-quadrupole interactions (MQQIs). The magnetic quadrupoles are built as pairs of dipoles and antidipoles polarized along the x-axis. The MQQIs are induced by applying an external magnetic field that varies along the x-axis. The system is modeled by the Gross-Pitaevskii equations including the MQQIs and Lee-Huang-Yang correction to the mean-field approximation. Stable 2D fundamental QDs and quasi-isotropic vortex QDs with topological charges S ≤ 4 are produced by means of the imaginary-time-integration method for configurations with the quadrupoles polarized parallel to the system’s two-dimensional plane. Effects of the norm and MQQI strength on the QDs are studied in detail. Some results, including an accurate prediction of the effective area, chemical potential, and peak density of QDs, are obtained in an analytical form by means of the Thomas-Fermi approximation. Collisions between moving QDs are studied by means of systematic simulations.

Bright solitons and interaction in the higher-order Gross-Pitaevskii equation investigated with Hirota's bilinear method

In this paper, we investigate bright solitons and their interactions in trapless Bose-Einstein condensate described by a one-dimensional Gross-Pitaevskii equation in the presence of higher-order nonlinearity. By constructing appropriate Hirota bilinear form of the problem, we derive the one- and two-bright soliton solutions where the effects of the higher-order interaction term are discussed in details. The profile of different solutions obtained clearly presents the phenomenon of soliton interaction that embodies the properties of soliton. It also highlights the impact of higher-order interactions that plays the role of wave amplification/compression resulting from the condensate. The theoretical results confirm that Hirota bilinear method is an efficient and interesting tool for the analysis of nonlinearity in physical science. In addition, the higher-order interactions have significant effects on the stabilization process of Bose-Einstein condensates.

Ground-state phases and collective modes of supersolid spin-orbit-coupled Bose-Einstein condensates

Ground-state phases and collective modes of supersolid spin-orbit-coupled Bose-Einstein condensates

Quantum control of classical motion: piston dynamics in a Rabi-coupled Bose-Einstein condensate

Abstract We develop a model and explore the dynamics of a hybrid classical-quantum system consisting of a classical piston and a self-interacting pseudospin 1/2 Bose-Einstein condensate with a time-dependent Rabi coupling. We investigate the mechanical work produced by the piston moving as a result of the quantum pressure of the condensate. The time-dependent Rabi field redistributes the condensate density between the spin components and, as a result, causes a time-dependent pressure acting on the piston. Correspondingly, the motion of the piston produces quantum evolution of the condensate mass- and spin density profiles. We show how by optimised design of the time-dependent direction of the Rabi field based on a quasi-stationary quantum pressure approximation, one can control both the position and velocity of the piston.

Neural-network quantum states for ultra-cold Fermi gases

Ultra-cold Fermi gases exhibit a rich array of quantum mechanical properties, including the transition from a fermionic superfluid Bardeen-Cooper-Schrieffer (BCS) state to a bosonic superfluid Bose-Einstein condensate (BEC). While these properties can be precisely probed experimentally, accurately describing them poses significant theoretical challenges due to strong pairing correlations and the non-perturbative nature of particle interactions. In this work, we introduce a Pfaffian-Jastrow neural-network quantum state featuring a message-passing architecture to efficiently capture pairing and backflow correlations. We benchmark our approach on existing Slater-Jastrow frameworks and state-of-the-art diffusion Monte Carlo methods, demonstrating a performance advantage and the scalability of our scheme. We show that transfer learning stabilizes the training process in the presence of strong, short-ranged interactions, and allows for an effective exploration of the BCS-BEC crossover region. Our findings highlight the potential of neural-network quantum states as a promising strategy for investigating ultra-cold Fermi gases.

Nonequilibrium dynamics of two-component Bose gas with tunable Rydberg interactions: From ring dark soliton to self-structured pattern formation

We explore the nonequilibrium dynamics of ring dark solitons in a two-dimensional binary Bose–Einstein condensate with tunable Rydberg interactions by numerical simulation of the time-dependent Gross–Pitaevskii equation. Our results show that both the vortex dynamics and self-structured pattern formation show strong dependence on the periodic modulation of Rydberg interactions. For the cases without periodic modulation of the interactions, or the periodic modulation part is almost equal to the fixed part, the system exhibits exotic vortex dynamics without self-structured pattern formation. Finally, the effect of periodically varying Rydberg interactions on the lifetime of ring dark soliton is also considered.

Superfluid fraction tensor of a two-dimensional supersolid

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.

Axion dark matter

Axions have a double motivation: they solve the ‘strong CP problem’ of the Standard Model of elementary particles and they are a candidate for the dark matter of the Universe. Dark matter axions can be detected on Earth by converting them to photons in an electromagnetic cavity permeated by a strong magnetic field. A signal in such a detector, called an axion haloscope, would immediately reveal the velocity spectrum of dark matter axions on Earth in great detail. This prospect motivated the study of the special properties that axions have in large scale structure formation. It is shown that cold dark matter axions thermalize through their gravitational self-interactions, and form a Bose-Einstein condensate. As a result, axion dark matter behaves differently from the other proposed forms of dark matter. The differences are observable.

Ground state of two-species spin–orbit-coupled in mass-imbalanced Bose condensates

In this paper, we study the ground state of two-component spin–orbit-coupled (SOC) Bose–Einstein condensates with mass imbalance. Our results are based on the framework of mean-field Gross–Pitaevskii theory. The effects of unequal atomic mass and SOC strength are studied. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. Different density structures such as heliciform stripes, linear stripes and string vortex chains are found. With the increase of SOC strength, the azimuthal phase separation is kept while radial phase separation is broken. In addition, increasing the mass ratio is unfavorable to vortex formation, whereas more vortices can be generated by increasing the SOC strength. We also discuss the physical quantities such as angular momentum per atom and spin polarisation, for a larger mass ratio, showing that angular momentum gets a little bigger as the SOC strength increases and the first-order phase transition does not exist.

Bose-Einstein condensation of non-ground-state caesium atoms

Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology and quantum computing. For stability reasons, in the majority of cases the energetically lowest-lying atomic spin state is used. Here, we report the Bose-Einstein condensation of caesium atoms in the Zeeman-excited mf = 2 state, realizing a non-ground-state Bose-Einstein condensate with tunable interactions and tunable loss. We identify two regions of magnetic field in which the two-body relaxation rate is low enough that condensation is possible. We characterize the phase transition and quantify the loss processes, finding unusually high three-body losses in one of the two regions. Our results open up new possibilities for the mixing of quantum-degenerate gases, for polaron and impurity physics, and in particular for the study of impurity transport in strongly correlated one-dimensional quantum wires.

Excitation and manipulation of recurring rogue waves via nonlinear compression

We theoretically propose a feasible scheme to generate high-density waves and manipulate them quantitatively. We show that a wave with greater density compression called “recurring rogue wave” can be excited by first generating a rogue wave via quenching and Gaussian space modulation techniques followed by employing a nonlinear compression method. The formation of recurring rogue wave is verified to be a consequence of the combined interaction of nonlinear compression and “self compression”. We find that the maximal density of recurring rogue wave exhibits a nonmonotonic dependence on compression time, which allows us to manipulate recurring rogue waves quantitatively through changing compression time and modulation parameters within a certain range. The analytical results based on variational method qualitatively support the numerical simulation results. Our study provides potential strategies for efficiently generating high-density waves in Bose–Einstein condensate experiments.

Introduction to Theoretical and Experimental aspects of Quantum Optimal Control

Abstract Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Expansion dynamics of a cylindrical-shell-shaped strongly dipolar condensate

A Bose–Einstein condensate (BEC) formed on a curved surface with a distinct topology has been a hot topic of intense research, in search of new phenomena in quantum physics as well as for its possible application in quantum computing. In addition to the study of a spherical-shell-shaped BEC, we studied the formation of a cylindrical-shell-shaped harmonically-trapped dipolar BEC of 164Dy atoms theoretically using an improved mean-field model including a Lee-Huang-Yang-type interaction, meant to stop a collapse at high atom density. To test the robustness of the cylindrical-shell-shaped BEC, here we study its expansion in the same model. We find that as the harmonic trap in the x and y directions are removed, maintaining the axial trap, the cylindrical-shell-shaped BEC expands in the x-y plane without deformation, maintaining its shell-shaped structure. After an adequate radial expansion, the axial trap can be relaxed for a desired axial expansion of the cylindrical-shell-shaped BEC allowing its observation.

Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross-Pitaevskii equation in Bose-Einstein condensations with attractive interaction.

This paper investigates dynamical behaviors and controllability of some nonautonomous localized waves based on the Gross-Pitaevskii equation with attractive interatomic interactions. Our approach is a relation constructed between the Gross-Pitaevskii equation and the standard nonlinear Schrödinger equation through a new self-similarity transformation which is to convert the exact solutions of the latter to the former's. Subsequently, one can obtain the nonautonomous breather solutions and higher-order rogue wave solutions of the Gross-Pitaevskii equation. It has been shown that the nonautonomous localized waves can be controlled by the parameters within the self-similarity transformation, rather than relying solely on the nonlinear intensity, spectral parameters, and external potential. The control mechanism can induce an unusual number of loosely bound higher-order rogue waves. The asymptotic analysis of unusual loosely bound rogue waves shows that their essence is energy transfer among rogue waves. Numerical simulations test the dynamical stability of obtained localized wave solutions, which indicate that modifying the parameters in the self-similarity transformation can improve the stability of unstable localized waves and prolong their lifespan. We numerically confirm that the rogue wave controlled by the self-similarity transformation can be reproduced from a chaotic initial background field, hence anticipating the feasibility of its experimental observation, and propose an experimental method for observing these phenomena in Bose-Einstein condensates. The method presented in this paper can help to induce and observe new stable localized waves in some physical systems.

Exploration of soliton solution of coupled Drinfel’d–Sokolov–Wilson equation under conformable differential operator

The aim of this paper is to study the nonlinear couple Drinfel’d–Sokolov–Wilson (DSW) equation under conformable differential operator (CDO) that plays an important role in describing the shallow water in fluid mechanics, plasma physics, nonlinear optics and Bose–Einstein condensate (soliton formation). The Tanh-Coth and energy balance techniques are implemented in this work to explore some travelling wave solutions. These analytical methods yield various solutions for the considered DSW equation. The solutions obtained from both method are expressed in the form of hyperbolic and trigonometric function. Furthermore, the dynamic behaviour of the obtained solutions are illustrated, via 2D and 3D curves. Additionally, the effect of the conformable differential operator on dynamics of wave solutions is studied via 2D graphs.